1
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Cadi Tazi L, Thom AJW. Folded Spectrum VQE: A Quantum Computing Method for the Calculation of Molecular Excited States. J Chem Theory Comput 2024; 20:2491-2504. [PMID: 38492238 DOI: 10.1021/acs.jctc.3c01378] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/18/2024]
Abstract
The recent developments of quantum computing present novel potential pathways for quantum chemistry as the scaling of the computational power of quantum computers could be harnessed to naturally encode and solve electronic structure problems. Theoretically exact quantum algorithms for chemistry have been proposed (e.g., quantum phase estimation), but the limited capabilities of current noisy intermediate-scale quantum devices motivated the development of less demanding hybrid algorithms. In this context, the variational quantum eigensolver (VQE) algorithm was successfully introduced as an effective method to compute the ground-state energies of small molecules. This study investigates the folded spectrum (FS) method as an extension of the VQE algorithm for the computation of molecular excited states. It provides the possibility of directly computing excited states around a selected target energy using the same quantum circuit as for the ground-state calculation. Inspired by the variance-based methods from the quantum Monte Carlo literature, the FS method minimizes the energy variance, thus, in principle, requiring a computationally expensive squared Hamiltonian to be applied. We alleviate this potentially poor scaling by employing a Pauli grouping procedure to identify sets of commuting Pauli strings that can be evaluated simultaneously. This allows for a significant reduction in the computational cost. We applied the FS-VQE method to small molecules (H2, LiH), obtaining all electronic excited states with chemical accuracy on ideal quantum simulators. Furthermore, we explore the application of quantum error mitigation techniques, demonstrating improved energy accuracy on noisy simulators compared with simulations without mitigation.
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Affiliation(s)
- Lila Cadi Tazi
- École Normale Supérieure Paris-Saclay, Université Paris-Saclay, Gif-sur-Yvette 91190, France
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, U.K
| | - Alex J W Thom
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, U.K
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2
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Nokkala J. Online quantum time series processing with random oscillator networks. Sci Rep 2023; 13:7694. [PMID: 37169824 PMCID: PMC10175294 DOI: 10.1038/s41598-023-34811-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2021] [Accepted: 05/08/2023] [Indexed: 05/13/2023] Open
Abstract
Reservoir computing is a powerful machine learning paradigm for online time series processing. It has reached state-of-the-art performance in tasks such as chaotic time series prediction and continuous speech recognition thanks to its unique combination of high computational power and low training cost which sets it aside from alternatives such as traditionally trained recurrent neural networks, and furthermore is amenable to implementations in dedicated hardware, potentially leading to extremely compact and efficient reservoir computers. Recently the use of random quantum systems has been proposed, leveraging the complexity of quantum dynamics for classical time series processing. Extracting the output from a quantum system without disturbing its state too much is problematic however, and can be expected to become a bottleneck in such approaches. Here we propose a reservoir computing inspired approach to online processing of time series consisting of quantum information, sidestepping the measurement problem. We illustrate its power by generalizing two paradigmatic benchmark tasks from classical reservoir computing to quantum information and introducing a task without a classical analogue where a random system is trained to both create and distribute entanglement between systems that never directly interact. Finally, we discuss partial generalizations where only the input or only the output time series is quantum.
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Affiliation(s)
- Johannes Nokkala
- Department for Physics and Astronomy, University of Turku, 20014, Turun Yliopisto, Finland.
- IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (UIB-CSIC) UIB Campus, 07122, Palma de Mallorca, Spain.
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3
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Lee S, Lee J, Zhai H, Tong Y, Dalzell AM, Kumar A, Helms P, Gray J, Cui ZH, Liu W, Kastoryano M, Babbush R, Preskill J, Reichman DR, Campbell ET, Valeev EF, Lin L, Chan GKL. Evaluating the evidence for exponential quantum advantage in ground-state quantum chemistry. Nat Commun 2023; 14:1952. [PMID: 37029105 PMCID: PMC10082187 DOI: 10.1038/s41467-023-37587-6] [Citation(s) in RCA: 25] [Impact Index Per Article: 25.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2023] [Accepted: 03/22/2023] [Indexed: 04/09/2023] Open
Abstract
Due to intense interest in the potential applications of quantum computing, it is critical to understand the basis for potential exponential quantum advantage in quantum chemistry. Here we gather the evidence for this case in the most common task in quantum chemistry, namely, ground-state energy estimation, for generic chemical problems where heuristic quantum state preparation might be assumed to be efficient. The availability of exponential quantum advantage then centers on whether features of the physical problem that enable efficient heuristic quantum state preparation also enable efficient solution by classical heuristics. Through numerical studies of quantum state preparation and empirical complexity analysis (including the error scaling) of classical heuristics, in both ab initio and model Hamiltonian settings, we conclude that evidence for such an exponential advantage across chemical space has yet to be found. While quantum computers may still prove useful for ground-state quantum chemistry through polynomial speedups, it may be prudent to assume exponential speedups are not generically available for this problem.
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Affiliation(s)
- Seunghoon Lee
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA, 91125, USA
| | - Joonho Lee
- Department of Chemistry, Columbia University, New York, NY, 10027, USA
| | - Huanchen Zhai
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA, 91125, USA
| | - Yu Tong
- Department of Mathematics, University of California, Berkeley, CA, 94720, USA
| | | | - Ashutosh Kumar
- Department of Chemistry, Virginia Tech, Blacksburg, VA, 24061, USA
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - Phillip Helms
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA, 91125, USA
| | - Johnnie Gray
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA, 91125, USA
| | - Zhi-Hao Cui
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA, 91125, USA
| | - Wenyuan Liu
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA, 91125, USA
| | - Michael Kastoryano
- AWS Center for Quantum Computing, Pasadena, CA, 91125, USA
- Amazon Quantum Solutions Lab, Seattle, WA, 98170, USA
| | - Ryan Babbush
- Google Quantum AI, 340 Main Street, Venice, CA, 90291, USA
| | - John Preskill
- AWS Center for Quantum Computing, Pasadena, CA, 91125, USA
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, 91125, USA
| | - David R Reichman
- Department of Chemistry, Columbia University, New York, NY, 10027, USA
| | | | - Edward F Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, VA, 24061, USA
| | - Lin Lin
- Department of Mathematics, University of California, Berkeley, CA, 94720, USA
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA, 91125, USA.
