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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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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3
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Prasad VK, Cheng F, Fekl U, Jacobsen HA. Applications of noisy quantum computing and quantum error mitigation to "adamantaneland": a benchmarking study for quantum chemistry. Phys Chem Chem Phys 2024; 26:4071-4082. [PMID: 38225897 DOI: 10.1039/d3cp03523a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2024]
Abstract
The field of quantum computing has the potential to transform quantum chemistry. The variational quantum eigensolver (VQE) algorithm has allowed quantum computing to be applied to chemical problems in the noisy intermediate-scale quantum (NISQ) era. Applications of VQE have generally focused on predicting absolute energies instead of chemical properties that are relative energy differences and that are most interesting to chemists studying a chemical problem. We address this shortcoming by constructing a molecular benchmark data set in this work containing isomers of C10H16 and carbocationic rearrangements of C10H15+, calculated at a high-level of theory. Using the data set, we compared noiseless VQE simulations to conventionally performed density functional and wavefunction theory-based methods to understand the quality of results. We also investigated the effectiveness of a quantum state tomography-based error mitigation technique in applications of VQE under noise (simulated and real). Our findings reveal that the use of quantum error mitigation is crucial in the NISQ era and advantageous to yield almost noiseless quality results.
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Affiliation(s)
- Viki Kumar Prasad
- The Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, 10 Kings College Road, Toronto, Ontario, Canada, M5S 3G4. arno,
- Department of Chemical and Physical Sciences, University of Toronto Mississauga, 3359 Mississauga Road, Mississauga, Ontario, Canada, L5L 1C6.
| | - Freeman Cheng
- Department of Computer Science, University of Toronto, 40 St. George Street, Toronto, Ontario, Canada, M5S 2E4
| | - Ulrich Fekl
- Department of Chemical and Physical Sciences, University of Toronto Mississauga, 3359 Mississauga Road, Mississauga, Ontario, Canada, L5L 1C6.
| | - Hans-Arno Jacobsen
- The Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, 10 Kings College Road, Toronto, Ontario, Canada, M5S 3G4. arno,
- Department of Computer Science, University of Toronto, 40 St. George Street, Toronto, Ontario, Canada, M5S 2E4
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4
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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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5
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Evangelista FA, Batista VS. Editorial: Quantum Computing for Chemistry. J Chem Theory Comput 2023; 19:7435-7436. [PMID: 37961754 DOI: 10.1021/acs.jctc.3c01043] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2023]
Affiliation(s)
- Francesco A Evangelista
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
| | - Victor S Batista
- Department of Chemistry, Yale University, New Haven, Connecticut 06520-8107, United States
- Yale Quantum Institute, Yale University, New Haven, Connecticut 06520-8263, United States
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6
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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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7
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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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8
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Ghasempouri SE, Dueck GW, De Baerdemacker S. Modular Cluster Circuits for the Variational Quantum Eigensolver. J Phys Chem A 2023; 127:8168-8178. [PMID: 37729640 DOI: 10.1021/acs.jpca.3c03015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/22/2023]
Abstract
The variational quantum eigensolver algorithm recently became a popular method to compute the quantum chemical properties of molecules on noisy intermediate scale quantum (NISQ) devices. In order to avoid noise accumulation from the NISQ device in the quantum circuit, it is important to keep the so-called quantum depth of the circuit at a minimum, defined as the minimum number of quantum gates that must be operated sequentially. In the present work, we introduce a modular 2-qubit cluster circuit that allows for the design of a shallow-depth quantum circuit compared to previously proposed architectures without loss of chemical accuracy. Moreover, by virtue of the simplicity of the cluster circuit, it is possible to assign a valence bond chemical interpretation to the cluster circuit. The design was tested on the H2, (H2)2, and LiH molecules, as well as the finite-size transverse-field Ising model, as the latter provides additional insights into the construction of the circuit in a resonating valence bond picture.
