1
|
Yoshida Y, Takemori N, Mizukami W. Ab initio extended Hubbard model of short polyenes for efficient quantum computing. J Chem Phys 2024; 161:084303. [PMID: 39193941 DOI: 10.1063/5.0213525] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2024] [Accepted: 08/05/2024] [Indexed: 08/29/2024] Open
Abstract
We propose introducing an extended Hubbard Hamiltonian derived via the ab initio downfolding method, which was originally formulated for periodic materials, toward efficient quantum computing of molecular electronic structure calculations. By utilizing this method, the first-principles Hamiltonian of chemical systems can be coarse-grained by eliminating the electronic degrees of freedom in higher energy space and reducing the number of terms of electron repulsion integral from O(N4) to O(N2). Our approach is validated numerically on the vertical excitation energies and excitation characters of ethylene, butadiene, and hexatriene. The dynamical electron correlation is incorporated within the framework of the constrained random phase approximation in advance of quantum computations, and the constructed models capture the trend of experimental and high-level quantum chemical calculation results. As expected, the L1-norm of the fermion-to-qubit mapped model Hamiltonians is significantly lower than that of conventional ab initio Hamiltonians, suggesting improved scalability of quantum computing. Those numerical outcomes and the results of the simulation of excited-state sampling demonstrate that the ab initio extended Hubbard Hamiltonian may hold significant potential for quantum chemical calculations using quantum computers.
Collapse
Affiliation(s)
- Yuichiro Yoshida
- Center for Quantum Information and Quantum Biology, Osaka University, 1-2 Machikaneyama, Toyonaka, Osaka 560-0043, Japan
| | - Nayuta Takemori
- Center for Quantum Information and Quantum Biology, Osaka University, 1-2 Machikaneyama, Toyonaka, Osaka 560-0043, Japan
- Center for Emergent Matter Science, RIKEN, Wako, Saitama 351-0198, Japan
| | - Wataru Mizukami
- Center for Quantum Information and Quantum Biology, Osaka University, 1-2 Machikaneyama, Toyonaka, Osaka 560-0043, Japan
- Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan
| |
Collapse
|
2
|
Capone M, Romanelli M, Castaldo D, Parolin G, Bello A, Gil G, Vanzan M. A Vision for the Future of Multiscale Modeling. ACS PHYSICAL CHEMISTRY AU 2024; 4:202-225. [PMID: 38800726 PMCID: PMC11117712 DOI: 10.1021/acsphyschemau.3c00080] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/30/2023] [Revised: 01/31/2024] [Accepted: 02/01/2024] [Indexed: 05/29/2024]
Abstract
The rise of modern computer science enabled physical chemistry to make enormous progresses in understanding and harnessing natural and artificial phenomena. Nevertheless, despite the advances achieved over past decades, computational resources are still insufficient to thoroughly simulate extended systems from first principles. Indeed, countless biological, catalytic and photophysical processes require ab initio treatments to be properly described, but the breadth of length and time scales involved makes it practically unfeasible. A way to address these issues is to couple theories and algorithms working at different scales by dividing the system into domains treated at different levels of approximation, ranging from quantum mechanics to classical molecular dynamics, even including continuum electrodynamics. This approach is known as multiscale modeling and its use over the past 60 years has led to remarkable results. Considering the rapid advances in theory, algorithm design, and computing power, we believe multiscale modeling will massively grow into a dominant research methodology in the forthcoming years. Hereby we describe the main approaches developed within its realm, highlighting their achievements and current drawbacks, eventually proposing a plausible direction for future developments considering also the emergence of new computational techniques such as machine learning and quantum computing. We then discuss how advanced multiscale modeling methods could be exploited to address critical scientific challenges, focusing on the simulation of complex light-harvesting processes, such as natural photosynthesis. While doing so, we suggest a cutting-edge computational paradigm consisting in performing simultaneous multiscale calculations on a system allowing the various domains, treated with appropriate accuracy, to move and extend while they properly interact with each other. Although this vision is very ambitious, we believe the quick development of computer science will lead to both massive improvements and widespread use of these techniques, resulting in enormous progresses in physical chemistry and, eventually, in our society.