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4
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Kowalski K. Sub-system self-consistency in coupled cluster theory. J Chem Phys 2023; 158:054101. [PMID: 36754799 DOI: 10.1063/5.0125696] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Abstract
In this article, we provide numerical evidence indicating that the single-reference coupled-cluster (CC) energies can be calculated alternatively to their copybook definition. We demonstrate that the CC energy can be reconstructed by diagonalizing the effective Hamiltonians describing correlated sub-systems of the many-body system. In the extreme case, we provide numerical evidence that the CC energy can be reproduced through the diagonalization of the effective Hamiltonian describing sub-system composed of a single electron. These properties of the CC formalism can be exploited to design protocols to define effective interactions in sub-systems used as probes to calculate the energy of the entire system and introduce a new type of self-consistency for approximate CC approaches.
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Affiliation(s)
- Karol Kowalski
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, USA
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5
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Alghamdi S, Abbas F, Hussein R, Alhamzani A, El‐Shamy N. Spectroscopic characterization (IR, UV-Vis), and HOMO-LUMO, MEP, NLO, NBO Analysis and the Antifungal Activity for 4-Bromo-N-(2-nitrophenyl) benzamide; Using DFT Modeling and In silico Molecular Docking. J Mol Struct 2023. [DOI: 10.1016/j.molstruc.2022.134001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/15/2022]
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6
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Liu R, V. Romero S, Oregi I, Osaba E, Villar-Rodriguez E, Ban Y. Digital Quantum Simulation and Circuit Learning for the Generation of Coherent States. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1529. [PMID: 36359621 PMCID: PMC9689327 DOI: 10.3390/e24111529] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/28/2022] [Revised: 10/20/2022] [Accepted: 10/21/2022] [Indexed: 06/16/2023]
Abstract
Coherent states, known as displaced vacuum states, play an important role in quantum information processing, quantum machine learning, and quantum optics. In this article, two ways to digitally prepare coherent states in quantum circuits are introduced. First, we construct the displacement operator by decomposing it into Pauli matrices via ladder operators, i.e., creation and annihilation operators. The high fidelity of the digitally generated coherent states is verified compared with the Poissonian distribution in Fock space. Secondly, by using Variational Quantum Algorithms, we choose different ansatzes to generate coherent states. The quantum resources-such as numbers of quantum gates, layers and iterations-are analyzed for quantum circuit learning. The simulation results show that quantum circuit learning can provide high fidelity on learning coherent states by choosing appropriate ansatzes.
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Affiliation(s)
- Ruilin Liu
- School of Materials Science and Engineering, Shanghai University, Shanghai 200444, China
| | - Sebastián V. Romero
- TECNALIA, Basque Research and Technology Alliance (BRTA), 48160 Derio, Spain
| | - Izaskun Oregi
- TECNALIA, Basque Research and Technology Alliance (BRTA), 48160 Derio, Spain
- Faculty of New Interactive Technologies, Universidad EUNEIZ, 01013 Vitoria-Gasteiz, Spain
| | - Eneko Osaba
- TECNALIA, Basque Research and Technology Alliance (BRTA), 48160 Derio, Spain
| | | | - Yue Ban
- TECNALIA, Basque Research and Technology Alliance (BRTA), 48160 Derio, Spain
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7
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Lan Z, Liang W. Amplitude Reordering Accelerates the Adaptive Variational Quantum Eigensolver Algorithms. J Chem Theory Comput 2022; 18:5267-5275. [PMID: 35971280 DOI: 10.1021/acs.jctc.2c00403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The variational quantum eigensolver (VQE) algorithm can simulate the chemical systems such as molecules in the noisy-intermediate-scale quantum devices and shows promising applications in quantum chemistry simulations. The accuracy and computational cost of the VQE simulations are determined by the underlying ansatz. Therefore, the most important issue is to generate a compact and accurate ansatz, which requires a shallower parametric quantum circuit and can achieve an acceptable accuracy. The newly developed adaptive algorithms (AAs) such as the adaptive derivative-assembled pseudo-Trotter VQE (ADAPT-VQE) can solve this issue via generating compact and accurate ansatzes. However, these AAs show very low computational efficiency because they require a large number of additional measurements. Here we propose an amplitude reordering (AR) strategy to accelerate the promising but expensive AAs by adding operators in a "batched" fashion in a way that their order is still quasi-optimal. We first introduce the AR method into ADAPT-VQE and build the AR-ADAPT-VQE algorithm. We then endow the energy-sorting VQE (ES-VQE) algorithm with the adaptive feature and introduce the AR into AES-VQE to form the AR-AES-VQE algorithm. To demonstrate the performance of these algorithms, we calculate the dissociation curves of three small molecules, LiH, linear BeH2, and linear H6, by using (AR-)ADAPT-VQE and (AR-)AES-VQE algorithms. It is found that all of the AR-equipped AAs (AR-AAs) can significantly reduce the number of iterations and subsequently accelerate the calculations with a speedup of up to more than ten times without the obvious loss of accuracy. The final ansatz generated by the AR-AAs not only avoids extra circuit depth but also maintains the computational accuracy; sometimes the AR-AAs even outperforms their original counterparts.