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Affiliation(s)
- Seyed Ehsan Ghasempouri
- Department of Chemistry, University of New Brunswick, 30 Dineen Dr,Fredericton, New Brunswick E3B 5A3, Canada
| | - Gerhard W Dueck
- Faculty of Computer Science, University of New Brunswick, 550 Windsor Street, Fredericton, New Brunswick E3B 5A3, Canada
| | - Stijn De Baerdemacker
- Department of Chemistry, University of New Brunswick, 30 Dineen Dr,Fredericton, New Brunswick E3B 5A3, Canada
- Department of Mathematics and Statistics, University of New Brunswick, P.O. Box 4400, Fredericton, New Brunswick E3B 5A3, Canada
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9
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Kovalsky LK, Calderon-Vargas FA, Grace MD, Magann AB, Larsen JB, Baczewski AD, Sarovar M. Self-Healing of Trotter Error in Digital Adiabatic State Preparation. PHYSICAL REVIEW LETTERS 2023; 131:060602. [PMID: 37625062 DOI: 10.1103/physrevlett.131.060602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/02/2022] [Revised: 04/18/2023] [Accepted: 06/29/2023] [Indexed: 08/27/2023]
Abstract
Adiabatic time evolution can be used to prepare a complicated quantum many-body state from one that is easier to synthesize and Trotterization can be used to implement such an evolution digitally. The complex interplay between nonadiabaticity and digitization influences the infidelity of this process. We prove that the first-order Trotterization of a complete adiabatic evolution has a cumulative infidelity that scales as O(T^{-2}δt^{2}) instead of O(T^{2}δt^{2}) expected from general Trotter error bounds, where δt is the time step and T is the total time. This result suggests a self-healing mechanism and explains why, despite increasing T, infidelities for fixed-δt digitized evolutions still decrease for a wide variety of Hamiltonians. It also establishes a correspondence between the quantum approximate optimization algorithm and digitized quantum annealing.
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Affiliation(s)
- Lucas K Kovalsky
- Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Livermore, California 94550, USA
| | - Fernando A Calderon-Vargas
- Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Livermore, California 94550, USA
| | - Matthew D Grace
- Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Livermore, California 94550, USA
| | - Alicia B Magann
- Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - James B Larsen
- Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
- Department of Mathematics, Brigham Young University, Provo, Utah 84602, USA
| | - Andrew D Baczewski
- Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Mohan Sarovar
- Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Livermore, California 94550, USA
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10
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Liu Y, Meitei OR, Chin ZE, Dutt A, Tao M, Chuang IL, Van Voorhis T. Bootstrap Embedding on a Quantum Computer. J Chem Theory Comput 2023; 19:2230-2247. [PMID: 37001026 DOI: 10.1021/acs.jctc.3c00012] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/03/2023]
Abstract
We extend molecular bootstrap embedding to make it appropriate for implementation on a quantum computer. This enables solution of the electronic structure problem of a large molecule as an optimization problem for a composite Lagrangian governing fragments of the total system, in such a way that fragment solutions can harness the capabilities of quantum computers. By employing state-of-art quantum subroutines including the quantum SWAP test and quantum amplitude amplification, we show how a quadratic speedup can be obtained over the classical algorithm, in principle. Utilization of quantum computation also allows the algorithm to match─at little additional computational cost─full density matrices at fragment boundaries, instead of being limited to 1-RDMs. Current quantum computers are small, but quantum bootstrap embedding provides a potentially generalizable strategy for harnessing such small machines through quantum fragment matching.
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Affiliation(s)
- Yuan Liu
- Department of Physics, Co-Design Center for Quantum Advantage, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Oinam R. Meitei
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Zachary E. Chin
- Department of Physics, Co-Design Center for Quantum Advantage, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Arkopal Dutt
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Max Tao
- Department of Physics, Co-Design Center for Quantum Advantage, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Isaac L. Chuang
- Department of Physics, Co-Design Center for Quantum Advantage, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Troy Van Voorhis
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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11
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Iouchtchenko D, Gonthier JF, Perdomo-Ortiz A, Melko RG. Neural network enhanced measurement efficiency for molecular groundstates. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2023. [DOI: 10.1088/2632-2153/acb4df] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/11/2023] Open
Abstract
Abstract
It is believed that one of the first useful applications for a quantum computer will be the preparation of groundstates of molecular Hamiltonians. A crucial task involving state preparation and readout is obtaining physical observables of such states, which are typically estimated using projective measurements on the qubits. At present, measurement data is costly and time-consuming to obtain on any quantum computing architecture, which has significant consequences for the statistical errors of estimators. In this paper, we adapt common neural network models (restricted Boltzmann machines and recurrent neural networks) to learn complex groundstate wavefunctions for several prototypical molecular qubit Hamiltonians from typical measurement data. By relating the accuracy ɛ of the reconstructed groundstate energy to the number of measurements, we find that using a neural network model provides a robust improvement over using single-copy measurement outcomes alone to reconstruct observables. This enhancement yields an asymptotic scaling near ɛ
−1 for the model-based approaches, as opposed to ɛ
−2 in the case of classical shadow tomography.
