1
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Sugisaki K, Nakano T, Mochizuki Y. Size-consistency and orbital-invariance issues revealed by VQE-UCCSD calculations with the FMO scheme. J Comput Chem 2024; 45:2204-2213. [PMID: 38795375 DOI: 10.1002/jcc.27438] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2024] [Revised: 05/08/2024] [Accepted: 05/09/2024] [Indexed: 05/27/2024]
Abstract
The fragment molecular orbital (FMO) scheme is one of the popular fragmentation-based methods and has the potential advantage of making the circuit shallow for quantum chemical calculations on quantum computers. In this study, we used a GPU-accelerated quantum simulator (cuQuantum) to perform the electron correlation part of the FMO calculation as unitary coupled-cluster singles and doubles (UCCSD) with the variational quantum eigensolver (VQE) for hydrogen-bonded (FH) 3 and (FH) 2 -H 2 O systems with the STO-3G basis set. VQE-UCCSD calculations were performed using both canonical and localized MO sets, and the results were examined from the point of view of size-consistency and orbital-invariance affected by the Trotter error. It was found that the use of localized MO leads to better results, especially for (FH) 2 -H 2 O. The GPU acceleration was substantial for the simulations with larger numbers of qubits, and was about a factor of 6.7-7.7 for 18 qubit systems.
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Affiliation(s)
- Kenji Sugisaki
- Graduate School of Science and Technology, Keio University, Kawasaki, Japan
- Quantum Computing Center, Keio University, Yokohama, Japan
- Centre for Quantum Engineering, Research and Education, TCG Centres for Research and Education in Science and Technology, Kolkata, India
| | - Tatsuya Nakano
- Division of Medicinal Safety Science, National Institute of Health Sciences, Kawasaki, Japan
| | - Yuji Mochizuki
- Department of Chemistry and Research Center for Smart Molecules, Faculty of Science, Rikkyo University, Toshima-ku, Japan
- Institute of Industrial Science, The University of Tokyo, Meguro-ku, Japan
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2
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Cainelli M, Baba R, Kurashige Y. Numerical Investigation of the Quantum Inverse Algorithm on Small Molecules. J Chem Theory Comput 2024. [PMID: 39259504 DOI: 10.1021/acs.jctc.4c00483] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/13/2024]
Abstract
We evaluate the accuracy of the quantum inverse (Q-Inv) algorithm, in which the multiplication of Ĥ-k to the reference wave function is replaced by the Fourier transformed multiplication of e-iλĤ, as a function of the integration parameters and the iteration power k for various systems, including H2, LiH, BeH2 and the notorious H4 molecule at square geometry. We further consider the possibility of employing the Gaussian-quadrature rule as an alternate integration method and compared it to the results employing trapezoidal integration. The Q-Inv algorithm is compared to the inverse iteration method using the Ĥ-1 inverse (I-Iter) and the exact inverse by lower-upper decomposition. Energy values are evaluated as the expectation values of the Hamiltonian. Results suggest that the Q-Inv method provides lower energy results than the I-Iter method up to a certain k, after which the energy increases due to errors in the numerical integration that are dependent on the integration interval. A combined Gaussian-quadrature and trapezoidal integration method proved to be more effective at reaching convergence while decreasing the number of operations. For systems like H4, in which the Q-Inv cannot reach the expected error threshold, we propose a combination of Q-Inv and I-Iter methods to further decrease the error with k at lower computational cost. Finally, we summarize the recommended procedure when treating unknown systems.
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Affiliation(s)
- Mauro Cainelli
- Department of Chemistry, Graduate School of Science, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Reo Baba
- Department of Chemistry, Graduate School of Science, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Yuki Kurashige
- Department of Chemistry, Graduate School of Science, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan
- FOREST, JST, Honcho 4-1-8, Kawaguchi, Saitama 332-0012, Japan
- CREST, JST, Honcho 4-1-8, Kawaguchi, Saitama 332-0012, Japan
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3
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Kumar S, Wilmott CM. Generalising quantum imaginary time evolution to solve linear partial differential equations. Sci Rep 2024; 14:20156. [PMID: 39215097 PMCID: PMC11364816 DOI: 10.1038/s41598-024-70423-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2024] [Accepted: 08/16/2024] [Indexed: 09/04/2024] Open
Abstract
The quantum imaginary time evolution (QITE) methodology was developed to overcome a critical issue as regards non-unitarity in the implementation of imaginary time evolution on a quantum computer. QITE has since been used to approximate ground states of various physical systems. In this paper, we demonstrate a practical application of QITE as a quantum numerical solver for linear partial differential equations. Our algorithm takes inspiration from QITE in that the quantum state follows the same normalised trajectory in both algorithms. However, it is our QITE methodology's ability to track the scale of the state vector over time that allows our algorithm to solve differential equations. We demonstrate our methodology with numerical simulations and use it to solve the heat equation in one and two dimensions using six and ten qubits, respectively.
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Affiliation(s)
- Swagat Kumar
- Department of Physics and Mathematics, Nottingham Trent University, Nottingham, NG11 8NS, UK.
| | - Colin Michael Wilmott
- Department of Physics and Mathematics, Nottingham Trent University, Nottingham, NG11 8NS, UK.
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4
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Payne Torres LI, Schouten AO, Mazziotti DA. Lifetime of Strongly Correlated States on Near-Term Quantum Computers. J Phys Chem A 2024; 128:7269-7276. [PMID: 39150036 DOI: 10.1021/acs.jpca.4c02665] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/17/2024]
Abstract
Here we study the lifetime of strongly correlated stationary states on quantum computers. We find that these states develop a nontrivial time dependence due to the presence of noise on current devices. After an exciton-condensate state is prepared, its behavior is observed with respect to unitary operations that should preserve the stationarity of the state. Instead of stationarity, however, we observe nontrivial time dependence in which the large eigenvalue of the particle-hole reduced density matrix─the exciton population of the condensate─decays toward unity, reflecting the loss of entanglement and off-diagonal long-range order. The result offers insight into the challenge of simulating strongly correlated systems on near-term quantum devices and highlights the importance of developing novel strategies for error mitigation that can preserve many-body correlations.
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Affiliation(s)
- Lillian I Payne Torres
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, United States
| | - Anna O Schouten
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, United States
| | - David A Mazziotti
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, United States
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5
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Yoshida Y, Takemori N, Mizukami W. Ab initio extended Hubbard model of short polyenes for efficient quantum computing. J Chem Phys 2024; 161:084303. [PMID: 39193941 DOI: 10.1063/5.0213525] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2024] [Accepted: 08/05/2024] [Indexed: 08/29/2024] Open
Abstract
We propose introducing an extended Hubbard Hamiltonian derived via the ab initio downfolding method, which was originally formulated for periodic materials, toward efficient quantum computing of molecular electronic structure calculations. By utilizing this method, the first-principles Hamiltonian of chemical systems can be coarse-grained by eliminating the electronic degrees of freedom in higher energy space and reducing the number of terms of electron repulsion integral from O(N4) to O(N2). Our approach is validated numerically on the vertical excitation energies and excitation characters of ethylene, butadiene, and hexatriene. The dynamical electron correlation is incorporated within the framework of the constrained random phase approximation in advance of quantum computations, and the constructed models capture the trend of experimental and high-level quantum chemical calculation results. As expected, the L1-norm of the fermion-to-qubit mapped model Hamiltonians is significantly lower than that of conventional ab initio Hamiltonians, suggesting improved scalability of quantum computing. Those numerical outcomes and the results of the simulation of excited-state sampling demonstrate that the ab initio extended Hubbard Hamiltonian may hold significant potential for quantum chemical calculations using quantum computers.
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Affiliation(s)
- Yuichiro Yoshida
- Center for Quantum Information and Quantum Biology, Osaka University, 1-2 Machikaneyama, Toyonaka, Osaka 560-0043, Japan
| | - Nayuta Takemori
- Center for Quantum Information and Quantum Biology, Osaka University, 1-2 Machikaneyama, Toyonaka, Osaka 560-0043, Japan
- Center for Emergent Matter Science, RIKEN, Wako, Saitama 351-0198, Japan
| | - Wataru Mizukami
- Center for Quantum Information and Quantum Biology, Osaka University, 1-2 Machikaneyama, Toyonaka, Osaka 560-0043, Japan
- Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan
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6
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Hakoshima H, Endo S, Yamamoto K, Matsuzaki Y, Yoshioka N. Localized Virtual Purification. PHYSICAL REVIEW LETTERS 2024; 133:080601. [PMID: 39241702 DOI: 10.1103/physrevlett.133.080601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2023] [Revised: 04/08/2024] [Accepted: 06/18/2024] [Indexed: 09/09/2024]
Abstract
Analog and digital quantum simulators can efficiently simulate quantum many-body systems that appear in natural phenomena. However, experimental limitations of near-term devices still make it challenging to perform the entire process of quantum simulation. The purification-based quantum simulation methods can alleviate the limitations in experiments such as the cooling temperature and noise from the environment, while this method has the drawback that it requires global entangled measurement with a prohibitively large number of measurements that scales exponentially with the system size. In this Letter, we propose that we can overcome these problems by restricting the entangled measurements to the vicinity of the local observables to be measured, when the locality of the system can be exploited. We provide theoretical guarantees that the global purification operation can be replaced with local operations under some conditions, in particular for the task of cooling and error mitigation. We furthermore give a numerical verification that the localized purification is valid even when conditions are not satisfied. Our method bridges the fundamental concept of locality with quantum simulators, and therefore is expected to open a path to unexplored quantum many-body phenomena.
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Affiliation(s)
- Hideaki Hakoshima
- Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan
- Center for Quantum Information and Quantum Biology, Osaka University, 1-2 Machikaneyama, Toyonaka, Osaka 560-0043, Japan
| | | | | | - Yuichiro Matsuzaki
- Department of Electrical, Electronic, and Communication Engineering, Faculty of Science and Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan
| | - Nobuyuki Yoshioka
- JST, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan
- Department of Applied Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research (CPR), Wako-shi, Saitama 351-0198, Japan
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7
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Alfonso D, Avramidis B, Paudel HP, Duan Y. How Well Can Quantum Embedding Method Predict the Reaction Profiles for Hydrogenation of Small Li Clusters? NANOMATERIALS (BASEL, SWITZERLAND) 2024; 14:1267. [PMID: 39120372 PMCID: PMC11313742 DOI: 10.3390/nano14151267] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2024] [Revised: 07/22/2024] [Accepted: 07/23/2024] [Indexed: 08/10/2024]
Abstract
Quantum computing leverages the principles of quantum mechanics in novel ways to tackle complex chemistry problems that cannot be accurately addressed using traditional quantum chemistry methods. However, the high computational cost and available number of physical qubits with high fidelity limit its application to small chemical systems. This work employed a quantum-classical framework which features a quantum active space-embedding approach to perform simulations of chemical reactions that require up to 14 qubits. This framework was applied to prototypical example metal hydrogenation reactions: the coupling between hydrogen and Li2, Li3, and Li4 clusters. Particular attention was paid to the computation of barriers and reaction energies. The predicted reaction profiles compare well with advanced classical quantum chemistry methods, demonstrating the potential of the quantum embedding algorithm to map out reaction profiles of realistic gas-phase chemical reactions to ascertain qualitative energetic trends. Additionally, the predicted potential energy curves provide a benchmark to compare against both current and future quantum embedding approaches.
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Affiliation(s)
- Dominic Alfonso
- National Energy Technology Laboratory, U. S. Department of Energy, Pittsburgh, PA 15236, USA
| | - Benjamin Avramidis
- NETL Support Contractor, 626 Cochran Mill Road, Pittsburgh, PA 15236, USA; (B.A.); (H.P.P.)