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Affiliation(s)
- Zhihao Lan
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, Fujian Province, Peoples' Republic of China
| | - WanZhen Liang
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, Fujian Province, Peoples' Republic of China
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8
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Yoshikawa T, Takanashi T, Nakai H. Quantum Algorithm of the Divide-and-Conquer Unitary Coupled Cluster Method with a Variational Quantum Eigensolver. J Chem Theory Comput 2022; 18:5360-5373. [PMID: 35926142 DOI: 10.1021/acs.jctc.2c00602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The variational quantum eigensolver (VQE) with shallow or constant-depth quantum circuits is one of the most pursued approaches in the noisy intermediate-scale quantum (NISQ) devices with incoherent errors. In this study, the divide-and-conquer (DC) linear scaling technique, which divides the entire system into several fragments, is applied to the VQE algorithm based on the unitary coupled cluster (UCC) method, denoted as DC-qUCC/VQE, to reduce the number of required qubits. The unitarity of the UCC ansatz that enables the evaluation of the total energy as well as various molecular properties as expectation values can be easily implemented on quantum devices because the quantum gates are unitary operators themselves. Based on this feature, the present DC-qUCC/VQE algorithm is designed to conserve the total number of electrons in the entire system using the density matrix evaluated on a quantum computer. Numerical assessments clarified that the energy errors of the DC-qUCC/VQE calculations decrease by using the constraint of the total number of electrons. Furthermore, the DC-qUCC/VQE algorithm could reduce the number of quantum gates and shows the possibility of decreasing incoherent errors.
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Affiliation(s)
- Takeshi Yoshikawa
- Faculty of Pharmaceutical Sciences, Toho University, 2-2-1 Miyama, Funabashi, Chiba 274-8510, Japan.,Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
| | - Tomoya Takanashi
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
| | - Hiromi Nakai
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan.,Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan.,Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Katsura, Kyoto 615-8520, Japan
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9
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Sugisaki K, Toyota K, Sato K, Shiomi D, Takui T. Adiabatic state preparation of correlated wave functions with nonlinear scheduling functions and broken-symmetry wave functions. Commun Chem 2022; 5:84. [PMID: 36698020 PMCID: PMC9814591 DOI: 10.1038/s42004-022-00701-8] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2022] [Accepted: 06/30/2022] [Indexed: 01/28/2023] Open
Abstract
Adiabatic state preparation (ASP) can generate the correlated wave function by simulating the time evolution of wave function under the time-dependent Hamiltonian that interpolates the Fock operator and the full electronic Hamiltonian. However, ASP is inherently unsuitable for studying strongly correlated systems, and furthermore practical computational conditions for ASP are unknown. In quest for the suitable computational conditions for practical applications of ASP, we performed numerical simulations of ASP in the potential energy curves of N2, BeH2, and in the C2v quasi-reaction pathway of the Be atom insertion to the H2 molecule, examining the effect of nonlinear scheduling functions and the ASP with broken-symmetry wave functions with the S2 operator as the penalty term, contributing to practical applications of quantum computing to quantum chemistry. Eventually, computational guidelines to generate the correlated wave functions having the square overlap with the complete-active space self-consistent field wave function close to unity are discussed.
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Affiliation(s)
- Kenji Sugisaki
- grid.261445.00000 0001 1009 6411Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585 Japan ,grid.419082.60000 0004 1754 9200JST PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012 Japan ,grid.510650.7Centre for Quantum Engineering, Research and Education (CQuERE), TCG Centres for Research and Education in Science and Technology (TCG CREST), Sector V, Salt Lake, Kolkata, 700091 India
| | - Kazuo Toyota
- grid.261445.00000 0001 1009 6411Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585 Japan
| | - Kazunobu Sato
- grid.261445.00000 0001 1009 6411Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585 Japan
| | - Daisuke Shiomi
- grid.261445.00000 0001 1009 6411Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585 Japan
| | - Takeji Takui
- grid.261445.00000 0001 1009 6411Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585 Japan ,grid.261445.00000 0001 1009 6411Research Support Department/University Research Administrator Center, University Administration Division, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka, 558-8585 Japan
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10
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Hussein RK, Khouqeer G, Alkaoud AM, El-Khayatt AM. Probing the Action of Screened Anticancer Triazole–Tetrazole Derivatives Against COVID-19 Using Molecular Docking and DFT Investigations. Nat Prod Commun 2022. [DOI: 10.1177/1934578x221093915] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Drugs are continuously being evaluated for novel therapeutic uses. The purpose of this work was to screen anticancer triazole/tetrazole derivatives for effectiveness against the SARS-CoV-2 main protease (Mpro). First, the chemical structures’ activity was derived from conceptual quantum chemical calculations. According to molecular docking analysis, the compounds scored good interactions against SAR-COV-2's Mpro, with binding energies extending from −8.21 to −8.97 kcal/mol. The docked complexes included various bindings with His41 and Cys145, both catalytic residues responsible for cleavage of the SARS-CoV-2 Mpro. Among the 4 studied compounds, TD3 exhibited the highest affinity by achieving the most stable binding energy and lowest value for the inhibition constant. Most striking was that TD3 not only formed strong bonds with the catalytic residues His41 and Cys145, but also captured the residues of the catalytic loop (Cys44 to Pro52), which flank the catalytic dyads in Mpro's active site. As a result, the studied triazole/tetrazole derivatives, notably TD3, must be reviewed as potent drugs that could be repurposed for SARS-CoV-2 treatment.