Collapse
Affiliation(s)
- Matteo Capone
- Department
of Physical and Chemical Sciences, University
of L’Aquila, L’Aquila 67010, Italy
| | - Marco Romanelli
- Department
of Chemical Sciences, University of Padova, Padova 35131, Italy
| | - Davide Castaldo
- Department
of Chemical Sciences, University of Padova, Padova 35131, Italy
| | - Giovanni Parolin
- Department
of Chemical Sciences, University of Padova, Padova 35131, Italy
| | - Alessandro Bello
- Department
of Chemical Sciences, University of Padova, Padova 35131, Italy
- Department
of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, Modena 41125, Italy
| | - Gabriel Gil
- Department
of Chemical Sciences, University of Padova, Padova 35131, Italy
- Instituto
de Cibernética, Matemática y Física (ICIMAF), La Habana 10400, Cuba
| | - Mirko Vanzan
- Department
of Chemical Sciences, University of Padova, Padova 35131, Italy
- Department
of Physics, University of Milano, Milano 20133, Italy
| |
Collapse
|
3
|
Xie J, Zhou Y, Faizan M, Li Z, Li T, Fu Y, Wang X, Zhang L. Designing semiconductor materials and devices in the post-Moore era by tackling computational challenges with data-driven strategies. NATURE COMPUTATIONAL SCIENCE 2024; 4:322-333. [PMID: 38783137 DOI: 10.1038/s43588-024-00632-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2023] [Accepted: 04/18/2024] [Indexed: 05/25/2024]
Abstract
In the post-Moore's law era, the progress of electronics relies on discovering superior semiconductor materials and optimizing device fabrication. Computational methods, augmented by emerging data-driven strategies, offer a promising alternative to the traditional trial-and-error approach. In this Perspective, we highlight data-driven computational frameworks for enhancing semiconductor discovery and device development by elaborating on their advances in exploring the materials design space, predicting semiconductor properties and optimizing device fabrication, with a concluding discussion on the challenges and opportunities in these areas.
Collapse
Affiliation(s)
- Jiahao Xie
- State Key Laboratory of Integrated Optoelectronics, Key Laboratory of Automobile Materials of MOE, Key Laboratory of Material Simulation Methods & Software of MOE, and School of Materials Science and Engineering, Jilin University, Changchun, China
| | - Yansong Zhou
- State Key Laboratory of Superhard Materials, International Center of Computational Method and Software, School of Physics, Jilin University, Changchun, China
| | - Muhammad Faizan
- State Key Laboratory of Integrated Optoelectronics, Key Laboratory of Automobile Materials of MOE, Key Laboratory of Material Simulation Methods & Software of MOE, and School of Materials Science and Engineering, Jilin University, Changchun, China
| | - Zewei Li
- State Key Laboratory of Integrated Optoelectronics, Key Laboratory of Automobile Materials of MOE, Key Laboratory of Material Simulation Methods & Software of MOE, and School of Materials Science and Engineering, Jilin University, Changchun, China
| | - Tianshu Li
- State Key Laboratory of Integrated Optoelectronics, Key Laboratory of Automobile Materials of MOE, Key Laboratory of Material Simulation Methods & Software of MOE, and School of Materials Science and Engineering, Jilin University, Changchun, China
| | - Yuhao Fu
- State Key Laboratory of Superhard Materials, International Center of Computational Method and Software, School of Physics, Jilin University, Changchun, China
| | - Xinjiang Wang
- State Key Laboratory of Integrated Optoelectronics, Key Laboratory of Automobile Materials of MOE, Key Laboratory of Material Simulation Methods & Software of MOE, and School of Materials Science and Engineering, Jilin University, Changchun, China.
| | - Lijun Zhang
- State Key Laboratory of Integrated Optoelectronics, Key Laboratory of Automobile Materials of MOE, Key Laboratory of Material Simulation Methods & Software of MOE, and School of Materials Science and Engineering, Jilin University, Changchun, China.