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12
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Choy B, Wales DJ. Molecular Energy Landscapes of Hardware-Efficient Ansätze in Quantum Computing. J Chem Theory Comput 2023; 19:1197-1206. [PMID: 36749922 PMCID: PMC9979602 DOI: 10.1021/acs.jctc.2c01057] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/09/2023]
Abstract
Rapid advances in quantum computing have opened up new opportunities for solving the central electronic structure problem in computational chemistry. In the noisy intermediate-scale quantum (NISQ) era, where qubit coherence times are limited, it is essential to exploit quantum algorithms with sufficiently short quantum circuits to maximize qubit efficiency. The procedural construction of hardware-efficient ansätze provides one approach to design such circuits. However, refining the accuracy of the global minimum by increasing circuit depth may lead to a proliferation of local minima that hinders global optimization. To investigate this phenomenon, we explore the energy landscapes of hardware-efficient circuits to identify ground-state energies of the hydrogen, lithium hydride, and beryllium hydride molecules. We also propose a simple dimensionality reduction procedure that reduces quantum gate depth while retaining high accuracy for the global minimum, simplifying the energy landscape, and hence speeding up optimization from both software and hardware perspectives.
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Affiliation(s)
- Boy Choy
- School
of Chemistry, Chemical Engineering and Biotechnology, Nanyang Technological University, Block N1.2, B3-13, 62 Nanyang Drive, Singapore 637459,
| | - David J. Wales
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Lensfield
Road, Cambridge CB2 1EW, United Kingdom
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13
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Izsák R, Riplinger C, Blunt NS, de Souza B, Holzmann N, Crawford O, Camps J, Neese F, Schopf P. Quantum computing in pharma: A multilayer embedding approach for near future applications. J Comput Chem 2023; 44:406-421. [PMID: 35789492 DOI: 10.1002/jcc.26958] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2022] [Revised: 06/09/2022] [Accepted: 06/10/2022] [Indexed: 01/03/2023]
Abstract
Quantum computers are special purpose machines that are expected to be particularly useful in simulating strongly correlated chemical systems. The quantum computer excels at treating a moderate number of orbitals within an active space in a fully quantum mechanical manner. We present a quantum phase estimation calculation on F2 in a (2,2) active space on Rigetti's Aspen-11 QPU. While this is a promising start, it also underlines the need for carefully selecting the orbital spaces treated by the quantum computer. In this work, a scheme for selecting such an active space automatically is described and simulated results obtained using both the quantum phase estimation (QPE) and variational quantum eigensolver (VQE) algorithms are presented and combined with a subtractive method to enable accurate description of the environment. The active occupied space is selected from orbitals localized on the chemically relevant fragment of the molecule, while the corresponding virtual space is chosen based on the magnitude of interactions with the occupied space calculated from perturbation theory. This protocol is then applied to two chemical systems of pharmaceutical relevance: the enzyme [Fe] hydrogenase and the photosenzitizer temoporfin. While the sizes of the active spaces currently amenable to a quantum computational treatment are not enough to demonstrate quantum advantage, the procedure outlined here is applicable to any active space size, including those that are outside the reach of classical computation.
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Affiliation(s)
| | | | | | | | - Nicole Holzmann
- Riverlane Research Ltd, Cambridge, UK.,Astex Pharmaceuticals, Cambridge, UK
| | | | | | - Frank Neese
- Max-Planck Institut für Kohlenforschung, Mülheim an der Ruhr, Germany
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14
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Blunt NS, Camps J, Crawford O, Izsák R, Leontica S, Mirani A, Moylett AE, Scivier SA, Sünderhauf C, Schopf P, Taylor JM, Holzmann N. Perspective on the Current State-of-the-Art of Quantum Computing for Drug Discovery Applications. J Chem Theory Comput 2022; 18:7001-7023. [PMID: 36355616 DOI: 10.1021/acs.jctc.2c00574] [Citation(s) in RCA: 20] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
Computational chemistry is an essential tool in the pharmaceutical industry. Quantum computing is a fast evolving technology that promises to completely shift the computational capabilities in many areas of chemical research by bringing into reach currently impossible calculations. This perspective illustrates the near-future applicability of quantum computation of molecules to pharmaceutical problems. We briefly summarize and compare the scaling properties of state-of-the-art quantum algorithms and provide novel estimates of the quantum computational cost of simulating progressively larger embedding regions of a pharmaceutically relevant covalent protein-drug complex involving the drug Ibrutinib. Carrying out these calculations requires an error-corrected quantum architecture that we describe. Our estimates showcase that recent developments on quantum phase estimation algorithms have dramatically reduced the quantum resources needed to run fully quantum calculations in active spaces of around 50 orbitals and electrons, from estimated over 1000 years using the Trotterization approach to just a few days with sparse qubitization, painting a picture of fast and exciting progress in this nascent field.