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Affiliation(s)
- Rageh K. Hussein
- College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Kingdom of Saudi Arabia
| | - Ghada Khouqeer
- College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Kingdom of Saudi Arabia
| | - Ahmed M. Alkaoud
- College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Kingdom of Saudi Arabia
| | - Ahmed M. El-Khayatt
- College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Kingdom of Saudi Arabia
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11
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McClean JR, Rubin NC, Lee J, Harrigan MP, O'Brien TE, Babbush R, Huggins WJ, Huang HY. What the foundations of quantum computer science teach us about chemistry. J Chem Phys 2021; 155:150901. [PMID: 34686056 DOI: 10.1063/5.0060367] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Abstract
With the rapid development of quantum technology, one of the leading applications that has been identified is the simulation of chemistry. Interestingly, even before full scale quantum computers are available, quantum computer science has exhibited a remarkable string of results that directly impact what is possible in a chemical simulation with any computer. Some of these results even impact our understanding of chemistry in the real world. In this Perspective, we take the position that direct chemical simulation is best understood as a digital experiment. While on the one hand, this clarifies the power of quantum computers to extend our reach, it also shows us the limitations of taking such an approach too directly. Leveraging results that quantum computers cannot outpace the physical world, we build to the controversial stance that some chemical problems are best viewed as problems for which no algorithm can deliver their solution, in general, known in computer science as undecidable problems. This has implications for the predictive power of thermodynamic models and topics such as the ergodic hypothesis. However, we argue that this Perspective is not defeatist but rather helps shed light on the success of existing chemical models such as transition state theory, molecular orbital theory, and thermodynamics as models that benefit from data. We contextualize recent results, showing that data-augmented models are a more powerful rote simulation. These results help us appreciate the success of traditional chemical theory and anticipate new models learned from experimental data. Not only can quantum computers provide data for such models, but they can also extend the class and power of models that utilize data in fundamental ways. These discussions culminate in speculation on new ways for quantum computing and chemistry to interact and our perspective on the eventual roles of quantum computers in the future of chemistry.
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Affiliation(s)
- Jarrod R McClean
- Google Quantum AI, 340 Main Street, Venice, California 90291, USA
| | - Nicholas C Rubin
- Google Quantum AI, 340 Main Street, Venice, California 90291, USA
| | - Joonho Lee
- Google Quantum AI, 340 Main Street, Venice, California 90291, USA
| | | | - Thomas E O'Brien
- Google Quantum AI, 340 Main Street, Venice, California 90291, USA
| | - Ryan Babbush
- Google Quantum AI, 340 Main Street, Venice, California 90291, USA
| | | | - Hsin-Yuan Huang
- Institute for Quantum Information and Matter and Department of Computing and Mathematical Sciences, Caltech, Pasadena, California 91125, USA
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12
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Zhao A, Rubin NC, Miyake A. Fermionic Partial Tomography via Classical Shadows. PHYSICAL REVIEW LETTERS 2021; 127:110504. [PMID: 34558940 DOI: 10.1103/physrevlett.127.110504] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2020] [Revised: 07/23/2021] [Accepted: 07/26/2021] [Indexed: 06/13/2023]
Abstract
We propose a tomographic protocol for estimating any k-body reduced density matrix (k-RDM) of an n-mode fermionic state, a ubiquitous step in near-term quantum algorithms for simulating many-body physics, chemistry, and materials. Our approach extends the framework of classical shadows, a randomized approach to learning a collection of quantum-state properties, to the fermionic setting. Our sampling protocol uses randomized measurement settings generated by a discrete group of fermionic Gaussian unitaries, implementable with linear-depth circuits. We prove that estimating all k-RDM elements to additive precision ϵ requires on the order of (n/k)k^{3/2}log(n)/ϵ^{2} repeated state preparations, which is optimal up to the logarithmic factor. Furthermore, numerical calculations show that our protocol offers a substantial improvement in constant overheads for k≥2, as compared to prior deterministic strategies. We also adapt our method to particle-number symmetry, wherein the additional circuit depth may be halved at the cost of roughly 2-5 times more repetitions.
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Affiliation(s)
- Andrew Zhao
- Center for Quantum Information and Control, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87106, USA
| | | | - Akimasa Miyake
- Center for Quantum Information and Control, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87106, USA
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13
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Barkoutsos PK, Gkritsis F, Ollitrault PJ, Sokolov IO, Woerner S, Tavernelli I. Quantum algorithm for alchemical optimization in material design. Chem Sci 2021; 12:4345-4352. [PMID: 34163697 PMCID: PMC8179438 DOI: 10.1039/d0sc05718e] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
The development of tailored materials for specific applications is an active field of research in chemistry, material science and drug discovery. The number of possible molecules obtainable from a set of atomic species grow exponentially with the size of the system, limiting the efficiency of classical sampling algorithms. On the other hand, quantum computers can provide an efficient solution to the sampling of the chemical compound space for the optimization of a given molecular property. In this work, we propose a quantum algorithm for addressing the material design problem with a favourable scaling. The core of this approach is the representation of the space of candidate structures as a linear superposition of all possible atomic compositions. The corresponding ‘alchemical’ Hamiltonian drives the optimization in both the atomic and electronic spaces leading to the selection of the best fitting molecule, which optimizes a given property of the system, e.g., the interaction with an external potential as in drug design. The quantum advantage resides in the efficient calculation of the electronic structure properties together with the sampling of the exponentially large chemical compound space. We demonstrate both in simulations and with IBM Quantum hardware the efficiency of our scheme and highlight the results in a few test cases. This preliminary study can serve as a basis for the development of further material design quantum algorithms for near-term quantum computers. ‘Alchemical’ quantum algorithm for the simultaneous optimisation of chemical composition and electronic structure for material design. By exploiting quantum mechanical principles this approach will boost drug discovery in the near future.![]()