| |
Collapse
|
4
|
Kundu A, Galli G. Quantum Vibronic Effects on the Excitation Energies of the Nitrogen-Vacancy Center in Diamond. J Phys Chem Lett 2024; 15:802-810. [PMID: 38232151 DOI: 10.1021/acs.jpclett.3c03269] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2024]
Abstract
We investigated the impact of quantum vibronic coupling on the electronic properties of solid-state spin defects using stochastic methods and first-principles molecular dynamics with a quantum thermostat. Focusing on the negatively charged nitrogen-vacancy center in diamond as an exemplary case, we found a significant dynamic Jahn-Teller splitting of the doubly degenerate single-particle levels within the diamond's band gap, even at 0 K, with a magnitude exceeding 180 meV. This pronounced splitting leads to substantial renormalizations of these levels and, subsequently, of the vertical excitation energies of the doubly degenerate singlet and triplet excited states. Our findings underscore the pressing need to incorporate quantum vibronic effects into first-principles calculations, particularly when comparing computed vertical excitation energies with experimental data. Our study also reveals the efficiency of stochastic thermal line sampling for studying phonon renormalizations of solid-state spin defects.
Collapse
Affiliation(s)
- Arpan Kundu
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, United States
| | - Giulia Galli
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, United States
- Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, United States
- Materials Science Division and Center for Molecular Engineering, Argonne National Laboratory, Lemont, Illinois 60439, United States
| |
Collapse
|
5
|
Jin Y, Yu VWZ, Govoni M, Xu AC, Galli G. Excited State Properties of Point Defects in Semiconductors and Insulators Investigated with Time-Dependent Density Functional Theory. J Chem Theory Comput 2023. [PMID: 38039161 DOI: 10.1021/acs.jctc.3c00986] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/03/2023]
Abstract
We present a formulation of spin-conserving and spin-flip hybrid time-dependent density functional theory (TDDFT), including the calculation of analytical forces, which allows for efficient calculations of excited state properties of solid-state systems with hundreds to thousands of atoms. We discuss an implementation on both GPU- and CPU-based architectures along with several acceleration techniques. We then apply our formulation to the study of several point defects in semiconductors and insulators, specifically the negatively charged nitrogen-vacancy and neutral silicon-vacancy centers in diamond, the neutral divacancy center in 4H silicon carbide, and the neutral oxygen-vacancy center in magnesium oxide. Our results highlight the importance of taking into account structural relaxations in excited states in order to interpret and predict optical absorption and emission mechanisms in spin defects.
Collapse
Affiliation(s)
- Yu Jin
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Victor Wen-Zhe Yu
- Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Marco Govoni
- Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, United States
- Department of Physics, Computer Science, and Mathematics, University of Modena and Reggio Emilia, Modena 41125, Italy
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Andrew C Xu
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Giulia Galli
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
- Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, United States
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| |
Collapse
|
6
|
Verma S, Mitra A, Jin Y, Haldar S, Vorwerk C, Hermes MR, Galli G, Gagliardi L. Optical Properties of Neutral F Centers in Bulk MgO with Density Matrix Embedding. J Phys Chem Lett 2023; 14:7703-7710. [PMID: 37606586 DOI: 10.1021/acs.jpclett.3c01875] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/23/2023]
Abstract
The optical spectra of neutral oxygen vacancies (F0 centers) in the bulk MgO lattice are investigated using density matrix embedding theory. The impurity Hamiltonian is solved with the complete active space self-consistent field and second-order n-electron valence state perturbation theory (NEVPT2-DMET) multireference methods. To estimate defect-localized vertical excitation energies at the nonembedding and thermodynamic limits, a double extrapolation scheme is employed. The extrapolated NEVPT2-DMET vertical excitation energy value of 5.24 eV agrees well with the experimental absorption maxima at 5.03 eV, whereas the excitation energy value of 2.89 eV at the relaxed triplet defect-localized state geometry overestimates the experimental emission at 2.4 eV by only nearly 0.5 eV, indicating the involvement of the triplet-singlet decay pathway.