- Department of Chemistry, University of Pittsburgh, Pittsburgh, PA 15260, USA
| | - Hari P. Paudel
- National Energy Technology Laboratory, U. S. Department of Energy, Pittsburgh, PA 15236, USA
- NETL Support Contractor, 626 Cochran Mill Road, Pittsburgh, PA 15236, USA; (B.A.); (H.P.P.)
| | - Yuhua Duan
- National Energy Technology Laboratory, U. S. Department of Energy, Pittsburgh, PA 15236, USA
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8
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Filip MA. Fighting Noise with Noise: A Stochastic Projective Quantum Eigensolver. J Chem Theory Comput 2024; 20:5964-5981. [PMID: 38954827 PMCID: PMC11270749 DOI: 10.1021/acs.jctc.4c00295] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2024] [Revised: 06/13/2024] [Accepted: 06/14/2024] [Indexed: 07/04/2024]
Abstract
In the current noisy intermediate scale quantum era of quantum computation, available hardware is severely limited by both qubit count and noise levels, precluding the application of many current hybrid quantum-classical algorithms to nontrivial quantum chemistry problems. In this paper we propose applying some of the fundamental ideas of conventional Quantum Monte Carlo algorithms─stochastic sampling of both the wave function and the Hamiltonian─to quantum algorithms in order to significantly decrease quantum resource costs. In the context of an imaginary-time propagation based projective quantum eigensolver, we present a novel approach to estimating physical observables which can lead to an order of magnitude reduction in the required sampling of the quantum state to converge the ground state energy of a system relative to current state-of-the-art eigensolvers. The method can be equally applied to excited-state calculations and, combined with stochastic approximations of the system Hamiltonian, provides a promising near-term approach to Hamiltonian simulation for general chemistry on quantum devices.
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Affiliation(s)
- Maria-Andreea Filip
- Yusuf Hamied Department of
Chemistry, University of Cambridge, Cambridge CB2 1EW, U.K.
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9
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Choi S, Loaiza I, Lang RA, Martínez-Martínez LA, Izmaylov AF. Probing Quantum Efficiency: Exploring System Hardness in Electronic Ground State Energy Estimation. J Chem Theory Comput 2024; 20:5982-5993. [PMID: 38950444 DOI: 10.1021/acs.jctc.4c00298] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/03/2024]
Abstract
We consider the question of how correlated the system hardness is between classical algorithms of electronic structure theory in ground state estimation and quantum algorithms. To define the system hardness for classical algorithms, we employ empirical criterion based on the deviation of electronic energies produced by coupled cluster and configuration interaction methods from the exact ones along multiple bonds dissociation in a set of molecular systems. For quantum algorithms, we have selected the Variational Quantum Eigensolver (VQE) and Quantum Phase Estimation (QPE) methods. As characteristics of the system hardness for quantum methods, we analyzed circuit depths for the state preparation, the number of quantum measurements needed for the energy expectation value, and various cost characteristics for the Hamiltonian encodings via Trotter approximation and linear combination of unitaries (LCU). Our results show that the quantum resource requirements are mostly unaffected by classical hardness, with the only exception being the state preparation part, which contributes to both VQE and QPE algorithm costs. However, there are clear indications that constructing the initial state with a significant overlap with the true ground state is easier than obtaining the state with an energy expectation value within chemical precision. These results support optimism regarding the identification of a molecular system where a quantum algorithm excels over its classical counterpart, as quantum methods can maintain efficiency in classically challenging systems.
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Affiliation(s)
- Seonghoon Choi
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | - Ignacio Loaiza
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
- Zapata Computing Canada Inc., Toronto, Ontario M5C 3A1, Canada
| | - Robert A Lang
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | - Luis A Martínez-Martínez
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | - Artur F Izmaylov
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
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10
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Zhu HH, Sen Chen H, Chen T, Li Y, Luo SB, Karim MF, Luo XS, Gao F, Li Q, Cai H, Chin LK, Kwek LC, Nordén B, Zhang XD, Liu AQ. Large-scale photonic network with squeezed vacuum states for molecular vibronic spectroscopy. Nat Commun 2024; 15:6057. [PMID: 39025843 PMCID: PMC11258230 DOI: 10.1038/s41467-024-50060-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2023] [Accepted: 06/28/2024] [Indexed: 07/20/2024] Open
Abstract
Although molecular vibronic spectra generation is pivotal for chemical analysis, tackling such exponentially complex tasks on classical computers remains inefficient. Quantum simulation, though theoretically promising, faces technological challenges in experimentally extracting vibronic spectra for molecules with multiple modes. Here, we propose a nontrivial algorithm to generate the vibronic spectra using states with zero displacements (squeezed vacuum states) coupled to a linear optical network, offering ease of experimental implementation. We also fabricate an integrated quantum photonic microprocessor chip as a versatile simulation platform containing 16 modes of single-mode squeezed vacuum states and a fully programmable interferometer network. Molecular vibronic spectra of formic acid and thymine under the Condon approximation are simulated using the quantum microprocessor chip with high reconstructed fidelity ( > 92%). Furthermore, vibronic spectra of naphthalene, phenanthrene, and benzene under the non-Condon approximation are also experimentally simulated. Such demonstrations could pave the way for solving complicated quantum chemistry problems involving vibronic spectra and computational tasks beyond the reach of classical computers.
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Affiliation(s)
- Hui Hui Zhu
- Quantum Science and Engineering Centre (QSec), Nanyang Technological University, Singapore, Singapore
| | - Hao Sen Chen
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements of Ministry of Education, School of Physics, Beijing Institute of Technology, Beijing, China
| | - Tian Chen
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements of Ministry of Education, School of Physics, Beijing Institute of Technology, Beijing, China.
| | - Yuan Li
- Quantum Science and Engineering Centre (QSec), Nanyang Technological University, Singapore, Singapore
| | - Shao Bo Luo
- School of Microelectronics, Southern University of Science and Technology, Shenzhen, China
| | - Muhammad Faeyz Karim
- Quantum Science and Engineering Centre (QSec), Nanyang Technological University, Singapore, Singapore
| | | | - Feng Gao
- Advanced Micro Foundry, Singapore, Singapore
| | - Qiang Li
- Advanced Micro Foundry, Singapore, Singapore
| | - Hong Cai
- Institute of Microelectronics, A*STAR (Agency for Science, Technology, and Research), Singapore, Singapore
| | - Lip Ket Chin
- Department of Electrical Engineering, City University of Hong Kong, Hong Kong SAR, China.
| | - Leong Chuan Kwek
- Quantum Science and Engineering Centre (QSec), Nanyang Technological University, Singapore, Singapore.
- Centre for Quantum Technologies, National University of Singapore, Singapore, Singapore.
| | - Bengt Nordén
- Department of Chemistry and Chemical Engineering, Chalmers University of Technology, Gothenburg, Sweden.
| | - Xiang Dong Zhang
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements of Ministry of Education, School of Physics, Beijing Institute of Technology, Beijing, China.
| | - Ai Qun Liu
- Quantum Science and Engineering Centre (QSec), Nanyang Technological University, Singapore, Singapore.
- Institute of Quantum Technology (IQT), The Hong Kong Polytechnic University, Hong Kong SAR, China.
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11
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Zhao S, Tang D, Xiao X, Wang R, Sun Q, Chen Z, Cai X, Li Z, Yu H, Fang WH. Quantum Computation of Conical Intersections on a Programmable Superconducting Quantum Processor. J Phys Chem Lett 2024; 15:7244-7253. [PMID: 38976358 DOI: 10.1021/acs.jpclett.4c01314] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/10/2024]
Abstract
Conical intersections (CIs) are pivotal in many photochemical processes. Traditional quantum chemistry methods, such as the state-average multiconfigurational methods, face computational hurdles in solving the electronic Schrödinger equation within the active space on classical computers. While quantum computing offers a potential solution, its feasibility in studying CIs, particularly on real quantum hardware, remains largely unexplored. Here, we present the first successful realization of a hybrid quantum-classical state-average complete active space self-consistent field method based on the variational quantum eigensolver (VQE-SA-CASSCF) on a superconducting quantum processor. This approach is applied to investigate CIs in two prototypical systems─ethylene (C2H4) and triatomic hydrogen (H3). We illustrate that VQE-SA-CASSCF, coupled with ongoing hardware and algorithmic enhancements, can lead to a correct description of CIs on existing quantum devices. These results lay the groundwork for exploring the potential of quantum computing to study CIs in more complex systems in the future.
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Affiliation(s)
- Shoukuan Zhao
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Diandong Tang
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Xiaoxiao Xiao
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Ruixia Wang
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Qiming Sun
- Quantum Engine LLC, Lacey, Washington 98516, United States
| | - Zhen Chen
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Xiaoxia Cai
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Zhendong Li
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Haifeng Yu
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
- Hefei National Laboratory, Hefei 230088, China
| | - Wei-Hai Fang
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education College of Chemistry, Beijing Normal University, Beijing 100875, China
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12
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Koh JM, Tai T, Lee CH. Realization of higher-order topological lattices on a quantum computer. Nat Commun 2024; 15:5807. [PMID: 38987264 PMCID: PMC11237062 DOI: 10.1038/s41467-024-49648-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2023] [Accepted: 06/12/2024] [Indexed: 07/12/2024] Open
Abstract
Programmable quantum simulators may one day outperform classical computers at certain tasks. But at present, the range of viable applications with noisy intermediate-scale quantum (NISQ) devices remains limited by gate errors and the number of high-quality qubits. Here, we develop an approach that places digital NISQ hardware as a versatile platform for simulating multi-dimensional condensed matter systems. Our method encodes a high-dimensional lattice in terms of many-body interactions on a reduced-dimension model, thereby taking full advantage of the exponentially large Hilbert space of the host quantum system. With circuit optimization and error mitigation techniques, we measured on IBM superconducting quantum processors the topological state dynamics and protected mid-gap spectra of higher-order topological lattices, in up to four dimensions, with high accuracy. Our projected resource requirements scale favorably with system size and lattice dimensionality compared to classical computation, suggesting a possible route to useful quantum advantage in the longer term.
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Affiliation(s)
- Jin Ming Koh
- Division of Physics, Mathematics and Astronomy, Caltech, Pasadena, CA, 91125, USA
- A*STAR Quantum Innovation Centre (Q.InC), Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR), 1 Fusionopolis Way, #16-16 Connexis, Singapore, 138632, Republic of Singapore
| | - Tommy Tai
- Department of Physics, MIT, Cambridge, MA, 02142, USA
- Department of Physics, National University of Singapore, Singapore, 117542, Singapore
| | - Ching Hua Lee
- Department of Physics, National University of Singapore, Singapore, 117542, Singapore.
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13
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Li J, Gao X. Quantum circuit for high order perturbation theory corrections. Sci Rep 2024; 14:13963. [PMID: 38886483 PMCID: PMC11183151 DOI: 10.1038/s41598-024-64854-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2024] [Accepted: 06/12/2024] [Indexed: 06/20/2024] Open
Abstract
Perturbation theory (PT) might be one of the most powerful and fruitful tools for both physicists and chemists, which has led to a wide variety of applications. Over the past decades, advances in quantum computing provide opportunities for alternatives to classical methods. Recently, a general quantum circuit estimating the low order PT corrections has been proposed. In this article, we revisit the quantum circuits for PT calculations, and develop the methods for higher order PT corrections of eigenenergy, especially the 3rd and 4th order corrections. We present the feasible quantum circuit to estimate each term in these PT corrections. There are two the fundamental operations in the proposed circuit. One approximates the perturbation terms, the other approximates the inverse of unperturbed energy difference. The proposed method can be generalized to higher order PT corrections.
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Affiliation(s)
- Junxu Li
- Department of Physics, College of Science, Northeastern University, Shenyang, 110819, China.
| | - Xingyu Gao
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, United States
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14
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Rocca D, Cortes CL, Gonthier JF, Ollitrault PJ, Parrish RM, Anselmetti GL, Degroote M, Moll N, Santagati R, Streif M. Reducing the Runtime of Fault-Tolerant Quantum Simulations in Chemistry through Symmetry-Compressed Double Factorization. J Chem Theory Comput 2024; 20:4639-4653. [PMID: 38788209 DOI: 10.1021/acs.jctc.4c00352] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/26/2024]
Abstract
Quantum phase estimation based on qubitization is the state-of-the-art fault-tolerant quantum algorithm for computing ground-state energies in chemical applications. In this context, the 1-norm of the Hamiltonian plays a fundamental role in determining the total number of required iterations and also the overall computational cost. In this work, we introduce the symmetry-compressed double factorization (SCDF) approach, which combines a CDF of the Hamiltonian with the symmetry shift technique, significantly reducing the 1-norm value. The effectiveness of this approach is demonstrated numerically by considering various benchmark systems, including the FeMoco molecule, cytochrome P450, and hydrogen chains of different sizes. To compare the efficiency of SCDF to other methods in absolute terms, we estimate Toffoli gate requirements, which dominate the execution time on fault-tolerant quantum computers. For the systems considered here, SCDF leads to a sizable reduction of the Toffoli gate count in comparison to other variants of DF or even tensor hypercontraction, which is usually regarded as the most efficient approach for qubitization.