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Affiliation(s)
| | - Fotios Gkritsis
- IBM Quantum, IBM Research - Zurich 8803 Rüschlikon Switzerland .,King's College London London UK
| | - Pauline J Ollitrault
- IBM Quantum, IBM Research - Zurich 8803 Rüschlikon Switzerland .,Laboratory of Physical Chemistry, ETH Zürich 8093 Zürich Switzerland
| | - Igor O Sokolov
- IBM Quantum, IBM Research - Zurich 8803 Rüschlikon Switzerland .,Department of Chemistry, University of Zürich Switzerland
| | - Stefan Woerner
- IBM Quantum, IBM Research - Zurich 8803 Rüschlikon Switzerland
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14
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Outeiral C, Strahm M, Shi J, Morris GM, Benjamin SC, Deane CM. The prospects of quantum computing in computational molecular biology. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2020. [DOI: 10.1002/wcms.1481] [Citation(s) in RCA: 39] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Carlos Outeiral
- Department of Statistics University of Oxford Oxford UK
- Department of Materials University of Oxford Oxford UK
| | - Martin Strahm
- Pharma Research and Early Development F. Hoffmann‐La Roche Basel Switzerland
| | - Jiye Shi
- Computer‐Aided Drug Design UCB Pharma Slough UK
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15
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Miyagawa K, Shoji M, Isobe H, Yamanaka S, Kawakami T, Okumura M, Yamaguchi K. Theory of chemical bonds in metalloenzymes XXIV electronic and spin structures of FeMoco and Fe-S clusters by classical and quantum computing. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1760388] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Koichi Miyagawa
- The Institute for Scientific and Industrial Research, Osaka University, Ibaraki, Japan
| | - Mitsuo Shoji
- Center of Computational Sciences, Tsukuba University, Tsukuba, Japan
| | - Hiroshi Isobe
- Graduate School of Natural Science and Technology, Okayama University, Okayama, Japan
| | - Shusuke Yamanaka
- Graduate School of Science, Osaka University, Toyonaka, Japan
- Division of Quantum Information and Quantum Biology (QIQB), Osaka University, Toyonaka, Japan
| | - Takashi Kawakami
- Graduate School of Science, Osaka University, Toyonaka, Japan
- RIKEN Center for Computational Science, Kobe, Japan
| | | | - Kizashi Yamaguchi
- The Institute for Scientific and Industrial Research, Osaka University, Ibaraki, Japan
- Division of Quantum Information and Quantum Biology (QIQB), Osaka University, Toyonaka, Japan
- RIKEN Center for Computational Science, Kobe, Japan
- Institute for Nanoscience Design, Osaka University, Toyonaka, Japan
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16
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Wei S, Li H, Long G. A Full Quantum Eigensolver for Quantum Chemistry Simulations. RESEARCH 2020; 2020:1486935. [PMID: 32274468 PMCID: PMC7125455 DOI: 10.34133/2020/1486935] [Citation(s) in RCA: 34] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/22/2019] [Accepted: 02/20/2020] [Indexed: 12/05/2022]
Abstract
Quantum simulation of quantum chemistry is one of the most compelling applications of quantum computing. It is of particular importance in areas ranging from materials science, biochemistry, and condensed matter physics. Here, we propose a full quantum eigensolver (FQE) algorithm to calculate the molecular ground energies and electronic structures using quantum gradient descent. Compared to existing classical-quantum hybrid methods such as variational quantum eigensolver (VQE), our method removes the classical optimizer and performs all the calculations on a quantum computer with faster convergence. The gradient descent iteration depth has a favorable complexity that is logarithmically dependent on the system size and inverse of the precision. Moreover, the FQE can be further simplified by exploiting a perturbation theory for the calculations of intermediate matrix elements and obtaining results with a precision that satisfies the requirement of chemistry application. The full quantum eigensolver can be implemented on a near-term quantum computer. With the rapid development of quantum computing hardware, the FQE provides an efficient and powerful tool to solve quantum chemistry problems.
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Affiliation(s)
- Shijie Wei
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China.,State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
| | - Hang Li
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
| | - GuiLu Long
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China.,State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China.,Beijing National Research Center for Information Science and Technology and School of Information Tsinghua University, Beijing 100084, China.,Frontier Science Center for Quantum Information, Beijing 100084, China
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17
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Matsuzawa Y, Kurashige Y. Jastrow-type Decomposition in Quantum Chemistry for Low-Depth Quantum Circuits. J Chem Theory Comput 2020; 16:944-952. [DOI: 10.1021/acs.jctc.9b00963] [Citation(s) in RCA: 33] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Yuta Matsuzawa
- 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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18
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Cao Y, Romero J, Olson JP, Degroote M, Johnson PD, Kieferová M, Kivlichan ID, Menke T, Peropadre B, Sawaya NPD, Sim S, Veis L, Aspuru-Guzik A. Quantum Chemistry in the Age of Quantum Computing. Chem Rev 2019; 119:10856-10915. [PMID: 31469277 DOI: 10.1021/acs.chemrev.8b00803] [Citation(s) in RCA: 273] [Impact Index Per Article: 54.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
Abstract
Practical challenges in simulating quantum systems on classical computers have been widely recognized in the quantum physics and quantum chemistry communities over the past century. Although many approximation methods have been introduced, the complexity of quantum mechanics remains hard to appease. The advent of quantum computation brings new pathways to navigate this challenging and complex landscape. By manipulating quantum states of matter and taking advantage of their unique features such as superposition and entanglement, quantum computers promise to efficiently deliver accurate results for many important problems in quantum chemistry, such as the electronic structure of molecules. In the past two decades, significant advances have been made in developing algorithms and physical hardware for quantum computing, heralding a revolution in simulation of quantum systems. This Review provides an overview of the algorithms and results that are relevant for quantum chemistry. The intended audience is both quantum chemists who seek to learn more about quantum computing and quantum computing researchers who would like to explore applications in quantum chemistry.