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Affiliation(s)
- Nick S Blunt
- Riverlane, St. Andrews House, 59 St. Andrews Street, Cambridge CB2 3BZ, United Kingdom
| | - Joan Camps
- Riverlane, St. Andrews House, 59 St. Andrews Street, Cambridge CB2 3BZ, United Kingdom
| | - Ophelia Crawford
- Riverlane, St. Andrews House, 59 St. Andrews Street, Cambridge CB2 3BZ, United Kingdom
| | - Róbert Izsák
- Riverlane, St. Andrews House, 59 St. Andrews Street, Cambridge CB2 3BZ, United Kingdom
| | - Sebastian Leontica
- Riverlane, St. Andrews House, 59 St. Andrews Street, Cambridge CB2 3BZ, United Kingdom
| | - Arjun Mirani
- Riverlane, St. Andrews House, 59 St. Andrews Street, Cambridge CB2 3BZ, United Kingdom
| | - Alexandra E Moylett
- Riverlane, St. Andrews House, 59 St. Andrews Street, Cambridge CB2 3BZ, United Kingdom
| | - Sam A Scivier
- Riverlane, St. Andrews House, 59 St. Andrews Street, Cambridge CB2 3BZ, United Kingdom
| | - Christoph Sünderhauf
- Riverlane, St. Andrews House, 59 St. Andrews Street, Cambridge CB2 3BZ, United Kingdom
| | - Patrick Schopf
- Astex Pharmaceuticals, 436 Cambridge Science Park, Cambridge CB4 0QA, United Kingdom
| | - Jacob M Taylor
- Riverlane, St. Andrews House, 59 St. Andrews Street, Cambridge CB2 3BZ, United Kingdom
| | - Nicole Holzmann
- Riverlane, St. Andrews House, 59 St. Andrews Street, Cambridge CB2 3BZ, United Kingdom.,Astex Pharmaceuticals, 436 Cambridge Science Park, Cambridge CB4 0QA, United Kingdom
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15
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Langkabel F, Bande A. Quantum-Compute Algorithm for Exact Laser-Driven Electron Dynamics in Molecules. J Chem Theory Comput 2022; 18:7082-7092. [PMID: 36399652 DOI: 10.1021/acs.jctc.2c00878] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Abstract
In this work, we investigate the capability of known quantum computing algorithms for fault-tolerant quantum computing to simulate the laser-driven electron dynamics of excitation and ionization processes in small molecules such as lithium hydride, which can be benchmarked against the most accurate time-dependent full configuration interaction (TD-FCI) calculations. The conventional TD-FCI wave packet propagation is reproduced using the Jordan-Wigner transformation for wave function and operators and the Trotter product formula for expressing the propagator. In addition, the time-dependent dipole moment, as an example of a time-dependent expectation value, is calculated using the Hadamard test. To include non-Hermitian operators in the ionization dynamics, a similar approach to the quantum imaginary time evolution (QITE) algorithm is employed to translate the propagator, including a complex absorption potential, into quantum gates. The computations are executed on a quantum computer simulator. By construction, all quantum computer algorithms, except for the QITE algorithm used only for ionization but not for excitation dynamics, would scale polynomially on a quantum computer with fully entangled qubits. In contrast, TD-FCI scales exponentially. Hence, quantum computation holds promises for substantial progress in the understanding of electron dynamics of excitation processes in increasingly large molecular systems, as has already been witnessed in electronic structure theory.
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Affiliation(s)
- Fabian Langkabel
- Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Hahn-Meitner-Platz 1, 14109Berlin, Germany.,Institute of Chemistry and Biochemistry, Freie Universität Berlin, Arnimallee 22, 14195Berlin, Germany
| | - Annika Bande
- Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Hahn-Meitner-Platz 1, 14109Berlin, Germany
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16
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Exactly solving the Kitaev chain and generating Majorana-zero-modes out of noisy qubits. Sci Rep 2022; 12:19882. [DOI: 10.1038/s41598-022-24341-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2022] [Accepted: 11/14/2022] [Indexed: 11/19/2022] Open
Abstract
AbstractMajorana-zero-modes (MZMs) were predicted to exist as edge states of a physical system called the Kitaev chain. MZMs should host particles that are their own antiparticles and could be used as a basis for a qubit which is robust-to-noise. However, all attempts to prove their existence gave inconclusive results. Here, the Kitaev chain is exactly solved with a quantum computing methodology and properties of MZMs are probed by generating eigenstates of the Kitev Hamiltonian on 3 noisy qubits of a publicly available quantum computer. After an ontological elaboration I show that two eigenstates of the Kitaev Hamiltonian exhibit eight signatures attributed to MZMs. The results presented here are a most comprehensive set of validations of MZMs ever conducted in an actual physical system. Furthermore, the findings of this manuscript are easily reproducible for any user of publicly available quantum computers, solving another important problem of research with MZMs—the result reproducibility crisis.