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Affiliation(s)
- Dario Rocca
- QC Ware Corporation, Palo Alto, California 94306, United States
| | | | | | | | | | | | - Matthias Degroote
- Quantum Lab, Boehringer Ingelheim, 55218 Ingelheim am Rhein, Germany
| | - Nikolaj Moll
- Quantum Lab, Boehringer Ingelheim, 55218 Ingelheim am Rhein, Germany
| | | | - Michael Streif
- Quantum Lab, Boehringer Ingelheim, 55218 Ingelheim am Rhein, Germany
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15
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Montero-Cabrera LA, Montero-Alejo AL, Aspuru-Guzik A, García de la Vega JM, Piris M, Díaz-Fernández LA, Pérez-Badell Y, Guerra-Barroso A, Alfonso-Ramos JE, Rodríguez J, Fuentes ME, de Armas CM. Alternative CNDOL Fockians for fast and accurate description of molecular exciton properties. J Chem Phys 2024; 160:214108. [PMID: 38828812 DOI: 10.1063/5.0208809] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2024] [Accepted: 05/14/2024] [Indexed: 06/05/2024] Open
Abstract
CNDOL is an a priori, approximate Fockian for molecular wave functions. In this study, we employ several modes of singly excited configuration interaction (CIS) to model molecular excitation properties by using four combinations of the one electron operator terms. Those options are compared to the experimental and theoretical data for a carefully selected set of molecules. The resulting excitons are represented by CIS wave functions that encompass all valence electrons in the system for each excited state energy. The Coulomb-exchange term associated to the calculated excitation energies is rationalized to evaluate theoretical exciton binding energies. This property is shown to be useful for discriminating the charge donation ability of molecular and supermolecular systems. Multielectronic 3D maps of exciton formal charges are showcased, demonstrating the applicability of these approximate wave functions for modeling properties of large molecules and clusters at nanoscales. This modeling proves useful in designing molecular photovoltaic devices. Our methodology holds potential applications in systematic evaluations of such systems and the development of fundamental artificial intelligence databases for predicting related properties.
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Affiliation(s)
- Luis A Montero-Cabrera
- Laboratorio de Química Computacional y Teórica, Departamento de Química Física, Universidad de La Habana, 10400 Havana, Cuba
- Donostia International Physics Center (DIPC), 20018 Donostia - San Sebastián, Basque Country, Spain
| | - Ana L Montero-Alejo
- Departamento de Física, Facultad de Ciencias Naturales, Matemática y del Medio Ambiente (FCNMM), Universidad Tecnológica Metropolitana; Ñuñoa, Santiago 7800002, Chile
| | - Alan Aspuru-Guzik
- Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | | | - Mario Piris
- Donostia International Physics Center (DIPC), 20018 Donostia - San Sebastián, Basque Country, Spain
| | - Lourdes A Díaz-Fernández
- Laboratorio de Química Computacional y Teórica, Departamento de Química Física, Universidad de La Habana, 10400 Havana, Cuba
| | - Yoana Pérez-Badell
- Laboratorio de Química Computacional y Teórica, Departamento de Química Física, Universidad de La Habana, 10400 Havana, Cuba
| | - Alberto Guerra-Barroso
- Laboratorio de Química Computacional y Teórica, Departamento de Química Física, Universidad de La Habana, 10400 Havana, Cuba
| | - Javier E Alfonso-Ramos
- Laboratorio de Química Computacional y Teórica, Departamento de Química Física, Universidad de La Habana, 10400 Havana, Cuba
| | - Javier Rodríguez
- Laboratorio de Química Computacional y Teórica, Departamento de Química Física, Universidad de La Habana, 10400 Havana, Cuba
| | - María E Fuentes
- Facultad de Ciencias Químicas, Universidad Autónoma de Chihuahua, Chihuahua, 31100 Chihuahua, Mexico
| | - Carlos M de Armas
- Laboratorio de Química Computacional y Teórica, Departamento de Química Física, Universidad de La Habana, 10400 Havana, Cuba
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16
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Liu J, Ma H, Shang H, Li Z, Yang J. Quantum-centric high performance computing for quantum chemistry. Phys Chem Chem Phys 2024; 26:15831-15843. [PMID: 38787657 DOI: 10.1039/d4cp00436a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/26/2024]
Abstract
High performance computing (HPC) is renowned for its capacity to tackle complex problems. Meanwhile, quantum computing (QC) provides a potential way to accurately and efficiently solve quantum chemistry problems. The emerging field of quantum-centric high performance computing (QCHPC), which merges these two powerful technologies, is anticipated to enhance computational capabilities for solving challenging problems in quantum chemistry. The implementation of QCHPC for quantum chemistry requires interdisciplinary research and collaboration across multiple fields, including quantum chemistry, quantum physics, computer science and so on. This perspective provides an introduction to the quantum algorithms that are suitable for deployment in QCHPC, focusing on conceptual insights rather than technical details. Parallel strategies to implement these algorithms on quantum-centric supercomputers are discussed. We also summarize high performance quantum emulating simulators, which are considered a viable tool to explore QCHPC. We conclude with challenges and outlooks in this field.
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Affiliation(s)
- Jie Liu
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China.
| | - Huan Ma
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China.
| | - Honghui Shang
- Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China, Hefei, Anhui 230026, China.
| | - Zhenyu Li
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China.
- Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China, Hefei, Anhui 230026, China.
| | - Jinlong Yang
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China.
- Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China, Hefei, Anhui 230026, China.
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17
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Olarte Hernandez R, Champagne B, Soldera A. Simulating Vibronic Spectra by Direct Application of Doktorov Formulas on a Superconducting Quantum Simulator. J Phys Chem A 2024; 128:4369-4377. [PMID: 38751235 DOI: 10.1021/acs.jpca.4c01234] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/31/2024]
Abstract
In this work, a direct quantum implementation of the Doktorov formulas for calculating the vibronic spectrum of molecules under the harmonic approximation is presented. It is applied to the three-atom molecules H2O, SO2, ClO2, HS2, and ZnOH. The method solves the classically hard problem of estimating the Franck-Condon (FC) factors by using the Duschinsky matrices as the only input via the Doktorov quantum circuit. This has the advantage of avoiding basis changes, artificial squeezing parameters, and symmetry dependencies. In other words, it is a general method for three-atom molecules that can easily be generalized to bigger molecules. The results are compared with other quantum algorithms and classical anharmonic algorithms. Furthermore, the circuit requirements are studied in order to estimate its applicability on real superconducting quantum hardware.
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Affiliation(s)
- Renato Olarte Hernandez
- Theoretical Chemistry Lab, Unit of Theoretical and Structural Physical Chemistry, Namur Institute of Structured Matter, University of Namur, rue de Bruxelles 61, B-5000 Namur, Belgium
- Laboratory of Physical Chemistry of Matter, Department of Chemistry, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
| | - Benoît Champagne
- Theoretical Chemistry Lab, Unit of Theoretical and Structural Physical Chemistry, Namur Institute of Structured Matter, University of Namur, rue de Bruxelles 61, B-5000 Namur, Belgium
| | - Armand Soldera
- Laboratory of Physical Chemistry of Matter, Department of Chemistry, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
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18
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Singh H, Majumder S, Mishra S. Hückel molecular orbital theory on a quantum computer: A scalable system-agnostic variational implementation with compact encoding. J Chem Phys 2024; 160:194106. [PMID: 38767256 DOI: 10.1063/5.0210597] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2024] [Accepted: 05/01/2024] [Indexed: 05/22/2024] Open
Abstract
Hückel molecular orbital (HMO) theory provides a semi-empirical treatment of the electronic structure in conjugated π-electronic systems. A scalable system-agnostic execution of HMO theory on a quantum computer is reported here based on a variational quantum deflation (VQD) algorithm for excited state quantum simulation. A compact encoding scheme is proposed here that provides an exponential advantage over the direct mapping and allows for quantum simulation of the HMO model for systems with up to 2n conjugated centers with n qubits. The transformation of the Hückel Hamiltonian to qubit space is achieved by two different strategies: an iterative refinement transformation and the Frobenius-inner-product-based transformation. These methods are tested on a series of linear, cyclic, and hetero-nuclear conjugated π-electronic systems. The molecular orbital energy levels and wavefunctions from the quantum simulation are in excellent agreement with the exact classical results. However, the higher excited states of large systems are found to suffer from error accumulation in the VQD simulation. This is mitigated by formulating a variant of VQD that exploits the symmetry of the Hamiltonian. This strategy has been successfully demonstrated for the quantum simulation of C60 fullerene containing 680 Pauli strings encoded on six qubits. The methods developed in this work are easily adaptable to similar problems of different complexity in other fields of research.
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Affiliation(s)
- Harshdeep Singh
- Center of Computational and Data Sciences, Indian Institute of Technology, Kharagpur, India
| | - Sonjoy Majumder
- Department of Physics, Indian Institute of Technology, Kharagpur, India
| | - Sabyashachi Mishra
- Department of Chemistry, Indian Institute of Technology, Kharagpur, India
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19
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Ziems KM, Kjellgren ER, Reinholdt P, Jensen PWK, Sauer SPA, Kongsted J, Coriani S. Which Options Exist for NISQ-Friendly Linear Response Formulations? J Chem Theory Comput 2024; 20:3551-3565. [PMID: 38662999 DOI: 10.1021/acs.jctc.3c01402] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/15/2024]
Abstract
Linear response (LR) theory is a powerful tool in classic quantum chemistry crucial to understanding photoinduced processes in chemistry and biology. However, performing simulations for large systems and in the case of strong electron correlation remains challenging. Quantum computers are poised to facilitate the simulation of such systems, and recently, a quantum linear response formulation (qLR) was introduced [Kumar et al., J. Chem. Theory Comput. 2023, 19, 9136-9150]. To apply qLR to near-term quantum computers beyond a minimal basis set, we here introduce a resource-efficient qLR theory, using a truncated active-space version of the multiconfigurational self-consistent field LR ansatz. Therein, we investigate eight different near-term qLR formalisms that utilize novel operator transformations that allow the qLR equations to be performed on near-term hardware. Simulating excited state potential energy curves and absorption spectra for various test cases, we identify two promising candidates, dubbed "proj LRSD" and "all-proj LRSD".
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Affiliation(s)
- Karl Michael Ziems
- Department of Chemistry, Technical University of Denmark, Kemitorvet Building 207, DK-2800 Kongens Lyngby, Denmark
| | - Erik Rosendahl Kjellgren
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, 5230 Odense, Denmark
| | - Peter Reinholdt
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, 5230 Odense, Denmark
| | - Phillip W K Jensen
- Department of Chemistry, University of Copenhagen, DK-2100 Copenhagen, Denmark
| | - Stephan P A Sauer
- Department of Chemistry, University of Copenhagen, DK-2100 Copenhagen, Denmark
| | - Jacob Kongsted
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, 5230 Odense, Denmark
| | - Sonia Coriani
- Department of Chemistry, Technical University of Denmark, Kemitorvet Building 207, DK-2800 Kongens Lyngby, Denmark
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20
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Laskar MR, Bhattacharya A, Dasgputa K. Efficient simulation of potential energy operators on quantum hardware: a study on sodium iodide (NaI). Sci Rep 2024; 14:10831. [PMID: 38734700 DOI: 10.1038/s41598-024-60605-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2023] [Accepted: 04/25/2024] [Indexed: 05/13/2024] Open
Abstract
This study introduces a conceptually novel polynomial encoding algorithm for simulating potential energy operators encoded in diagonal unitary forms in a quantum computing machine. The current trend in quantum computational chemistry is effective experimentation to achieve high-precision quantum computational advantage. However, high computational gate complexity and fidelity loss are some of the impediments to the realization of this advantage in a real quantum hardware. In this study, we address the challenges of building a diagonal Hamiltonian operator having exponential functional form, and its implementation in the context of the time evolution problem (Hamiltonian simulation and encoding). Potential energy operators when represented in the first quantization form is an example of such types of operators. Through systematic decomposition and construction, we demonstrate the efficacy of the proposed polynomial encoding method in reducing gate complexity from O ( 2 n ) to O ∑ i = 1 r n C r (for some r ≪ n ). This offers a solution with lower complexity in comparison to the conventional Hadamard basis encoding approach. The effectiveness of the proposed algorithm was validated with its implementation in the IBM quantum simulator and IBM quantum hardware. This study demonstrates the proposed approach by taking the example of the potential energy operator of the sodium iodide molecule (NaI) in the first quantization form. The numerical results demonstrate the potential applicability of the proposed method in quantum chemistry problems, while the analytical bound for error analysis and computational gate complexity discussed, throw light on issues regarding its implementation.