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Affiliation(s)
- Yudong Cao
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Jonathan Romero
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Jonathan P Olson
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Matthias Degroote
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Department of Chemistry , University of Toronto , Toronto , Ontario M5G 1Z8 , Canada.,Department of Computer Science , University of Toronto , Toronto , Ontario M5G 1Z8 , Canada
| | - Peter D Johnson
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Mária Kieferová
- Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States.,Department of Physics and Astronomy , Macquarie University , Sydney , NSW 2109 , Australia.,Institute for Quantum Computing and Department of Physics and Astronomy , University of Waterloo , Waterloo , Ontario N2L 3G1 , Canada
| | - Ian D Kivlichan
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Department of Physics , Harvard University , Cambridge , Massachusetts 02138 , United States
| | - Tim Menke
- Department of Physics , Harvard University , Cambridge , Massachusetts 02138 , United States.,Research Laboratory of Electronics , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States.,Department of Physics , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States
| | - Borja Peropadre
- Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Nicolas P D Sawaya
- Intel Laboratories , Intel Corporation , Santa Clara , California 95054 United States
| | - Sukin Sim
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Libor Veis
- J. Heyrovský Institute of Physical Chemistry , Academy of Sciences of the Czech Republic v.v.i. , Doleǰskova 3 , 18223 Prague 8, Czech Republic
| | - Alán Aspuru-Guzik
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States.,Department of Chemistry , University of Toronto , Toronto , Ontario M5G 1Z8 , Canada.,Department of Computer Science , University of Toronto , Toronto , Ontario M5G 1Z8 , Canada.,Canadian Institute for Advanced Research , Toronto , Ontario M5G 1Z8 , Canada.,Vector Institute for Artificial Intelligence , Toronto , Ontario M5S 1M1 , Canada
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19
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McArdle S, Mayorov A, Shan X, Benjamin S, Yuan X. Digital quantum simulation of molecular vibrations. Chem Sci 2019; 10:5725-5735. [PMID: 31293758 PMCID: PMC6568047 DOI: 10.1039/c9sc01313j] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2019] [Accepted: 04/23/2019] [Indexed: 01/30/2023] Open
Abstract
Molecular vibrations underpin important phenomena such as spectral properties, energy transfer, and molecular bonding. However, obtaining a detailed understanding of the vibrational structure of even small molecules is computationally expensive. While several algorithms exist for efficiently solving the electronic structure problem on a quantum computer, there has been comparatively little attention devoted to solving the vibrational structure problem with quantum hardware. In this work, we discuss the use of quantum algorithms for investigating both the static and dynamic vibrational properties of molecules. We introduce a physically motivated unitary vibrational coupled cluster ansatz, which also makes our method accessible to noisy, near-term quantum hardware. We numerically test our proposals for the water and sulfur dioxide molecules.
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Affiliation(s)
- Sam McArdle
- Department of Materials , University of Oxford , Parks Road , Oxford OX1 3PH , UK .
| | - Alexander Mayorov
- Department of Materials , University of Oxford , Parks Road , Oxford OX1 3PH , UK .
- Department of Chemistry , University of Cambridge , Lensfield Road , Cambridge CB2 1EW , UK
| | - Xiao Shan
- Physical and Theoretical Chemical Laboratory , University of Oxford , South Parks Road , Oxford OX1 3QZ , UK
| | - Simon Benjamin
- Department of Materials , University of Oxford , Parks Road , Oxford OX1 3PH , UK .
| | - Xiao Yuan
- Department of Materials , University of Oxford , Parks Road , Oxford OX1 3PH , UK .
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20
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Li Y, Hu J, Zhang X, Song Z, Yung M. Variational Quantum Simulation for Quantum Chemistry. ADVANCED THEORY AND SIMULATIONS 2019. [DOI: 10.1002/adts.201800182] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Affiliation(s)
- Yifan Li
- Shenzhen Institute for Quantum Science and Engineering and Department of PhysicsSouthern University of Science and TechnologyShenzhen 518055 China
| | - Jiaqi Hu
- Shenzhen Institute for Quantum Science and Engineering and Department of PhysicsSouthern University of Science and TechnologyShenzhen 518055 China
| | - Xiao‐Ming Zhang
- Shenzhen Institute for Quantum Science and Engineering and Department of PhysicsSouthern University of Science and TechnologyShenzhen 518055 China
- Department of PhysicsCity University of Hong KongTat Chee Avenue Kowloon Hong Kong SAR 999077 China
| | - Zhigang Song
- Shenzhen Institute for Quantum Science and Engineering and Department of PhysicsSouthern University of Science and TechnologyShenzhen 518055 China
- Department of EngineeringUniversity of CambridgeJJ Thomson Avenue CB3 0FA Cambridge United Kingdom
| | - Man‐Hong Yung
- Shenzhen Institute for Quantum Science and Engineering and Department of PhysicsSouthern University of Science and TechnologyShenzhen 518055 China
- Shenzhen Key Laboratory of Quantum Science and EngineeringSouthern University of Science and TechnologyShenzhen 518055 China
- Central Research InstituteHuawei TechnologiesShenzhen 518129 China
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21
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Sugisaki K, Nakazawa S, Toyota K, Sato K, Shiomi D, Takui T. Quantum Chemistry on Quantum Computers: A Method for Preparation of Multiconfigurational Wave Functions on Quantum Computers without Performing Post-Hartree-Fock Calculations. ACS CENTRAL SCIENCE 2019; 5:167-175. [PMID: 30693335 PMCID: PMC6346626 DOI: 10.1021/acscentsci.8b00788] [Citation(s) in RCA: 28] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/29/2018] [Indexed: 06/09/2023]
Abstract
The full configuration interaction (full-CI) method is capable of providing the numerically best wave functions and energies of atoms and molecules within basis sets being used, although it is intractable for classical computers. Quantum computers can perform full-CI calculations in polynomial time against the system size by adopting a quantum phase estimation algorithm (QPEA). In the QPEA, the preparation of initial guess wave functions having sufficiently large overlap with the exact wave function is recommended. The Hartree-Fock (HF) wave function is a good initial guess only for closed shell singlet molecules and high-spin molecules carrying no spin-β unpaired electrons, around their equilibrium geometry, and thus, the construction of multiconfigurational wave functions without performing post-HF calculations on classical computers is highly desired for applying the method to a wide variety of chemistries and physics. In this work, we propose a method to construct multiconfigurational initial guess wave functions suitable for QPEA-based full-CI calculations on quantum computers, by utilizing diradical characters computed from spin-projected UHF wave functions. The proposed approach drastically improves the wave function overlap, particularly in molecules with intermediate diradical characters.