Collapse
Affiliation(s)
- Shreya Verma
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Abhishek Mitra
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Yu Jin
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Soumi Haldar
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Christian Vorwerk
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Matthew R Hermes
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Giulia Galli
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
- Materials Science Division and Center for Molecular Engineering, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Laura Gagliardi
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
- Argonne National Laboratory, 9700 S. Cass Avenue, Lemont, Illinois 60439, United States
| |
Collapse
|
7
|
Haldar S, Mitra A, Hermes MR, Gagliardi L. Local Excitations of a Charged Nitrogen Vacancy in Diamond with Multireference Density Matrix Embedding Theory. J Phys Chem Lett 2023; 14:4273-4280. [PMID: 37126760 DOI: 10.1021/acs.jpclett.3c00551] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
We investigate the negatively charged nitrogen-vacancy center in diamond using periodic density matrix embedding theory (pDMET). To describe the strongly correlated excited states of this system, the complete active space self-consistent field (CASSCF) followed by n-electron valence state second-order perturbation theory (NEVPT2) was used as the impurity solver. Since the NEVPT2-DMET energies show a linear dependence on the inverse of the size of the embedding subspace, we performed an extrapolation of the excitation energies to the nonembedding limit using a linear regression. The extrapolated NEVPT2-DMET first triplet-triplet excitation energy is 2.31 eV and that for the optically inactive singlet-singlet transition is 1.02 eV, both in agreement with the experimentally observed vertical excitation energies of ∼2.18 eV and ∼1.26 eV, respectively. This is the first application of pDMET to a charged periodic system and the first investigation of the NV- defect using NEVPT2 for periodic supercell models.
Collapse
Affiliation(s)
- Soumi Haldar
- Department of Chemistry, Chicago Center for Theoretical Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Abhishek Mitra
- Department of Chemistry, Chicago Center for Theoretical Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Matthew R Hermes
- Department of Chemistry, Chicago Center for Theoretical Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Laura Gagliardi
- Department of Chemistry, Pritzker School of Molecular Engineering, James Franck Institute, Chicago Center for Theoretical Chemistry, University of Chicago, Chicago, Illinois 60637, United States
- Argonne National Laboratory, 9700 S. Cass Avenue, Lemont, Illinois 60439, United States
| |
Collapse
|
8
|
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.
Collapse
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
| |
Collapse
|
9
|
Ma H, Liu J, Shang H, Fan Y, Li Z, Yang J. Multiscale quantum algorithms for quantum chemistry. Chem Sci 2023; 14:3190-3205. [PMID: 36970085 PMCID: PMC10034224 DOI: 10.1039/d2sc06875c] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2022] [Accepted: 02/15/2023] [Indexed: 02/18/2023] Open
Abstract
Exploring the potential applications of quantum computers in material design and drug discovery is attracting more and more attention after quantum advantage has been demonstrated using Gaussian boson sampling. However, quantum resource requirements in material and (bio)molecular simulations are far beyond the capacity of near-term quantum devices. In this work, multiscale quantum computing is proposed for quantum simulations of complex systems by integrating multiple computational methods at different scales of resolution. In this framework, most computational methods can be implemented in an efficient way on classical computers, leaving the critical portion of the computation to quantum computers. The simulation scale of quantum computing strongly depends on available quantum resources. As a near-term scheme, we integrate adaptive variational quantum eigensolver algorithms, second-order Møller-Plesset perturbation theory and Hartree-Fock theory within the framework of the many-body expansion fragmentation approach. This new algorithm is applied to model systems consisting of hundreds of orbitals with decent accuracy on the classical simulator. This work should encourage further studies on quantum computing for solving practical material and biochemistry problems.