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Affiliation(s)
- Mostafizur Rahaman Laskar
- IBM Research, Bangalore, India.
- G. S. Sanyal School of Telecommunications, Indian Institute of Technology Kharagpur, Kharagpur, India.
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21
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Veyrac G, Toffano Z. Geometric Algebra Jordan-Wigner Transformation for Quantum Simulation. ENTROPY (BASEL, SWITZERLAND) 2024; 26:410. [PMID: 38785659 PMCID: PMC11120067 DOI: 10.3390/e26050410] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2024] [Revised: 05/02/2024] [Accepted: 05/04/2024] [Indexed: 05/25/2024]
Abstract
Quantum simulation qubit models of electronic Hamiltonians rely on specific transformations in order to take into account the fermionic permutation properties of electrons. These transformations (principally the Jordan-Wigner transformation (JWT) and the Bravyi-Kitaev transformation) correspond in a quantum circuit to the introduction of a supplementary circuit level. In order to include the fermionic properties in a more straightforward way in quantum computations, we propose to use methods issued from Geometric Algebra (GA), which, due to its commutation properties, are well adapted for fermionic systems. First, we apply the Witt basis method in GA to reformulate the JWT in this framework and use this formulation to express various quantum gates. We then rewrite the general one and two-electron Hamiltonian and use it for building a quantum simulation circuit for the Hydrogen molecule. Finally, the quantum Ising Hamiltonian, widely used in quantum simulation, is reformulated in this framework.
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Affiliation(s)
| | - Zeno Toffano
- Laboratoire Signaux et Systèmes (L2S), UMR 8506, CentraleSupélec, Université Paris-Saclay, CNRS, 91190 Gif-sur-Yvette, France;
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22
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Kang M, Nuomin H, Chowdhury SN, Yuly JL, Sun K, Whitlow J, Valdiviezo J, Zhang Z, Zhang P, Beratan DN, Brown KR. Seeking a quantum advantage with trapped-ion quantum simulations of condensed-phase chemical dynamics. Nat Rev Chem 2024; 8:340-358. [PMID: 38641733 DOI: 10.1038/s41570-024-00595-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 03/07/2024] [Indexed: 04/21/2024]
Abstract
Simulating the quantum dynamics of molecules in the condensed phase represents a longstanding challenge in chemistry. Trapped-ion quantum systems may serve as a platform for the analog-quantum simulation of chemical dynamics that is beyond the reach of current classical-digital simulation. To identify a 'quantum advantage' for these simulations, performance analysis of both analog-quantum simulation on noisy hardware and classical-digital algorithms is needed. In this Review, we make a comparison between a noisy analog trapped-ion simulator and a few choice classical-digital methods on simulating the dynamics of a model molecular Hamiltonian with linear vibronic coupling. We describe several simple Hamiltonians that are commonly used to model molecular systems, which can be simulated with existing or emerging trapped-ion hardware. These Hamiltonians may serve as stepping stones towards the use of trapped-ion simulators for systems beyond the reach of classical-digital methods. Finally, we identify dynamical regimes in which classical-digital simulations seem to have the weakest performance with respect to analog-quantum simulations. These regimes may provide the lowest hanging fruit to make the most of potential quantum advantages.
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Affiliation(s)
- Mingyu Kang
- Duke Quantum Center, Duke University, Durham, NC, USA.
- Department of Physics, Duke University, Durham, NC, USA.
| | - Hanggai Nuomin
- Department of Chemistry, Duke University, Durham, NC, USA
| | | | - Jonathon L Yuly
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ, USA
| | - Ke Sun
- Duke Quantum Center, Duke University, Durham, NC, USA
- Department of Physics, Duke University, Durham, NC, USA
| | - Jacob Whitlow
- Duke Quantum Center, Duke University, Durham, NC, USA
- Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA
| | - Jesús Valdiviezo
- Kenneth S. Pitzer Theory Center, University of California, Berkeley, CA, USA
- Department of Chemistry, University of California, Berkeley, CA, USA
- Departamento de Ciencias, Sección Química, Pontificia Universidad Católica del Perú, Lima, Peru
| | - Zhendian Zhang
- Department of Chemistry, Duke University, Durham, NC, USA
| | - Peng Zhang
- Department of Chemistry, Duke University, Durham, NC, USA
| | - David N Beratan
- Department of Physics, Duke University, Durham, NC, USA.
- Department of Chemistry, Duke University, Durham, NC, USA.
- Department of Biochemistry, Duke University, Durham, NC, USA.
| | - Kenneth R Brown
- Duke Quantum Center, Duke University, Durham, NC, USA.
- Department of Physics, Duke University, Durham, NC, USA.
- Department of Chemistry, Duke University, Durham, NC, USA.
- Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA.
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23
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Majland M, Ettenhuber P, Zinner NT, Christiansen O. Vibrational ADAPT-VQE: Critical points lead to problematic convergence. J Chem Phys 2024; 160:154109. [PMID: 38634491 DOI: 10.1063/5.0191074] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2023] [Accepted: 04/02/2024] [Indexed: 04/19/2024] Open
Abstract
Quantum chemistry is one of the most promising applications for which quantum computing is expected to have a significant impact. Despite considerable research in the field of electronic structure, calculating the vibrational properties of molecules on quantum computers remains a relatively unexplored field. In this work, we develop a vibrational Adaptive Derivative-Assembled Pseudo-Trotter Variational Quantum Eigensolver (vADAPT-VQE) formalism based on an infinite product representation (IPR) of anti-Hermitian excitation operators of the Full Vibrational Configuration Interaction (FVCI) wavefunction, which allows for preparing eigenstates of vibrational Hamiltonians on quantum computers. In order to establish the vADAPT-VQE algorithm using the IPR, we study the exactness of disentangled Unitary Vibrational Coupled Cluster (dUVCC) theory and show that dUVCC can formally represent the FVCI wavefunction in an infinite expansion. To investigate the performance of the vADAPT-VQE algorithm, we numerically study whether the vADAPT-VQE algorithm generates a sequence of operators that may represent the FVCI wavefunction. Our numerical results indicate frequent appearance of critical points in the wavefunction preparation using vADAPT-VQE. These results imply that one may encounter diminishing usefulness when preparing vibrational wavefunctions on quantum computers using vADAPT-VQE and that additional studies are required to find methods that can circumvent this behavior.
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Affiliation(s)
- Marco Majland
- Kvantify Aps, DK-2300 Copenhagen S, Denmark
- Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark
- Department of Chemistry, Aarhus University, DK-8000 Aarhus C, Denmark
| | | | - Nikolaj Thomas Zinner
- Kvantify Aps, DK-2300 Copenhagen S, Denmark
- Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark
| | - Ove Christiansen
- Kvantify Aps, DK-2300 Copenhagen S, Denmark
- Department of Chemistry, Aarhus University, DK-8000 Aarhus C, Denmark
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24
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Fitzpatrick A, Nykänen A, Talarico NW, Lunghi A, Maniscalco S, García-Pérez G, Knecht S. Self-Consistent Field Approach for the Variational Quantum Eigensolver: Orbital Optimization Goes Adaptive. J Phys Chem A 2024; 128:2843-2856. [PMID: 38547028 DOI: 10.1021/acs.jpca.3c05882] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/12/2024]
Abstract
We present a self-consistent field (SCF) approach within the adaptive derivative-assembled problem-tailored ansatz variational quantum eigensolver (ADAPT-VQE) framework for efficient quantum simulations of chemical systems on near-term quantum computers. To this end, our ADAPT-VQE-SCF approach combines the idea of generating an ansatz with a small number of parameters, resulting in shallow-depth quantum circuits with a direct minimization of an energy expression that is correct to second order with respect to changes in the molecular orbital basis. Our numerical analysis, including calculations for the transition-metal complex ferrocene [Fe (C5H5)2], indicates that convergence in the self-consistent orbital optimization loop can be reached without a considerable increase in the number of two-qubit gates in the quantum circuit by comparison to a VQE optimization in the initial molecular orbital basis. Moreover, the orbital optimization can be carried out simultaneously within each iteration of the ADAPT-VQE cycle. ADAPT-VQE-SCF thus allows us to implement a routine analogous to the complete active space SCF, a cornerstone of state-of-the-art computational chemistry, in a hardware-efficient manner on near-term quantum computers. Hence, ADAPT-VQE-SCF paves the way toward a paradigm shift for quantitative quantum-chemistry simulations on quantum computers by requiring fewer qubits and opening up for the use of large and flexible atomic orbital basis sets in contrast to earlier methods that are predominantly based on the idea of full active spaces with minimal basis sets.
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Affiliation(s)
- Aaron Fitzpatrick
- Algorithmiq Ltd, Kanavakatu 3C, Helsinki FI-00160, Finland
- Trinity Quantum Alliance, Unit 16, Trinity Technology and Enterprise Centre, Pearse Street, Dublin 2 D02 YN67, Ireland
| | - Anton Nykänen
- Algorithmiq Ltd, Kanavakatu 3C, Helsinki FI-00160, Finland
| | | | - Alessandro Lunghi
- School of Physics, AMBER and CRANN Institute, Trinity College, Dublin 2, Ireland
| | | | | | - Stefan Knecht
- Algorithmiq Ltd, Kanavakatu 3C, Helsinki FI-00160, Finland
- ETH Zürich, Department of Chemistry and Applied Life Sciences Vladimir-Prelog-Weg 1-5/10, Zürich 8093, Switzerland
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25
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Kjellgren ER, Reinholdt P, Fitzpatrick A, Talarico WN, Jensen PWK, Sauer SPA, Coriani S, Knecht S, Kongsted J. The variational quantum eigensolver self-consistent field method within a polarizable embedded framework. J Chem Phys 2024; 160:124114. [PMID: 38533884 DOI: 10.1063/5.0190594] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2023] [Accepted: 03/10/2024] [Indexed: 03/28/2024] Open
Abstract
We formulate and implement the Variational Quantum Eigensolver Self Consistent Field (VQE-SCF) algorithm in combination with polarizable embedding (PE), thereby extending PE to the regime of quantum computing. We test the resulting algorithm, PE-VQE-SCF, on quantum simulators and demonstrate that the computational stress on the quantum device is only slightly increased in terms of gate counts compared to regular VQE-SCF. On the other hand, no increase in shot noise was observed. We illustrate how PE-VQE-SCF may lead to the modeling of real chemical systems using a simulation of the reaction barrier of the Diels-Alder reaction between furan and ethene as an example.
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Affiliation(s)
- Erik Rosendahl Kjellgren
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, DK-5230 Odense M, Denmark
| | - Peter Reinholdt
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, DK-5230 Odense M, Denmark
| | | | - Walter N Talarico
- Algorithmiq Ltd., Kanavakatu 3C, FI-00160 Helsinki, Finland
- Department of Applied Physics, QTF Centre of Excellence, Center for Quantum Engineering, Aalto University School of Science, FIN-00076 AALTO Espoo, Finland
| | - Phillip W K Jensen
- Department of Chemistry, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark
| | - Stephan P A Sauer
- Department of Chemistry, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark
| | - Sonia Coriani
- DTU Chemistry - Department of Chemistry, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
| | - Stefan Knecht
- Algorithmiq Ltd., Kanavakatu 3C, FI-00160 Helsinki, Finland
- ETH Zürich, Department of Chemistry and Applied Life Sciences, Vladimir-Prelog-Weg 1-5/10, CH-8093 Zürich, Switzerland
| | - Jacob Kongsted
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, DK-5230 Odense M, Denmark
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26
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Gong Q, Man Q, Zhao J, Li Y, Dou M, Wang Q, Wu YC, Guo GP. Simulating chemical reaction dynamics on quantum computer. J Chem Phys 2024; 160:124103. [PMID: 38526102 DOI: 10.1063/5.0192036] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2023] [Accepted: 03/06/2024] [Indexed: 03/26/2024] Open
Abstract
The electronic energies of molecules have been successfully evaluated on quantum computers. However, more attention is paid to the dynamics simulation of molecules in practical applications. Based on the variational quantum eigensolver (VQE) algorithm, Fedorov et al. proposed a correlated sampling (CS) method and demonstrated the vibrational dynamics of H2 molecules [J. Chem. Phys. 154, 164103 (2021)]. In this study, we have developed a quantum approach by extending the CS method based on the VQE algorithm (labeled eCS-VQE) for simulating chemical reaction dynamics. First, the CS method is extended to the three-dimensional cases for calculation of first-order energy gradients, and then, it is further generalized to calculate the second-order gradients of energies. By calculating atomic forces and vibrational frequencies for H2, LiH, H+ + H2, and Cl- + CH3Cl systems, we have seen that the approach has achieved the CCSD level of accuracy. Thus, we have simulated dynamics processes for two typical chemical reactions, hydrogen exchange and chlorine substitution, and obtained high-precision reaction dynamics trajectories consistent with the classical methods. Our eCS-VQE approach, as measurement expectations and ground-state wave functions can be reused, is less demanding in quantum computing resources and is, therefore, a feasible means for the dynamics simulation of chemical reactions on the current noisy intermediate-scale quantum-era quantum devices.