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Affiliation(s)
- Kenji Sugisaki
- Department
of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
| | - Shigeaki Nakazawa
- Department
of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
| | - Kazuo Toyota
- Department
of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
| | - Kazunobu Sato
- Department
of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
| | - Daisuke Shiomi
- Department
of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
| | - Takeji Takui
- Department
of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
- Research
Support Department/University Research Administrator Center, University
Administration Division, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
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22
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Open shell electronic state calculations on quantum computers: A quantum circuit for the preparation of configuration state functions based on Serber construction. Chem Phys Lett 2019. [DOI: 10.1016/j.cpletx.2018.100002] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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23
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Barren plateaus in quantum neural network training landscapes. Nat Commun 2018; 9:4812. [PMID: 30446662 PMCID: PMC6240101 DOI: 10.1038/s41467-018-07090-4] [Citation(s) in RCA: 138] [Impact Index Per Article: 23.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2018] [Accepted: 10/09/2018] [Indexed: 11/09/2022] Open
Abstract
Many experimental proposals for noisy intermediate scale quantum devices involve training a parameterized quantum circuit with a classical optimization loop. Such hybrid quantum-classical algorithms are popular for applications in quantum simulation, optimization, and machine learning. Due to its simplicity and hardware efficiency, random circuits are often proposed as initial guesses for exploring the space of quantum states. We show that the exponential dimension of Hilbert space and the gradient estimation complexity make this choice unsuitable for hybrid quantum-classical algorithms run on more than a few qubits. Specifically, we show that for a wide class of reasonable parameterized quantum circuits, the probability that the gradient along any reasonable direction is non-zero to some fixed precision is exponentially small as a function of the number of qubits. We argue that this is related to the 2-design characteristic of random circuits, and that solutions to this problem must be studied.
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24
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Tranter A, Love PJ, Mintert F, Coveney PV. A Comparison of the Bravyi-Kitaev and Jordan-Wigner Transformations for the Quantum Simulation of Quantum Chemistry. J Chem Theory Comput 2018; 14:5617-5630. [PMID: 30189144 PMCID: PMC6236472 DOI: 10.1021/acs.jctc.8b00450] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2018] [Indexed: 11/29/2022]
Abstract
The ability to perform classically intractable electronic structure calculations is often cited as one of the principal applications of quantum computing. A great deal of theoretical algorithmic development has been performed in support of this goal. Most techniques require a scheme for mapping electronic states and operations to states of and operations upon qubits. The two most commonly used techniques for this are the Jordan-Wigner transformation and the Bravyi-Kitaev transformation. However, comparisons of these schemes have previously been limited to individual small molecules. In this paper, we discuss resource implications for the use of the Bravyi-Kitaev mapping scheme, specifically with regard to the number of quantum gates required for simulation. We consider both small systems, which may be simulatable on near-future quantum devices, and systems sufficiently large for classical simulation to be intractable. We use 86 molecular systems to demonstrate that the use of the Bravyi-Kitaev transformation is typically at least approximately as efficient as the canonical Jordan-Wigner transformation and results in substantially reduced gate count estimates when performing limited circuit optimizations.
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Affiliation(s)
- Andrew Tranter
- Department
of Physics, Imperial College London, London SW7 2AZ, United Kingdom
| | - Peter J. Love
- Department
of Physics, Tufts University, Medford, Massachusetts 02155, United States
| | - Florian Mintert
- Department
of Physics, Imperial College London, London SW7 2AZ, United Kingdom
| | - Peter V. Coveney
- Centre
for Computational Science, University College
London, London WC1H 0AJ, United Kingdom
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25
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Wendin G. Quantum information processing with superconducting circuits: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2017; 80:106001. [PMID: 28682303 DOI: 10.1088/1361-6633/aa7e1a] [Citation(s) in RCA: 107] [Impact Index Per Article: 15.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
During the last ten years, superconducting circuits have passed from being interesting physical devices to becoming contenders for near-future useful and scalable quantum information processing (QIP). Advanced quantum simulation experiments have been shown with up to nine qubits, while a demonstration of quantum supremacy with fifty qubits is anticipated in just a few years. Quantum supremacy means that the quantum system can no longer be simulated by the most powerful classical supercomputers. Integrated classical-quantum computing systems are already emerging that can be used for software development and experimentation, even via web interfaces. Therefore, the time is ripe for describing some of the recent development of superconducting devices, systems and applications. As such, the discussion of superconducting qubits and circuits is limited to devices that are proven useful for current or near future applications. Consequently, the centre of interest is the practical applications of QIP, such as computation and simulation in Physics and Chemistry.
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Affiliation(s)
- G Wendin
- Department of Microtechnology and Nanoscience-MC2, Chalmers University of Technology, SE-41296 Gothenburg, Sweden
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26
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Programming languages and compiler design for realistic quantum hardware. Nature 2017; 549:180-187. [DOI: 10.1038/nature23459] [Citation(s) in RCA: 98] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2017] [Accepted: 06/04/2017] [Indexed: 11/08/2022]
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27
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Reiher M, Wiebe N, Svore KM, Wecker D, Troyer M. Elucidating reaction mechanisms on quantum computers. Proc Natl Acad Sci U S A 2017; 114:7555-7560. [PMID: 28674011 PMCID: PMC5530650 DOI: 10.1073/pnas.1619152114] [Citation(s) in RCA: 119] [Impact Index Per Article: 17.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023] Open
Abstract
With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources.