Collapse
Affiliation(s)
- Huan Ma
- Hefei National Laboratory, University of Science and Technology of China Hefei 230088 China
| | - Jie Liu
- Hefei National Laboratory, University of Science and Technology of China Hefei 230088 China
| | - Honghui Shang
- State Key Laboratory of Computer Architecture, Institute of Computing Technology, Chinese Academy of Sciences Beijing 100190 China
| | - Yi Fan
- Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China Hefei 230026 China
| | - Zhenyu Li
- Hefei National Laboratory, University of Science and Technology of China Hefei 230088 China
- Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China Hefei 230026 China
| | - Jinlong Yang
- Hefei National Laboratory, University of Science and Technology of China Hefei 230088 China
- Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China Hefei 230026 China
| |
Collapse
|
10
|
Huang B, Sheng N, Govoni M, Galli G. Quantum Simulations of Fermionic Hamiltonians with Efficient Encoding and Ansatz Schemes. J Chem Theory Comput 2023; 19:1487-1498. [PMID: 36791415 DOI: 10.1021/acs.jctc.2c01119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/17/2023]
Abstract
We propose a computational protocol for quantum simulations of fermionic Hamiltonians on a quantum computer, enabling calculations on spin defect systems which were previously not feasible using conventional encodings and a unitary coupled-cluster ansatz of variational quantum eigensolvers. We combine a qubit-efficient encoding scheme mapping Slater determinants onto qubits with a modified qubit-coupled cluster ansatz and noise-mitigation techniques. Our strategy leads to a substantial improvement in the scaling of circuit gate counts and in the number of required qubits, and to a decrease in the number of required variational parameters, thus increasing the resilience to noise. We present results for spin defects of interest for quantum technologies, going beyond minimum models for the negatively charged nitrogen vacancy center in diamonds and the double vacancy in 4H silicon carbide (4H-SiC) and tackling a defect as complex as negatively charged silicon vacancy in 4H-SiC for the first time.
Collapse
Affiliation(s)
- Benchen Huang
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Nan Sheng
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Marco Govoni
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States.,Materials Science Division and Center for Molecular Engineering, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Giulia Galli
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States.,Materials Science Division and Center for Molecular Engineering, Argonne National Laboratory, Lemont, Illinois 60439, United States.,Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| |
Collapse
|
11
|
Sun J, Endo S, Lin H, Hayden P, Vedral V, Yuan X. Perturbative Quantum Simulation. PHYSICAL REVIEW LETTERS 2022; 129:120505. [PMID: 36179156 DOI: 10.1103/physrevlett.129.120505] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2021] [Revised: 01/27/2022] [Accepted: 08/17/2022] [Indexed: 06/16/2023]
Abstract
Approximation based on perturbation theory is the foundation for most of the quantitative predictions of quantum mechanics, whether in quantum many-body physics, chemistry, quantum field theory, or other domains. Quantum computing provides an alternative to the perturbation paradigm, yet state-of-the-art quantum processors with tens of noisy qubits are of limited practical utility. Here, we introduce perturbative quantum simulation, which combines the complementary strengths of the two approaches, enabling the solution of large practical quantum problems using limited noisy intermediate-scale quantum hardware. The use of a quantum processor eliminates the need to identify a solvable unperturbed Hamiltonian, while the introduction of perturbative coupling permits the quantum processor to simulate systems larger than the available number of physical qubits. We present an explicit perturbative expansion that mimics the Dyson series expansion and involves only local unitary operations, and show its optimality over other expansions under certain conditions. We numerically benchmark the method for interacting bosons, fermions, and quantum spins in different topologies, and study different physical phenomena, such as information propagation, charge-spin separation, and magnetism, on systems of up to 48 qubits only using an 8+1 qubit quantum hardware. We demonstrate our scheme on the IBM quantum cloud, verifying its noise robustness and illustrating its potential for benchmarking large quantum processors with smaller ones.
Collapse
Affiliation(s)
- Jinzhao Sun
- Center on Frontiers of Computing Studies, Peking University, Beijing 100871, China
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
- Quantum Advantage Research, Beijing 100080, China
| | - Suguru Endo
- NTT Computer & Data Science Laboratories, NTT corporation, Musashino, Tokyo 180-8585, Japan
| | - Huiping Lin
- Center on Frontiers of Computing Studies, Peking University, Beijing 100871, China
- School of Computer Science, Peking University, Beijing 100871, China
| | - Patrick Hayden
- Stanford Institute for Theoretical Physics, Stanford University, Stanford, California 94305, USA
| | - Vlatko Vedral
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
- Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
| | - Xiao Yuan
- Center on Frontiers of Computing Studies, Peking University, Beijing 100871, China
- School of Computer Science, Peking University, Beijing 100871, China
- Stanford Institute for Theoretical Physics, Stanford University, Stanford, California 94305, USA
| |
Collapse
|