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Affiliation(s)
- Qiankun Gong
- Origin Quantum Computing Company Limited, Hefei, Anhui 230026, China
| | - Qingmin Man
- Origin Quantum Computing Company Limited, Hefei, Anhui 230026, China
| | - Jianyu Zhao
- Origin Quantum Computing Company Limited, Hefei, Anhui 230026, China
| | - Ye Li
- Origin Quantum Computing Company Limited, Hefei, Anhui 230026, China
| | - Menghan Dou
- Origin Quantum Computing Company Limited, Hefei, Anhui 230026, China
| | - Qingchun Wang
- Institute of Artificial Intelligence, Hefei Comprehensive National Science Center, Hefei, Anhui 230088, China
| | - Yu-Chun Wu
- Institute of Artificial Intelligence, Hefei Comprehensive National Science Center, Hefei, Anhui 230088, China
- CAS Key Laboratory of Quantum Information, School of Physics, University of Science and Technology of China, Hefei 230026, China
| | - Guo-Ping Guo
- Origin Quantum Computing Company Limited, Hefei, Anhui 230026, China
- Institute of Artificial Intelligence, Hefei Comprehensive National Science Center, Hefei, Anhui 230088, China
- CAS Key Laboratory of Quantum Information, School of Physics, University of Science and Technology of China, Hefei 230026, China
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27
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Liu S. Harvesting Chemical Understanding with Machine Learning and Quantum Computers. ACS PHYSICAL CHEMISTRY AU 2024; 4:135-142. [PMID: 38560751 PMCID: PMC10979482 DOI: 10.1021/acsphyschemau.3c00067] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/06/2023] [Revised: 12/29/2023] [Accepted: 01/02/2024] [Indexed: 04/04/2024]
Abstract
It is tenable to argue that nobody can predict the future with certainty, yet one can learn from the past and make informed projections for the years ahead. In this Perspective, we overview the status of how theory and computation can be exploited to obtain chemical understanding from wave function theory and density functional theory, and then outlook the likely impact of machine learning (ML) and quantum computers (QC) to appreciate traditional chemical concepts in decades to come. It is maintained that the development and maturation of ML and QC methods in theoretical and computational chemistry represent two paradigm shifts about how the Schrödinger equation can be solved. New chemical understanding can be harnessed in these two new paradigms by making respective use of ML features and QC qubits. Before that happens, however, we still have hurdles to face and obstacles to overcome in both ML and QC arenas. Possible pathways to tackle these challenges are proposed. We anticipate that hierarchical modeling, in contrast to multiscale modeling, will emerge and thrive, becoming the workhorse of in silico simulations in the next few decades.
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28
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Feniou C, Adjoua O, Claudon B, Zylberman J, Giner E, Piquemal JP. Sparse Quantum State Preparation for Strongly Correlated Systems. J Phys Chem Lett 2024; 15:3197-3205. [PMID: 38483286 DOI: 10.1021/acs.jpclett.3c03159] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/22/2024]
Abstract
Quantum computing allows, in principle, the encoding of the exponentially scaling many-electron wave function onto a linearly scaling qubit register, offering a promising solution to overcome the limitations of traditional quantum chemistry methods. An essential requirement for ground state quantum algorithms to be practical is the initialization of the qubits to a high-quality approximation of the sought-after ground state. Quantum state preparation enables the generation of approximate eigenstates derived from classical computations but is frequently treated as an oracle in quantum information. In this study, we investigate the quantum state preparation of prototypical strongly correlated systems' ground state, up to 28 qubits, using the Hyperion-1 GPU-accelerated state-vector emulator. Various variational and nonvariational methods are compared in terms of their circuit depth and classical complexity. Our results indicate that the recently developed Overlap-ADAPT-VQE algorithm offers the most advantageous performance for near-term applications.
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Affiliation(s)
- César Feniou
- Sorbonne Université, LCT, UMR 7616 CNRS, 75005 Paris, France
- Qubit Pharmaceuticals, Advanced Research Department, 75014 Paris, France
| | - Olivier Adjoua
- Sorbonne Université, LCT, UMR 7616 CNRS, 75005 Paris, France
| | - Baptiste Claudon
- Sorbonne Université, LCT, UMR 7616 CNRS, 75005 Paris, France
- Qubit Pharmaceuticals, Advanced Research Department, 75014 Paris, France
| | | | - Emmanuel Giner
- Sorbonne Université, LCT, UMR 7616 CNRS, 75005 Paris, France
| | - Jean-Philip Piquemal
- Sorbonne Université, LCT, UMR 7616 CNRS, 75005 Paris, France
- Qubit Pharmaceuticals, Advanced Research Department, 75014 Paris, France
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29
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Kim K, Lim S, Shin K, Lee G, Jung Y, Kyoung W, Rhee JKK, Rhee YM. Variational quantum eigensolver for closed-shell molecules with non-bosonic corrections. Phys Chem Chem Phys 2024; 26:8390-8396. [PMID: 38406868 DOI: 10.1039/d3cp05570a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/27/2024]
Abstract
The realization of quantum advantage with noisy-intermediate-scale quantum (NISQ) machines has become one of the major challenges in computational sciences. Maintaining coherence of a physical system with more than ten qubits is a critical challenge that motivates research on compact system representations to reduce algorithm complexity. Toward this end, the variational quantum eigensolver (VQE) used to perform quantum simulations is considered to be one of the most promising algorithms for quantum chemistry in the NISQ era. We investigate reduced mapping of one spatial orbital to a single qubit to analyze the ground state energy in a way that the Pauli operators of qubits are mapped to the creation/annihilation of singlet pairs of electrons. To include the effect of non-bosonic (or non-paired) excitations, we introduce a simple correction scheme in the electron correlation model approximated by the geometrical mean of the bosonic (or paired) terms. Employing it in a VQE algorithm, we assess ground state energies of H2O, N2, and Li2O in good agreement with full configuration interaction (FCI) models respectively, using only 6, 8, and 12 qubits with quantum gate depths proportional to the squares of the qubit counts. With the adopted seniority-zero approximation that uses only one half of the qubit counts of a conventional VQE algorithm, we find that our non-bosonic correction method reaches reliable quantum chemistry simulations at least for the tested systems.
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Affiliation(s)
- Kyungmin Kim
- Department of Chemistry, KAIST, Daejeon, 34141, Republic of Korea.
| | - Sumin Lim
- Department of Physics, KAIST, Daejeon, 34141, Republic of Korea
| | - Kyujin Shin
- Materials Research & Engineering Center, CTO Division, Hyundai Motor Company, Uiwang 16082, Republic of Korea
| | - Gwonhak Lee
- School of Electrical Engineering, KAIST, Daejeon, 34141, Republic of Korea.
| | - Yousung Jung
- Department of Chemical Engineering, Seoul National University, Seoul, 08826, Republic of Korea
| | - Woomin Kyoung
- Materials Research & Engineering Center, CTO Division, Hyundai Motor Company, Uiwang 16082, Republic of Korea
| | - June-Koo Kevin Rhee
- School of Electrical Engineering, KAIST, Daejeon, 34141, Republic of Korea.
- KAIST ITRC of Quantum Computing for AI, KAIST, Daejeon, 34141, Republic of Korea
- KAIST Institute for IT Convergence, KAIST, Daejeon, 34141, Republic of Korea
| | - Young Min Rhee
- Department of Chemistry, KAIST, Daejeon, 34141, Republic of Korea.
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30
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Halder S, Dey A, Shrikhande C, Maitra R. Machine learning assisted construction of a shallow depth dynamic ansatz for noisy quantum hardware. Chem Sci 2024; 15:3279-3289. [PMID: 38425512 PMCID: PMC10901498 DOI: 10.1039/d3sc05807g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2023] [Accepted: 01/16/2024] [Indexed: 03/02/2024] Open
Abstract
The development of various dynamic ansatz-constructing techniques has ushered in a new era, making the practical exploitation of Noisy Intermediate-Scale Quantum (NISQ) hardware for molecular simulations increasingly viable. However, such ansatz construction protocols incur substantial measurement costs during their execution. This work involves the development of a novel protocol that capitalizes on regenerative machine learning methodologies and many-body perturbation theoretical measures to construct a highly expressive and shallow ansatz within the variational quantum eigensolver (VQE) framework with limited measurement costs. The regenerative machine learning model used in our work is trained with the basis vectors of a low-rank expansion of the N-electron Hilbert space to identify the dominant high-rank excited determinants without requiring a large number of quantum measurements. These selected excited determinants are iteratively incorporated within the ansatz through their low-rank decomposition. The reduction in the number of quantum measurements and ansatz depth manifests in the robustness of our method towards hardware noise, as demonstrated through numerical applications. Furthermore, the proposed method is highly compatible with state-of-the-art neural error mitigation techniques. This resource-efficient approach is quintessential for determining spectroscopic and other molecular properties, thereby facilitating the study of emerging chemical phenomena in the near-term quantum computing framework.
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Affiliation(s)
- Sonaldeep Halder
- Department of Chemistry, Indian Institute of Technology Bombay Powai Mumbai 400076 India
| | - Anish Dey
- Department of Chemical Sciences, Indian Institute of Science Education and Research Kolkata West Bengal 741246 India
| | - Chinmay Shrikhande
- Department of Chemistry, Indian Institute of Technology Bombay Powai Mumbai 400076 India
| | - Rahul Maitra
- Department of Chemistry, Indian Institute of Technology Bombay Powai Mumbai 400076 India
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31
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Li Z, Roy T, Rodríguez Pérez D, Lee KH, Kapit E, Schuster DI. Autonomous error correction of a single logical qubit using two transmons. Nat Commun 2024; 15:1681. [PMID: 38395989 PMCID: PMC10891116 DOI: 10.1038/s41467-024-45858-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2023] [Accepted: 02/05/2024] [Indexed: 02/25/2024] Open
Abstract
Large-scale quantum computers will inevitably need quantum error correction to protect information against decoherence. Traditional error correction typically requires many qubits, along with high-efficiency error syndrome measurement and real-time feedback. Autonomous quantum error correction instead uses steady-state bath engineering to perform the correction in a hardware-efficient manner. In this work, we develop a new autonomous quantum error correction scheme that actively corrects single-photon loss and passively suppresses low-frequency dephasing, and we demonstrate an important experimental step towards its full implementation with transmons. Compared to uncorrected encoding, improvements are experimentally witnessed for the logical zero, one, and superposition states. Our results show the potential of implementing hardware-efficient autonomous quantum error correction to enhance the reliability of a transmon-based quantum information processor.
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Affiliation(s)
- Ziqian Li
- James Franck Institute, University of Chicago, Chicago, IL, 60637, USA
- Department of Physics, University of Chicago, Chicago, IL, 60637, USA
- Department of Applied Physics, Stanford University, Stanford, CA, 94305, USA
| | - Tanay Roy
- James Franck Institute, University of Chicago, Chicago, IL, 60637, USA
- Department of Physics, University of Chicago, Chicago, IL, 60637, USA
| | | | - Kan-Heng Lee
- James Franck Institute, University of Chicago, Chicago, IL, 60637, USA
- Department of Physics, University of Chicago, Chicago, IL, 60637, USA
| | - Eliot Kapit
- Department of Physics, Colorado School of Mines, Golden, CO, 80401, USA
| | - David I Schuster
- James Franck Institute, University of Chicago, Chicago, IL, 60637, USA.
- Department of Physics, University of Chicago, Chicago, IL, 60637, USA.
- Department of Applied Physics, Stanford University, Stanford, CA, 94305, USA.