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17
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Bansingh ZP, Yen TC, Johnson PD, Izmaylov AF. Fidelity Overhead for Nonlocal Measurements in Variational Quantum Algorithms. J Phys Chem A 2022; 126:7007-7012. [PMID: 36150139 DOI: 10.1021/acs.jpca.2c04726] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Measuring quantum observables by grouping terms that can be rotated to sums of only products of Pauli ẑ operators (Ising form) is proven to be efficient in near term quantum computing algorithms. This approach requires extra unitary transformations to rotate the state of interest so that the measurement of a fragment's Ising form would be equivalent to the measurement of the fragment for the unrotated state. These extra rotations allow one to perform a fewer number of measurements by grouping more terms into the measurable fragments with a lower overall estimator variance. However, previous estimations of the number of measurements did not take into account nonunit fidelity of quantum gates implementing the additional transformations. Through a circuit fidelity reduction, additional transformations introduce extra uncertainty and increase the needed number of measurements. Here we consider a simple model for errors introduced by additional gates needed in schemes involving groupings of commuting Pauli products. For a set of molecular electronic Hamiltonians, we confirm that the numbers of measurements in schemes using nonlocal qubit rotations are still lower than those in their local qubit rotation counterparts, even after accounting for uncertainties introduced by additional gates.
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Affiliation(s)
- Zachary Pierce Bansingh
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | - Tzu-Ching Yen
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | - Peter D Johnson
- Zapata Computing Inc., 100 Federal Street, Boston, Massachusetts 02110, United States
| | - Artur F Izmaylov
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada
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18
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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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19
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20
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Lim H, Jeon HN, Rhee JK, Oh B, No KT. Quantum computational study of chloride attack on chloromethane for chemical accuracy and quantum noise effects with UCCSD and k-UpCCGSD ansatzes. Sci Rep 2022; 12:7495. [PMID: 35523939 PMCID: PMC9076662 DOI: 10.1038/s41598-022-11537-6] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2022] [Accepted: 03/31/2022] [Indexed: 11/30/2022] Open
Abstract
Quantum computing is expected to play an important role in solving the problem of huge computational costs in various applications by utilizing the collective properties of quantum states, including superposition, interference, and entanglement, to perform computations. Quantum mechanical (QM) methods are candidates for various applications and can provide accurate absolute energy calculations in structure-based methods. QM methods are powerful tools for describing reaction pathways and their potential energy surfaces (PES). In this study, we applied quantum computing to describe the PES of the bimolecular nucleophilic substitution (SN2) reaction between chloromethane and chloride ions. We performed noiseless and noise simulations using quantum algorithms and compared the accuracy and noise effects of the ansatzes. In noiseless simulations, the results from UCCSD and k-UpCCGSD are similar to those of full configurational interaction (FCI) with the same active space, which indicates that quantum algorithms can describe the PES of the SN2 reaction. In noise simulations, UCCSD is more susceptible to quantum noise than k-UpCCGSD. Therefore, k-UpCCGSD can serve as an alternative to UCCSD to reduce quantum noisy effects in the noisy intermediate-scale quantum era, and k-UpCCGSD is sufficient to describe the PES of the SN2 reaction in this work. The results showed the applicability of quantum computing to the SN2 reaction pathway and provided valuable information for structure-based molecular simulations with quantum computing.
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Affiliation(s)
- Hocheol Lim
- The Interdisciplinary Graduate Program in Integrative Biotechnology and Translational Medicine, Yonsei University, Incheon, Republic of Korea.,Bioinformatics and Molecular Design Research Center (BMDRC), Incheon, Republic of Korea.,Department of Biotechnology, Yonsei University, Seoul, Republic of Korea
| | - Hyeon-Nae Jeon
- Department of Biotechnology, Yonsei University, Seoul, 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
- The Interdisciplinary Graduate Program in Integrative Biotechnology and Translational Medicine, Yonsei University, Incheon, Republic of Korea. .,Bioinformatics and Molecular Design Research Center (BMDRC), Incheon, Republic of Korea. .,Baobab AiBIO Co., Ltd., Incheon, Republic of Korea.