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Affiliation(s)
- Markus Reiher
- Laboratorium für Physikalische Chemie, ETH Zurich, 8093 Zurich, Switzerland
| | - Nathan Wiebe
- Station Q Quantum Architectures and Computation Group, Microsoft Research, Redmond, WA 98052
| | - Krysta M Svore
- Station Q Quantum Architectures and Computation Group, Microsoft Research, Redmond, WA 98052
| | - Dave Wecker
- Station Q Quantum Architectures and Computation Group, Microsoft Research, Redmond, WA 98052
| | - Matthias Troyer
- Station Q Quantum Architectures and Computation Group, Microsoft Research, Redmond, WA 98052;
- Theoretische Physik and Station Q Zurich, ETH Zurich, 8093 Zurich, Switzerland
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28
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Sugisaki K, Yamamoto S, Nakazawa S, Toyota K, Sato K, Shiomi D, Takui T. Quantum Chemistry on Quantum Computers: A Polynomial-Time Quantum Algorithm for Constructing the Wave Functions of Open-Shell Molecules. J Phys Chem A 2016; 120:6459-66. [DOI: 10.1021/acs.jpca.6b04932] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Kenji Sugisaki
- Department of Chemistry and
Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
| | - Satoru Yamamoto
- Department of Chemistry and
Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
| | - Shigeaki Nakazawa
- Department of Chemistry and
Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
| | - Kazuo Toyota
- Department of Chemistry and
Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
| | - Kazunobu Sato
- Department of Chemistry and
Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
| | - Daisuke Shiomi
- Department of Chemistry and
Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
| | - Takeji Takui
- Department of Chemistry and
Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
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29
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Wiebe N, Granade C. Efficient Bayesian Phase Estimation. PHYSICAL REVIEW LETTERS 2016; 117:010503. [PMID: 27419551 DOI: 10.1103/physrevlett.117.010503] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/08/2015] [Indexed: 06/06/2023]
Abstract
We introduce a new method called rejection filtering that we use to perform adaptive Bayesian phase estimation. Our approach has several advantages: it is classically efficient, easy to implement, achieves Heisenberg limited scaling, resists depolarizing noise, tracks time-dependent eigenstates, recovers from failures, and can be run on a field programmable gate array. It also outperforms existing iterative phase estimation algorithms such as Kitaev's method.
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Affiliation(s)
- Nathan Wiebe
- Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052, USA
| | - Chris Granade
- Centre for Engineered Quantum Systems, Sydney, New South Wales 2006, Australia
- School of Physics, University of Sydney, Sydney, New South Wales 2006, Australia
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30
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Sawaya NPD, Smelyanskiy M, McClean JR, Aspuru-Guzik A. Error Sensitivity to Environmental Noise in Quantum Circuits for Chemical State Preparation. J Chem Theory Comput 2016; 12:3097-108. [PMID: 27254482 DOI: 10.1021/acs.jctc.6b00220] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Calculating molecular energies is likely to be one of the first useful applications to achieve quantum supremacy, performing faster on a quantum than a classical computer. However, if future quantum devices are to produce accurate calculations, errors due to environmental noise and algorithmic approximations need to be characterized and reduced. In this study, we use the high performance qHiPSTER software to investigate the effects of environmental noise on the preparation of quantum chemistry states. We simulated 18 16-qubit quantum circuits under environmental noise, each corresponding to a unitary coupled cluster state preparation of a different molecule or molecular configuration. Additionally, we analyze the nature of simple gate errors in noise-free circuits of up to 40 qubits. We find that, in most cases, the Jordan-Wigner (JW) encoding produces smaller errors under a noisy environment as compared to the Bravyi-Kitaev (BK) encoding. For the JW encoding, pure dephasing noise is shown to produce substantially smaller errors than pure relaxation noise of the same magnitude. We report error trends in both molecular energy and electron particle number within a unitary coupled cluster state preparation scheme, against changes in nuclear charge, bond length, number of electrons, noise types, and noise magnitude. These trends may prove to be useful in making algorithmic and hardware-related choices for quantum simulation of molecular energies.
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Affiliation(s)
- Nicolas P D Sawaya
- Department of Chemistry and Chemical Biology, Harvard University , Cambridge, Massachusetts 02138, United States.,Parallel Computing Lab, Intel Corporation , Santa Clara, California 95054, United States
| | - Mikhail Smelyanskiy
- Parallel Computing Lab, Intel Corporation , Santa Clara, California 95054, United States
| | - Jarrod R McClean
- Computational Research Division, Lawrence Berkeley National Laboratory , Berkeley, California 94720, United States
| | - Alán Aspuru-Guzik
- Department of Chemistry and Chemical Biology, Harvard University , Cambridge, Massachusetts 02138, United States
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31
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32
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33
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Wang L, Prezhdo OV. Accurate and Efficient Quantum Chemistry by Locality of Chemical Interactions. J Phys Chem Lett 2014; 5:4317-4318. [PMID: 26273980 DOI: 10.1021/jz5024256] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Affiliation(s)
- Linjun Wang
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States
| | - Oleg V Prezhdo
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States
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34
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Babbush R, Love PJ, Aspuru-Guzik A. Adiabatic quantum simulation of quantum chemistry. Sci Rep 2014; 4:6603. [PMID: 25308187 PMCID: PMC4194464 DOI: 10.1038/srep06603] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2014] [Accepted: 09/22/2014] [Indexed: 11/09/2022] Open
Abstract
We show how to apply the quantum adiabatic algorithm directly to the quantum computation of molecular properties. We describe a procedure to map electronic structure Hamiltonians to 2-body qubit Hamiltonians with a small set of physically realizable couplings. By combining the Bravyi-Kitaev construction to map fermions to qubits with perturbative gadgets to reduce the Hamiltonian to 2-body, we obtain precision requirements on the coupling strengths and a number of ancilla qubits that scale polynomially in the problem size. Hence our mapping is efficient. The required set of controllable interactions includes only two types of interaction beyond the Ising interactions required to apply the quantum adiabatic algorithm to combinatorial optimization problems. Our mapping may also be of interest to chemists directly as it defines a dictionary from electronic structure to spin Hamiltonians with physical interactions.
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Affiliation(s)
- Ryan Babbush
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138 USA
| | - Peter J. Love
- Department of Physics, Haverford College, Haverford, PA 19041, USA
| | - Alán Aspuru-Guzik
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138 USA
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