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, 60637, USA.
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32
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Hassan M, Pavošević F, Wang DS, Flick J. Simulating Polaritonic Ground States on Noisy Quantum Devices. J Phys Chem Lett 2024; 15:1373-1381. [PMID: 38287217 DOI: 10.1021/acs.jpclett.3c02875] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2024]
Abstract
The recent advent of quantum algorithms for noisy quantum devices offers a new route toward simulating strong light-matter interactions of molecules in optical cavities for polaritonic chemistry. In this work, we introduce a general framework for simulating electron-photon-coupled systems on small, noisy quantum devices. This method is based on the variational quantum eigensolver (VQE) with the polaritonic unitary coupled cluster (PUCC) ansatz. To achieve chemical accuracy, we exploit various symmetries in qubit reduction methods, such as electron-photon parity, and use recently developed error mitigation schemes, such as the reference zero-noise extrapolation method. We explore the robustness of the VQE-PUCC approach across a diverse set of regimes for the bond length, cavity frequency, and coupling strength of the H2 molecule in an optical cavity. To quantify the performance, we measure two properties: ground-state energy, fundamentally relevant to chemical reactivity, and photon number, an experimentally accessible general indicator of electron-photon correlation.
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Affiliation(s)
- Mohammad Hassan
- Department of Physics, City College of New York, New York, New York 10031, United States
- Department of Physics, The Graduate Center, City University of New York, New York, New York 10016, United States
| | | | - Derek S Wang
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Johannes Flick
- Department of Physics, City College of New York, New York, New York 10031, United States
- Department of Physics, The Graduate Center, City University of New York, New York, New York 10016, United States
- Center for Computational Quantum Physics, Flatiron Institute, 162 Fifth Avenue, New York, New York 10010, United States
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33
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Li N, Li YH, Fan DJ, Han LC, Xu Y, Lin J, Guo C, Li DD, Gong M, Liao SK, Zhu XB, Peng CZ. Optical transmission of microwave control signal towards large-scale superconducting quantum computing. OPTICS EXPRESS 2024; 32:3989-3996. [PMID: 38297608 DOI: 10.1364/oe.514909] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2023] [Accepted: 01/08/2024] [Indexed: 02/02/2024]
Abstract
With the rapid development of superconducting quantum computing and the implementation of surface code, large-scale quantum computing is emerging as an urgent demand. In a superconducting computing system, the qubit is maintained in a cryogenic environment to avoid thermal excitation. Thus, the transmission of control signals, which are generated at room temperature, is needed. Typically, the transmission of these signals to the qubit relies on a coaxial cable wiring approach. However, in a large-scale computing system with hundreds or even thousands of qubits, the coaxial cables will pose great space and heat load to the dilution refrigerator. Here, to tackle this problem, we propose and demonstrate a direct-modulation-based optical transmission line. In our experiment, the average single-qubit XEB error and control error are measured as 0.139% and 0.014% separately, demonstrating the feasibility of the optical wiring approach and paving the way for large-scale superconducting quantum computing.
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34
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Lim H, Kang DH, Kim J, Pellow-Jarman A, McFarthing S, Pellow-Jarman R, Jeon HN, Oh B, Rhee JKK, No KT. Fragment molecular orbital-based variational quantum eigensolver for quantum chemistry in the age of quantum computing. Sci Rep 2024; 14:2422. [PMID: 38287087 PMCID: PMC10825197 DOI: 10.1038/s41598-024-52926-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2023] [Accepted: 01/25/2024] [Indexed: 01/31/2024] Open
Abstract
Quantum computers offer significant potential for complex system analysis, yet their application in large systems is hindered by limitations such as qubit availability and quantum hardware noise. While the variational quantum eigensolver (VQE) was proposed to address these issues, its scalability remains limited. Many efforts, including new ansätze and Hamiltonian modifications, have been made to overcome these challenges. In this work, we introduced the novel Fragment Molecular Orbital/Variational Quantum Eigensolver (FMO/VQE) algorithm. This method combines the fragment molecular orbital (FMO) approach with VQE and efficiently utilizes qubits for quantum chemistry simulations. Employing the UCCSD ansatz, the FMO/VQE achieved an absolute error of just 0.053 mHa with 8 qubits in a [Formula: see text] system using the STO-3G basis set, and an error of 1.376 mHa with 16 qubits in a [Formula: see text] system with the 6-31G basis set. These results indicated a significant advancement in scalability over conventional VQE, maintaining accuracy with fewer qubits. Therefore, our FMO/VQE method exemplifies how integrating fragment-based quantum chemistry with quantum algorithms can enhance scalability, facilitating more complex molecular simulations and aligning with quantum computing advancements.
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Affiliation(s)
- Hocheol Lim
- Bioinformatics and Molecular Design Research Center (BMDRC), Incheon, Republic of Korea.
| | | | - Jeonghoon Kim
- Bioinformatics and Molecular Design Research Center (BMDRC), Incheon, Republic of Korea
| | | | | | | | | | - Byungdu Oh
- Baobab AiBIO Co., Ltd., Incheon, Republic of Korea
- SKKU Advanced Institute of Nanotechnology, Sungkyunkwan University, Suwon, Republic of Korea
| | | | - Kyoung Tai No
- Bioinformatics and Molecular Design Research Center (BMDRC), Incheon, Republic of Korea.
- Baobab AiBIO Co., Ltd., Incheon, Republic of Korea.
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35
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Matoušek M, Pernal K, Pavošević F, Veis L. Variational Quantum Eigensolver Boosted by Adiabatic Connection. J Phys Chem A 2024; 128:687-698. [PMID: 38214999 PMCID: PMC10823474 DOI: 10.1021/acs.jpca.3c07590] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2023] [Revised: 12/28/2023] [Accepted: 12/29/2023] [Indexed: 01/14/2024]
Abstract
In this work, we integrate the variational quantum eigensolver (VQE) with the adiabatic connection (AC) method for efficient simulations of chemical problems on near-term quantum computers. Orbital-optimized VQE methods are employed to capture the strong correlation within an active space, and classical AC corrections recover the dynamical correlation effects comprising electrons outside of the active space. On two challenging strongly correlated problems, namely, the dissociation of N2 and the electronic structure of the tetramethyleneethane biradical, we show that the combined VQE-AC approach enhances the performance of VQE dramatically. Moreover, since the AC corrections do not bring any additional requirements on quantum resources or measurements, they can actually boost the VQE algorithms. Our work paves the way toward quantum simulations of real-life problems on near-term quantum computers.
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Affiliation(s)
- Mikuláš Matoušek
- J.
Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
- Faculty
of Mathematics and Physics, Charles University, 121 16 Prague, Czech Republic
| | - Katarzyna Pernal
- Institute
of Physics, Lodz University of Technology, ul. Wolczanska 217/221, 93-005 Lodz, Poland
| | | | - Libor Veis
- J.
Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
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36
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Peng L, Zhang X, Chan GKL. Fermionic Reduced Density Low-Rank Matrix Completion, Noise Filtering, and Measurement Reduction in Quantum Simulations. J Chem Theory Comput 2023; 19:9151-9160. [PMID: 38095484 PMCID: PMC10753808 DOI: 10.1021/acs.jctc.3c00851] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2023] [Revised: 11/20/2023] [Accepted: 11/27/2023] [Indexed: 12/27/2023]
Abstract
Fermionic reduced density matrices summarize the key observables in Fermionic systems. In electronic systems, the two-particle reduced density matrix (2-RDM) is sufficient to determine the energy and most physical observables of interest. Here, we consider the possibility of using matrix completion to reconstruct the two-particle reduced density matrix to chemical accuracy from partial information. We consider the case of noiseless matrix completion, where the partial information corresponds to a subset of the 2-RDM elements, as well as noisy completion, where the partial information corresponds to both a subset of elements and statistical noise in their values. Through experiments on a set of 24 molecular systems, we find that 2-RDM can be efficiently reconstructed from a reduced amount of information. In the case of noisy completion, this results in a multiple orders of magnitude reduction in the number of measurements needed to determine the 2-RDM with chemical accuracy. These techniques can be readily applied to both classical and quantum algorithms for quantum simulations.
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Affiliation(s)
- Linqing Peng
- Division of Chemistry and Chemical
Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Xing Zhang
- Division of Chemistry and Chemical
Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical
Engineering, California Institute of Technology, Pasadena, California 91125, United States
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37
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Nykänen A, Miller A, Talarico W, Knecht S, Kovyrshin A, Skogh M, Tornberg L, Broo A, Mensa S, Symons BCB, Sahin E, Crain J, Tavernelli I, Pavošević F. Toward Accurate Post-Born-Oppenheimer Molecular Simulations on Quantum Computers: An Adaptive Variational Eigensolver with Nuclear-Electronic Frozen Natural Orbitals. J Chem Theory Comput 2023; 19:9269-9277. [PMID: 38081802 DOI: 10.1021/acs.jctc.3c01091] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2023]
Abstract
Nuclear quantum effects such as zero-point energy and hydrogen tunneling play a central role in many biological and chemical processes. The nuclear-electronic orbital (NEO) approach captures these effects by treating selected nuclei quantum mechanically on the same footing as electrons. On classical computers, the resources required for an exact solution of NEO-based models grow exponentially with system size. By contrast, quantum computers offer a means of solving this problem with polynomial scaling. However, due to the limitations of current quantum devices, NEO simulations are confined to the smallest systems described by minimal basis sets, whereas realistic simulations beyond the Born-Oppenheimer approximation require more sophisticated basis sets. For this purpose, we herein extend a hardware-efficient ADAPT-VQE method to the NEO framework in the frozen natural orbital (FNO) basis. We demonstrate on H2 and D2 molecules that the NEO-FNO-ADAPT-VQE method reduces the CNOT count by several orders of magnitude relative to the NEO unitary coupled cluster method with singles and doubles while maintaining the desired accuracy. This extreme reduction in the CNOT gate count is sufficient to permit practical computations employing the NEO method─an important step toward accurate simulations involving nonclassical nuclei and non-Born-Oppenheimer effects on near-term quantum devices. We further show that the method can capture isotope effects, and we demonstrate that inclusion of correlation energy systematically improves the prediction of difference in the zero-point energy (ΔZPE) between isotopes.
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Affiliation(s)
- Anton Nykänen
- Algorithmiq Ltd., Kanavakatu 3C, Helsinki FI-00160, Finland
| | - Aaron Miller
- Algorithmiq Ltd., Kanavakatu 3C, Helsinki FI-00160, Finland
- School of Physics, Trinity College Dublin, College Green Dublin 2, Ireland
| | - Walter Talarico
- Algorithmiq Ltd., Kanavakatu 3C, Helsinki FI-00160, Finland
- Department of Applied Physics, QTF Centre of Excellence, Center for Quantum Engineering, Aalto University School of Science, Aalto FIN-00076, Finland
| | - Stefan Knecht
- Algorithmiq Ltd., Kanavakatu 3C, Helsinki FI-00160, Finland
- ETH Zürich, Department of Chemistry and Applied Life Sciences Vladimir-Prelog-Weg 1-5/10, Zürich 8093, Switzerland
| | - Arseny Kovyrshin
- Data Science and Modelling, Pharmaceutical Sciences, R&D, AstraZeneca Gothenburg, Pepparedsleden 1, Molndal SE-431 83, Sweden
| | - Mårten Skogh
- Data Science and Modelling, Pharmaceutical Sciences, R&D, AstraZeneca Gothenburg, Pepparedsleden 1, Molndal SE-431 83, Sweden
- Department of Chemistry and Chemical Engineering, Chalmers University of Technology, Gothenburg 412 96, Sweden
| | - Lars Tornberg
- Data Science and Modelling, Pharmaceutical Sciences, R&D, AstraZeneca Gothenburg, Pepparedsleden 1, Molndal SE-431 83, Sweden
| | - Anders Broo
- Data Science and Modelling, Pharmaceutical Sciences, R&D, AstraZeneca Gothenburg, Pepparedsleden 1, Molndal SE-431 83, Sweden
| | - Stefano Mensa
- The Hartree Centre, STFC, Sci-Tech Daresbury, Warrington WA4 4AD, U.K
| | | | - Emre Sahin
- The Hartree Centre, STFC, Sci-Tech Daresbury, Warrington WA4 4AD, U.K
| | - Jason Crain
- IBM Research Europe, Hartree Centre STFC Laboratory, Sci-Tech Daresbury, Warrington WA4 4AD, U.K
- Department of Biochemistry, University of Oxford, Oxford OX1 3QU, U.K
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38
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Kumar A, Asthana A, Abraham V, Crawford TD, Mayhall NJ, Zhang Y, Cincio L, Tretiak S, Dub PA. Quantum Simulation of Molecular Response Properties in the NISQ Era. J Chem Theory Comput 2023; 19:9136-9150. [PMID: 38054645 DOI: 10.1021/acs.jctc.3c00731] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/07/2023]
Abstract
Accurate modeling of the response of molecular systems to an external electromagnetic field is challenging on classical computers, especially in the regime of strong electronic correlation. In this article, we develop a quantum linear response (qLR) theory to calculate molecular response properties on near-term quantum computers. Inspired by the recently developed variants of the quantum counterpart of equation of motion (qEOM) theory, the qLR formalism employs "killer condition" satisfying excitation operator manifolds that offer a number of theoretical advantages along with reduced quantum resource requirements. We also used the qEOM framework in this work to calculate the state-specific response properties. Further, through noiseless quantum simulations, we show that response properties calculated using the qLR approach are more accurate than the ones obtained from the classical coupled-cluster-based linear response models due to the improved quality of the ground-state wave function obtained using the ADAPT-VQE algorithm.