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21
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Sugisaki K, Kato T, Minato Y, Okuwaki K, Mochizuki Y. Variational quantum eigensolver simulations with the multireference unitary coupled cluster ansatz: a case study of the C2v quasi-reaction pathway of beryllium insertion to H 2 molecule. Phys Chem Chem Phys 2022; 24:8439-8452. [DOI: 10.1039/d1cp04318h] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Variational quantum eigensolver (VQE)-based quantum chemical calculations have been extensively studied as a computational model using noisy intermediate-scale quantum devices. VQE uses a parametrized quantum circuit defined through an “ansatz”...
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22
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Sajjan M, Sureshbabu SH, Kais S. Quantum Machine-Learning for Eigenstate Filtration in Two-Dimensional Materials. J Am Chem Soc 2021; 143:18426-18445. [PMID: 34705449 DOI: 10.1021/jacs.1c06246] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Quantum machine-learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure calculations of molecular systems and spin models in magnetic systems. However, the discussion in all these recipes focuses specifically on targeting the ground state. Herein we demonstrate a quantum algorithm that can filter any energy eigenstate of the system based on either symmetry properties or a predefined choice of the user. The workhorse of our technique is a shallow neural network encoding the desired state of the system with the amplitude computed by sampling the Gibbs-Boltzmann distribution using a quantum circuit and the phase information obtained classically from the nonlinear activation of a separate set of neurons. We show that the resource requirements of our algorithm are strictly quadratic. To demonstrate its efficacy, we use state filtration in monolayer transition metal dichalcogenides which are hitherto unexplored in any flavor of quantum simulations. We implement our algorithm not only on quantum simulators but also on actual IBM-Q quantum devices and show good agreement with the results procured from conventional electronic structure calculations. We thus expect our protocol to provide a new alternative in exploring the band structures of exquisite materials to usual electronic structure methods or machine-learning techniques that are implementable solely on a classical computer.
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Affiliation(s)
- Manas Sajjan
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
| | - Shree Hari Sureshbabu
- Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, United States
| | - Sabre Kais
- Department of Chemistry, Department of Physics and Astronomy, and Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, United States
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23
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Fan Y, Liu J, Li Z, Yang J. Equation-of-Motion Theory to Calculate Accurate Band Structures with a Quantum Computer. J Phys Chem Lett 2021; 12:8833-8840. [PMID: 34492184 DOI: 10.1021/acs.jpclett.1c02153] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Band structure is a cornerstone to understand the electronic properties of materials. Accurate band structure calculations using a high-level quantum chemistry theory can be computationally very expensive. It is promising to speed up such calculations with a quantum computer. In this study, we present a quantum algorithm for band structure calculations based on the equation-of-motion (EOM) theory. First, we introduce a new variational quantum eigensolver algorithm named ADAPT-C for ground-state quantum simulation of solids, where the wave function is built adaptively from a complete set of anti-Hermitian operators. Then, on top of the ADAPT-C ground state, quasiparticle energies and the band structure can be calculated using the EOM theory in a quantum-subspace-expansion style, where the projected excitation operators guarantee that the killer condition is satisfied. As a proof of principle, such an EOM-ADAPT-C protocol is used to calculate the band structures of silicon and diamond using a quantum computer simulator.
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Affiliation(s)
- Yi Fan
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jie Liu
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Zhenyu Li
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jinlong Yang
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
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24
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Wang DZ, Gauthier AQ, Siegmund AE, Hunt KLC. Bell inequalities for entangled qubits: quantitative tests of quantum character and nonlocality on quantum computers. Phys Chem Chem Phys 2021; 23:6370-6387. [PMID: 33538732 DOI: 10.1039/d0cp05444e] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
This work provides quantitative tests of the extent of violation of two inequalities applicable to qubits coupled into Bell states, using IBM's publicly accessible quantum computers. Violations of the inequalities are well established. Our purpose is not to test the inequalities, but rather to determine how well quantum mechanical predictions can be reproduced on quantum computers, given their current fault rates. We present results for the spin projections of two entangled qubits, along three axes A, B, and C, with a fixed angle θ between A and B and a range of angles θ' between B and C. For any classical object that can be characterized by three observables with two possible values, inequalities govern relationships among the probabilities of outcomes for the observables, taken pairwise. From set theory, these inequalities must be satisfied by all such classical objects; but quantum systems may violate the inequalities. We have detected clear-cut violations of one inequality in runs on IBM's publicly accessible quantum computers. The Clauser-Horne-Shimony-Holt (CHSH) inequality governs a linear combination S of expectation values of products of spin projections, taken pairwise. Finding S > 2 rules out local, hidden variable theories for entangled quantum systems. We obtained values of S greater than 2 in our runs prior to error mitigation. To reduce the quantitative errors, we used a modification of the error-mitigation procedure in the IBM documentation. We prepared a pair of qubits in the state |00〉, found the probabilities to observe the states |00〉, |01〉, |10〉, and |11〉 in multiple runs, and used that information to construct the first column of an error matrix M. We repeated this procedure for states prepared as |01〉, |10〉, and |11〉 to construct the full matrix M, whose inverse is the filtering matrix. After applying filtering matrices to our averaged outcomes, we have found good quantitative agreement between the quantum computer output and the quantum mechanical predictions for the extent of violation of both inequalities as functions of θ'.
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Affiliation(s)
- David Z Wang
- Department of Chemistry, Michigan State University, East Lansing, MI 48824, USA.
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25
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Cerezo M, Sone A, Volkoff T, Cincio L, Coles PJ. Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nat Commun 2021; 12:1791. [PMID: 33741913 PMCID: PMC7979934 DOI: 10.1038/s41467-021-21728-w] [Citation(s) in RCA: 60] [Impact Index Per Article: 20.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2020] [Accepted: 02/05/2021] [Indexed: 11/09/2022] Open
Abstract
Variational quantum algorithms (VQAs) optimize the parameters θ of a parametrized quantum circuit V(θ) to minimize a cost function C. While VQAs may enable practical applications of noisy quantum computers, they are nevertheless heuristic methods with unproven scaling. Here, we rigorously prove two results, assuming V(θ) is an alternating layered ansatz composed of blocks forming local 2-designs. Our first result states that defining C in terms of global observables leads to exponentially vanishing gradients (i.e., barren plateaus) even when V(θ) is shallow. Hence, several VQAs in the literature must revise their proposed costs. On the other hand, our second result states that defining C with local observables leads to at worst a polynomially vanishing gradient, so long as the depth of V(θ) is [Formula: see text]. Our results establish a connection between locality and trainability. We illustrate these ideas with large-scale simulations, up to 100 qubits, of a quantum autoencoder implementation.
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Affiliation(s)
- M Cerezo
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA.
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM, USA.
| | - Akira Sone
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM, USA
| | - Tyler Volkoff
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA
| | - Lukasz Cincio
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA
| | - Patrick J Coles
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA.
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26
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Kottmann JS, Anand A, Aspuru-Guzik A. A feasible approach for automatically differentiable unitary coupled-cluster on quantum computers. Chem Sci 2021; 12:3497-3508. [PMID: 34163623 PMCID: PMC8179519 DOI: 10.1039/d0sc06627c] [Citation(s) in RCA: 27] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2020] [Accepted: 01/07/2021] [Indexed: 01/10/2023] Open
Abstract
We develop computationally affordable and encoding independent gradient evaluation procedures for unitary coupled-cluster type operators, applicable on quantum computers. We show that, within our framework, the gradient of an expectation value with respect to a parameterized n-fold fermionic excitation can be evaluated by four expectation values of similar form and size, whereas most standard approaches, based on the direct application of the parameter-shift-rule, come with an associated cost of expectation values. For real wavefunctions, this cost can be further reduced to two expectation values. Our strategies are implemented within the open-source package Tequila and allow blackboard style construction of differentiable objective functions. We illustrate initial applications through extended adaptive approaches for electronic ground and excited states.