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Affiliation(s)
- Ashutosh Kumar
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Ayush Asthana
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Vibin Abraham
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - T Daniel Crawford
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Nicholas J Mayhall
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Yu Zhang
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Lukasz Cincio
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Sergei Tretiak
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
- Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Pavel A Dub
- Chemistry Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
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39
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Ghosh K, Kumar S, Rajan NM, Yamijala SSRKC. Deep Neural Network Assisted Quantum Chemistry Calculations on Quantum Computers. ACS OMEGA 2023; 8:48211-48220. [PMID: 38144092 PMCID: PMC10734038 DOI: 10.1021/acsomega.3c07364] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/24/2023] [Revised: 11/07/2023] [Accepted: 11/10/2023] [Indexed: 12/26/2023]
Abstract
The variational quantum eigensolver (VQE) is a widely employed method to solve electronic structure problems in the current noisy intermediate-scale quantum (NISQ) devices. However, due to inherent noise in the NISQ devices, VQE results on NISQ devices often deviate significantly from the results obtained on noiseless statevector simulators or traditional classical computers. The iterative nature of VQE further amplifies the errors in each loop. Recent works have explored ways to integrate deep neural networks (DNN) with VQE to mitigate iterative errors, albeit primarily limited to the noiseless statevector simulators. In this work, we trained DNN models across various quantum circuits and examined the potential of two DNN-VQE approaches, DNN1 and DNNF, for predicting the ground state energies of small molecules in the presence of device noise. We carefully examined the accuracy of the DNN1, DNNF, and VQE methods on both noisy simulators and real quantum devices by considering different ansatzes of varying qubit counts and circuit depths. Our results illustrate the advantages and limitations of both VQE and DNN-VQE approaches. Notably, both DNN1 and DNNF methods consistently outperform the standard VQE method in providing more accurate ground state energies in noisy environments. However, despite being more accurate than VQE, the energies predicted using these methods on real quantum hardware remain meaningful only at reasonable circuit depths (depth = 15, gates = 21). At higher depths (depth = 83, gates = 112), they deviate significantly from the exact results. Additionally, we find that DNNF does not offer any notable advantage over VQE in terms of speed. Consequently, our study recommends DNN1 as the preferred method for obtaining quick and accurate ground state energies of molecules on current quantum hardware, particularly for quantum circuits with lower depth and fewer qubits.
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Affiliation(s)
- Kalpak Ghosh
- Department
of Chemistry, Indian Institute of Technology
Madras, Chennai, 600036, India
- Centre
for Quantum Information, Communication, and Computing, Indian Institute of Technology Madras, Chennai 600036, India
| | - Sumit Kumar
- Department
of Chemistry, Indian Institute of Technology
Madras, Chennai, 600036, India
- Centre
for Quantum Information, Communication, and Computing, Indian Institute of Technology Madras, Chennai 600036, India
| | | | - Sharma S. R. K. C. Yamijala
- Department
of Chemistry, Indian Institute of Technology
Madras, Chennai, 600036, India
- Centre
for Quantum Information, Communication, and Computing, Indian Institute of Technology Madras, Chennai 600036, India
- Centre
for Molecular Materials and Functions, Indian
Institute of Technology Madras, Chennai 600036, India
- Centre
for Atomistic Modelling and Materials Design, Indian Institute of Technology Madras, Chennai 600036, India
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40
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Zeng X, Fan Y, Liu J, Li Z, Yang J. Quantum Neural Network Inspired Hardware Adaptable Ansatz for Efficient Quantum Simulation of Chemical Systems. J Chem Theory Comput 2023. [PMID: 38044845 DOI: 10.1021/acs.jctc.3c00527] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/05/2023]
Abstract
The variational quantum eigensolver is a promising way to solve the Schrödinger equation on a noisy intermediate-scale quantum (NISQ) computer, while its success relies on a well-designed wave function ansatz. Inspired by the quantum neural network, we propose a new hardware heuristic ansatz where its expressibility can be improved by increasing either the depth or the width of the circuit. Such a character makes this ansatz adaptable to different hardware environments. More importantly, it provides a general framework to improve the efficiency of the quantum resource utilization. For example, on a superconducting quantum computer where circuit depth is usually the bottleneck and the qubits thus cannot be fully used, circuit depth can be significantly reduced by introducing ancilla qubits. Ancilla qubits also make the circuit less sensitive to noises in practical application. These results open a new avenue to develop practical applications of quantum computation in the NISQ era.
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Affiliation(s)
- Xiongzhi Zeng
- Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China
| | - Yi Fan
- Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China, Hefei 230026, China
| | - Jie Liu
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Zhenyu Li
- Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Jinlong Yang
- Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
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41
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Loaiza I, Izmaylov AF. Block-Invariant Symmetry Shift: Preprocessing Technique for Second-Quantized Hamiltonians to Improve Their Decompositions to Linear Combination of Unitaries. J Chem Theory Comput 2023; 19:8201-8209. [PMID: 37939198 DOI: 10.1021/acs.jctc.3c00912] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2023]
Abstract
Computational cost of energy estimation for molecular electronic Hamiltonians via quantum phase estimation (QPE) grows with the difference between the largest and smallest eigenvalues of the Hamiltonian. In this work, we propose a preprocessing procedure that reduces the norm of the Hamiltonian without changing its eigenspectrum for the target states of a particular symmetry. The new procedure, block-invariant symmetry shift (BLISS), builds an operator T̂ such that the cost of implementing H ^ - T ^ is reduced compared to that of Ĥ, yet H ^ - T ^ acts on the subspaces of interest the same way as Ĥ does. BLISS performance is demonstrated for a linear combination of unitaries (LCU)-based QPE approaches on a set of small molecules. Using the number of electrons as the symmetry specifying the target set of states, BLISS provided a factor of 2 reduction of 1-norm for several LCU decompositions compared to their unshifted versions.
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Affiliation(s)
- Ignacio Loaiza
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto M5S 3H6, Canada
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto M1C 1A4, Canada
- Zapata Computing Canada Inc., Toronto M5E 1E5, Canada
| | - Artur F Izmaylov
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto M5S 3H6, Canada
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto M1C 1A4, Canada
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42
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Wang W, Whitfield JD. Basis Set Generation and Optimization in the NISQ Era with Quiqbox.jl. J Chem Theory Comput 2023; 19:8032-8052. [PMID: 37924295 DOI: 10.1021/acs.jctc.3c00011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2023]
Abstract
In the noisy intermediate-scale quantum era, ab initio computation of electronic structure problems has become one of the major benchmarks for identifying the boundary between classical and quantum computational power. Basis sets play a key role in the electronic structure methods implemented on both classical and quantum devices. To investigate the consequences of single-particle basis sets, we propose a framework for more customizable basis set generation and optimization. This framework allows composite basis sets to go beyond typical basis set frameworks, such as atomic basis sets, by introducing the concept of mixed-contracted Gaussian-type orbitals. These basis set generations set the stage for more flexible variational optimization of basis set parameters. To realize this framework, we have developed an open-source software package named "Quiqbox" in the Julia programming language. We demonstrate various examples of using Quiqbox for basis set optimization and generation, ranging from optimizing atomic basis sets on the Hartree-Fock level, preparing the initial state for variational quantum eigensolver computation, and constructing basis sets with completely delocalized orbitals. We also include various benchmarks of Quiqbox for basis set optimization and ab initial electronic structure computation.
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Affiliation(s)
- Weishi Wang
- Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - James D Whitfield
- Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755, United States
- AWS Center for Quantum Computing, Pasadena, California 91106, United States
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43
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Nishio S, Oba Y, Kurashige Y. Statistical errors in reduced density matrices sampled from quantum circuit simulation and the impact on multireference perturbation theory. Phys Chem Chem Phys 2023; 25:30525-30535. [PMID: 37927233 DOI: 10.1039/d3cp03520d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2023]
Abstract
In this work, we present a detailed analysis of statistical errors in reduced density matrices (RDMs) of active space wavefunctions sampled from quantum circuit simulation and the impact on results obtained by the multireference theories. From the sampling experiments, it is shown that the errors in sampled RDMs have a larger value for higher-order RDMs, and that the errors in sampled RDMs for excited states are larger than those for the ground state. We analytically derive the expected value of the sum of squared errors between the true distribution and sample distribution of weights of the electron configurations based on a multinomial distribution model, with which we present an assessment of the dependency of RDM errors on the number of shots for the observation (Nshot) and on the character of the target electronic state. With the benchmark calculations of short polyenes, C4H6 and C6H8, we report the statistical errors in CASCI and complete active space second-order perturbation theory (CASPT2) energies obtained with the sampled 1,2-RDMs and 1,2,3,4-RDMs, respectively. It was found that the standard deviation (SD) of the sampled CASCI energies is proportional to as predicted. It was also found that the dependence of the SD of the second-order correction energies are somewhat different but the errors in the reference CASCI energies are dominant as compared with the corrections and the SD of the resulting CASPT2 energies are proportional to . This suggests that the required Nshot for 3,4-RDMs used only in the second-order perturbative corrections is smaller than that for 1,2-RDM used to calculate the reference CASCI energies. It was also suggested from the analysis of the errors in the sampled energies that the required Nshot for 3-RDM, which is used to calculate the perturbative correction energies, can be smaller than that for 2-RDM to calculate the CASCI energies. In fact, it was shown that the potential energy curve along the isomerization reaction of the {[Cu(NH3)3]2O2}2+ complex as an archetype of metalloenzyme, in which static and dynamical electron correlations are both important, can be reasonably reproduced with Nshot = 106 for 1,2-RDMs but Nshot = 105 for 3-RDM by the sampling simulation.
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Affiliation(s)
- Soichiro Nishio
- Department of Chemistry, Graduate School of Science, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku Kyoto, 606-8502, Japan.
| | - Yuki Oba
- Department of Chemistry, Graduate School of Science, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku Kyoto, 606-8502, Japan.
| | - Yuki Kurashige
- Department of Chemistry, Graduate School of Science, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku Kyoto, 606-8502, Japan.
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44
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Sugisaki K. Projective Measurement-Based Quantum Phase Difference Estimation Algorithm for the Direct Computation of Eigenenergy Differences on a Quantum Computer. J Chem Theory Comput 2023; 19:7617-7625. [PMID: 37874368 PMCID: PMC10653105 DOI: 10.1021/acs.jctc.3c00784] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2023] [Indexed: 10/25/2023]
Abstract
Quantum computers are capable of calculating the energy difference of two electronic states using the quantum phase difference estimation (QPDE) algorithm. The Bayesian inference-based implementations for the QPDE have been reported so far, but in this approach, the quality of the calculated energy difference depends on the input wave functions being used. Here, we report the inverse quantum Fourier transformation-based QPDE with Na of ancillary qubits, which allows us to compute the difference of eigenenergies based on the single-shot projective measurement. As proof-of-concept demonstrations, we report numerical experiments for the singlet-triplet energy difference of the hydrogen molecule and the vertical excitation energies of halogen-substituted methylenes (CHF, CHCl, CF2, CFCl, and CCl2) and formaldehyde (HCHO).