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Affiliation(s)
- Jakob S Kottmann
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto Toronto Ontario M5S 3H6 Canada
- Department of Computer Science, University of Toronto 214 College St Toronto ON M5T 3A1 Canada
| | - Abhinav Anand
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto Toronto Ontario M5S 3H6 Canada
| | - Alán Aspuru-Guzik
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto Toronto Ontario M5S 3H6 Canada
- Department of Computer Science, University of Toronto 214 College St Toronto ON M5T 3A1 Canada
- Vector Institute for Artificial Intelligence 661 University Ave. Suite 710 Toronto Ontario M5G 1M1 Canada
- Canadian Institute for Advanced Research (CIFAR) 661 University Ave. Toronto ON M5G 1M1 Canada
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27
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Coveney PV, Highfield RR. From digital hype to analogue reality: Universal simulation beyond the quantum and exascale eras. JOURNAL OF COMPUTATIONAL SCIENCE 2020; 46:101093. [PMID: 33312270 PMCID: PMC7709487 DOI: 10.1016/j.jocs.2020.101093] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2020] [Accepted: 03/03/2020] [Indexed: 05/23/2023]
Abstract
Many believe that the future of innovation lies in simulation. However, as computers are becoming ever more powerful, so does the hyperbole used to discuss their potential in modelling across a vast range of domains, from subatomic physics to chemistry, climate science, epidemiology, economics and cosmology. As we are about to enter the era of quantum and exascale computing, machine learning and artificial intelligence have entered the field in a significant way. In this article we give a brief history of simulation, discuss how machine learning can be more powerful if underpinned by deeper mechanistic understanding, outline the potential of exascale and quantum computing, highlight the limits of digital computing - classical and quantum - and distinguish rhetoric from reality in assessing the future of modelling and simulation, when we believe analogue computing will play an increasingly important role.
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Affiliation(s)
- Peter V. Coveney
- Centre for Computational Science, University College London, Gordon Street, London, WC1H 0AJ, UK
- Institute for Informatics, Science Park 904, University of Amsterdam, 1098 XH, Amsterdam, Netherlands
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28
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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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29
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Motta M, Gujarati TP, Rice JE, Kumar A, Masteran C, Latone JA, Lee E, Valeev EF, Takeshita TY. Quantum simulation of electronic structure with a transcorrelated Hamiltonian: improved accuracy with a smaller footprint on the quantum computer. Phys Chem Chem Phys 2020; 22:24270-24281. [DOI: 10.1039/d0cp04106h] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Molecular quantum computing simulations are currently limited by the use of minimal Gaussian bases, a problem we overcome using a canonical transcorrelated Hamiltonian to accelerate basis convergence, with unitary coupled cluster as an example.
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Affiliation(s)
- Mario Motta
- IBM Quantum
- IBM Research – Almaden
- San Jose
- USA
| | | | | | | | | | | | - Eunseok Lee
- Mercedes-Benz Research and Development North America
- Sunnyvale
- USA
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30
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Tranter A, Love PJ, Mintert F, Wiebe N, Coveney PV. Ordering of Trotterization: Impact on Errors in Quantum Simulation of Electronic Structure. ENTROPY 2019. [PMCID: PMC7514563 DOI: 10.3390/e21121218] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
Trotter–Suzuki decompositions are frequently used in the quantum simulation of quantum chemistry. They transform the evolution operator into a form implementable on a quantum device, while incurring an error—the Trotter error. The Trotter error can be made arbitrarily small by increasing the Trotter number. However, this increases the length of the quantum circuits required, which may be impractical. It is therefore desirable to find methods of reducing the Trotter error through alternate means. The Trotter error is dependent on the order in which individual term unitaries are applied. Due to the factorial growth in the number of possible orderings with respect to the number of terms, finding an optimal strategy for ordering Trotter sequences is difficult. In this paper, we propose three ordering strategies, and assess their impact on the Trotter error incurred. Initially, we exhaustively examine the possible orderings for molecular hydrogen in a STO-3G basis. We demonstrate how the optimal ordering scheme depends on the compatibility graph of the Hamiltonian, and show how it varies with increasing bond length. We then use 44 molecular Hamiltonians to evaluate two strategies based on coloring their incompatibility graphs, while considering the properties of the obtained colorings. We find that the Trotter error for most systems involving heavy atoms, using a reference magnitude ordering, is less than 1 kcal/mol. Relative to this, the difference between ordering schemes can be substantial, being approximately on the order of millihartrees. The coloring-based ordering schemes are reasonably promising—particularly for systems involving heavy atoms—however further work is required to increase dependence on the magnitude of terms. Finally, we consider ordering strategies based on the norm of the Trotter error operator, including an iterative method for generating the new error operator terms added upon insertion of a term into an ordered Hamiltonian.
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Affiliation(s)
- Andrew Tranter
- Department of Physics and Astronomy, Tufts University, Medford, MA 02155, USA
- Correspondence:
| | - Peter J. Love
- Department of Physics and Astronomy, Tufts University, Medford, MA 02155, USA
| | - Florian Mintert
- Department of Physics, Imperial College London, London SW7 2AZ, UK
| | - Nathan Wiebe
- Department of Physics, University of Washington, Seattle, WA 98105, USA
- Pacific Northwest National Laboratory, Richland, WA 98382, USA
| | - Peter V. Coveney
- Centre for Computational Science, University College London, London WC1H 0AJ, UK
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