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Affiliation(s)
- Kenji Sugisaki
- Graduate
School of Science and Technology, Keio University, 7-1 Shinkawasaki, Saiwai-ku, Kawasaki, Kanagawa 212-0032, Japan
- Quantum
Computing Center, Keio University, 3-14-1 Hiyoshi,
Kohoku-ku Yokohama, Kanagawa 223-8522, Japan
- Centre
for Quantum Engineering, Research and Education
TCG Centres for Research and Education in Science and Technology, Sector V, Salt Lake, Kolkata 700091, India
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45
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Iyengar SS, Zhang JH, Saha D, Ricard TC. Graph-| Q⟩⟨ C|: A Quantum Algorithm with Reduced Quantum Circuit Depth for Electronic Structure. J Phys Chem A 2023; 127:9334-9345. [PMID: 37906738 DOI: 10.1021/acs.jpca.3c04261] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2023]
Abstract
The accurate determination of chemical properties is known to have a critical impact on multiple fundamental chemical problems but is deeply hindered by the steep algebraic scaling of electron correlation calculations and the exponential scaling of quantum nuclear dynamics. With the advent of new quantum computing hardware and associated developments in creating new paradigms for quantum software, this avenue has been recognized as perhaps one way to address exponentially complex challenges in quantum chemistry and molecular dynamics. In this paper, we discuss a new approach to drastically reduce the quantum circuit depth (by several orders of magnitude) and help improve the accuracy in the quantum computation of electron correlation energies for large molecular systems. The method is derived from a graph-theoretic approach to molecular fragmentation and enables us to create a family of projection operators that decompose quantum circuits into separate unitary processes. Some of these processes can be treated on quantum hardware and others on classical hardware in a completely asynchronous and parallel fashion. Numerical benchmarks are provided through the computation of unitary coupled-cluster singles and doubles (UCCSD) energies for medium-sized protonated and neutral water clusters using the new quantum algorithms presented here.
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Affiliation(s)
- Srinivasan S Iyengar
- Department of Chemistry, Department of Physics, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Juncheng Harry Zhang
- Department of Chemistry, Department of Physics, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Debadrita Saha
- Department of Chemistry, Department of Physics, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Timothy C Ricard
- Department of Chemistry, Department of Physics, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
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46
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Fan Y, Cao C, Xu X, Li Z, Lv D, Yung MH. Circuit-Depth Reduction of Unitary-Coupled-Cluster Ansatz by Energy Sorting. J Phys Chem Lett 2023; 14:9596-9603. [PMID: 37862387 DOI: 10.1021/acs.jpclett.3c01804] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2023]
Abstract
Quantum computation represents a revolutionary approach to solving problems in quantum chemistry. However, due to the limited quantum resources in the current noisy intermediate-scale quantum (NISQ) devices, quantum algorithms for large chemical systems remain a major task. In this work, we demonstrate that the circuit depth of the unitary coupled cluster (UCC) and UCC-based ansatzes in the algorithm of the variational quantum eigensolver can be significantly reduced by an energy-sorting strategy. Specifically, subsets of excitation operators are first prescreened from the operator pool according to its contribution to the total energy. The quantum circuit ansatz is then iteratively constructed until convergence of the final energy to a typical accuracy. For demonstration, this method has been successfully applied to molecular and periodic systems. Particularly, a reduction of 50%-98% in the number of operators is observed while retaining the accuracy of the original UCCSD operator pools. This method can be straightforwardly extended to general parametric variational ansatzes.
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Affiliation(s)
- Yi Fan
- Central Research Institute, 2012 Laboratories, Huawei Technologies, Shenzhen 518129, China
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Changsu Cao
- Department of Chemistry, Tsinghua University, Beijing 100084, China
| | - Xusheng Xu
- Central Research Institute, 2012 Laboratories, Huawei Technologies, Shenzhen 518129, China
| | - Zhenyu Li
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Dingshun Lv
- Central Research Institute, 2012 Laboratories, Huawei Technologies, Shenzhen 518129, China
| | - Man-Hong Yung
- Central Research Institute, 2012 Laboratories, Huawei Technologies, Shenzhen 518129, China
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47
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Motta M, Sung KJ, Whaley KB, Head-Gordon M, Shee J. Bridging physical intuition and hardware efficiency for correlated electronic states: the local unitary cluster Jastrow ansatz for electronic structure. Chem Sci 2023; 14:11213-11227. [PMID: 37860666 PMCID: PMC10583744 DOI: 10.1039/d3sc02516k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2023] [Accepted: 09/20/2023] [Indexed: 10/21/2023] Open
Abstract
A prominent goal in quantum chemistry is to solve the molecular electronic structure problem for ground state energy with high accuracy. While classical quantum chemistry is a relatively mature field, the accurate and scalable prediction of strongly correlated states found, e.g., in bond breaking and polynuclear transition metal compounds remains an open problem. Within the context of a variational quantum eigensolver, we propose a new family of ansatzes which provides a more physically appropriate description of strongly correlated electrons than a unitary coupled cluster with single and double excitations (qUCCSD), with vastly reduced quantum resource requirements. Specifically, we present a set of local approximations to the unitary cluster Jastrow wavefunction motivated by Hubbard physics. As in the case of qUCCSD, exactly computing the energy scales factorially with system size on classical computers but polynomially on quantum devices. The local unitary cluster Jastrow ansatz removes the need for SWAP gates, can be tailored to arbitrary qubit topologies (e.g., square, hex, and heavy-hex), and is well-suited to take advantage of continuous sets of quantum gates recently realized on superconducting devices with tunable couplers. The proposed family of ansatzes demonstrates that hardware efficiency and physical transparency are not mutually exclusive; indeed, chemical and physical intuition regarding electron correlation can illuminate a useful path towards hardware-friendly quantum circuits.
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Affiliation(s)
- Mario Motta
- IBM Quantum, IBM Research - Almaden San Jose CA 95120 USA
| | - Kevin J Sung
- IBM Quantum, IBM T. J. Watson Research Center Yorktown Heights NY 10598 USA
| | - K Birgitta Whaley
- Department of Chemistry, University of California Berkeley CA 94720 USA
- Berkeley Quantum Information and Computation Center, University of California Berkeley CA 94720 USA
- Challenge Institute for Quantum Computation, University of California Berkeley CA 94720 USA
| | - Martin Head-Gordon
- Department of Chemistry, University of California Berkeley CA 94720 USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory Berkeley CA 94720 USA
| | - James Shee
- Department of Chemistry, University of California Berkeley CA 94720 USA
- Department of Chemistry, Rice University Houston TX 77005 USA
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48
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Yamaguchi K, Isobe H, Shoji M, Kawakami T, Miyagawa K. The Nature of the Chemical Bonds of High-Valent Transition-Metal Oxo (M=O) and Peroxo (MOO) Compounds: A Historical Perspective of the Metal Oxyl-Radical Character by the Classical to Quantum Computations. Molecules 2023; 28:7119. [PMID: 37894598 PMCID: PMC10609222 DOI: 10.3390/molecules28207119] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2023] [Revised: 10/08/2023] [Accepted: 10/10/2023] [Indexed: 10/29/2023] Open
Abstract
This review article describes a historical perspective of elucidation of the nature of the chemical bonds of the high-valent transition metal oxo (M=O) and peroxo (M-O-O) compounds in chemistry and biology. The basic concepts and theoretical backgrounds of the broken-symmetry (BS) method are revisited to explain orbital symmetry conservation and orbital symmetry breaking for the theoretical characterization of four different mechanisms of chemical reactions. Beyond BS methods using the natural orbitals (UNO) of the BS solutions, such as UNO CI (CC), are also revisited for the elucidation of the scope and applicability of the BS methods. Several chemical indices have been derived as the conceptual bridges between the BS and beyond BS methods. The BS molecular orbital models have been employed to explain the metal oxyl-radical character of the M=O and M-O-O bonds, which respond to their radical reactivity. The isolobal and isospin analogy between carbonyl oxide R2C-O-O and metal peroxide LFe-O-O has been applied to understand and explain the chameleonic chemical reactivity of these compounds. The isolobal and isospin analogy among Fe=O, O=O, and O have also provided the triplet atomic oxygen (3O) model for non-heme Fe(IV)=O species with strong radical reactivity. The chameleonic reactivity of the compounds I (Cpd I) and II (Cpd II) is also explained by this analogy. The early proposals obtained by these theoretical models have been examined based on recent computational results by hybrid DFT (UHDFT), DLPNO CCSD(T0), CASPT2, and UNO CI (CC) methods and quantum computing (QC).
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Affiliation(s)
- Kizashi Yamaguchi
- SANKEN, Osaka University, Ibaraki 567-0047, Osaka, Japan
- Center for Quantum Information and Quantum Biology (QIQB), Osaka University, Toyonaka 560-0043, Osaka, Japan
| | - Hiroshi Isobe
- Research Institute for Interdisciplinary Science, Okayama University, Okayama 700-8530, Okayama, Japan;
| | - Mitsuo Shoji
- Center for Computational Sciences, University of Tsukuba, Tsukuba 305-8577, Ibaraki, Japan; (M.S.); (K.M.)
| | - Takashi Kawakami
- Department of Chemistry, Graduate School of Science, Osaka University, Toyonaka 560-0043, Osaka, Japan;
| | - Koichi Miyagawa
- Center for Computational Sciences, University of Tsukuba, Tsukuba 305-8577, Ibaraki, Japan; (M.S.); (K.M.)
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49
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Iyengar SS, Kumar A, Saha D, Sabry A. Synthesis of Hidden Subgroup Quantum Algorithms and Quantum Chemical Dynamics. J Chem Theory Comput 2023; 19:6082-6092. [PMID: 37703187 DOI: 10.1021/acs.jctc.3c00404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/15/2023]
Abstract
We describe a general formalism for quantum dynamics and show how this formalism subsumes several quantum algorithms, including the Deutsch, Deutsch-Jozsa, Bernstein-Vazirani, Simon, and Shor algorithms as well as the conventional approach to quantum dynamics based on tensor networks. The common framework exposes similarities among quantum algorithms and natural quantum phenomena: we illustrate this connection by showing how the correlated behavior of protons in water wire systems that are common in many biological and materials systems parallels the structure of Shor's algorithm.
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Affiliation(s)
- Srinivasan S Iyengar
- Department of Chemistry, Indiana University, Bloomington, Indiana 47405-7102, United States
- Quantum Science and Engineering Center (QSEc), Indiana University, Bloomington, Indiana 47405-7102, United States
| | - Anup Kumar
- Department of Chemistry, Indiana University, Bloomington, Indiana 47405-7102, United States
| | - Debadrita Saha
- Department of Chemistry, Indiana University, Bloomington, Indiana 47405-7102, United States
| | - Amr Sabry
- Quantum Science and Engineering Center (QSEc), Indiana University, Bloomington, Indiana 47405-7102, United States
- Department of Computer Science, Luddy School of Informatics, Computing, and Engineering, Indiana University, Bloomington, Indiana 47405-7102, United States
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50
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Lai J, Fan Y, Fu Q, Li Z, Yang J. Accurate and efficient calculations of Hellmann-Feynman forces for quantum computation. J Chem Phys 2023; 159:114113. [PMID: 37724727 DOI: 10.1063/5.0167444] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2023] [Accepted: 08/31/2023] [Indexed: 09/21/2023] Open
Abstract
First-order derivatives of energies with respect to atomic coordinates are widely computed and used in quantum chemistry simulations. The rapidly emerging technology of quantum computing offers a new paradigm for solving relevant quantum chemistry equations. In this work, we have achieved analytical calculations of atomic forces based on the Hellmann-Feynman theorem within the framework of the variational quantum eigensolver. The accuracy of the approach is demonstrated by calculating the atomic forces of H2, LiH, H2O, and NH3 molecules, which are in excellent agreement with values obtained from full configuration interaction calculations. In particular, for systems with degenerate molecular orbitals, the analytical approach has a significant accuracy advantage over finite-difference-based methods and will not involve additional computational effort on a quantum computer. The calculated forces are further used to optimize the geometries of NH3 and CH4 molecules and to perform ab initio molecular dynamics simulations for the umbrella inversion of NH3, demonstrating the feasibility of the approach in practical quantum chemistry simulations.
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Affiliation(s)
- Juntao Lai
- School of Future Technology, University of Science and Technology of China, Hefei 230026, China
| | - Yi Fan
- Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China
| | - Qiang Fu
- School of Future Technology, University of Science and Technology of China, Hefei 230026, China
- Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Zhenyu Li
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
- Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jinlong Yang
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
- Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China, Hefei, Anhui 230026, China
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