1
|
Yang F, Chen X, Zhao D, Wei S, Wen J, Wang H, Xin T, Long G. Quantum Multi-Round Resonant Transition Algorithm. ENTROPY (BASEL, SWITZERLAND) 2022; 25:61. [PMID: 36673202 PMCID: PMC9857602 DOI: 10.3390/e25010061] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2022] [Revised: 12/14/2022] [Accepted: 12/23/2022] [Indexed: 06/01/2023]
Abstract
Solving the eigenproblems of Hermitian matrices is a significant problem in many fields. The quantum resonant transition (QRT) algorithm has been proposed and demonstrated to solve this problem using quantum devices. To better realize the capabilities of the QRT with recent quantum devices, we improve this algorithm and develop a new procedure to reduce the time complexity. Compared with the original algorithm, it saves one qubit and reduces the complexity with error ϵ from O(1/ϵ2) to O(1/ϵ). Thanks to these optimizations, we can obtain the energy spectrum and ground state of the effective Hamiltonian of the water molecule more accurately and in only 20 percent of the time in a four-qubit processor compared to previous work. More generally, for non-Hermitian matrices, a singular-value decomposition has essential applications in more areas, such as recommendation systems and principal component analysis. The QRT has also been used to prepare singular vectors corresponding to the largest singular values, demonstrating its potential for applications in quantum machine learning.
Collapse
Affiliation(s)
- Fan Yang
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Xinyu Chen
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
| | - Dafa Zhao
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
| | - Shijie Wei
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Jingwei Wen
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
| | - Hefeng Wang
- Department of Applied Physics, School of Science, Xi’an Jiaotong University, Xi’an 710049, China
| | - Tao Xin
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Guilu Long
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
- Tsinghua National Laboratory for Information Science and Technology, Beijing 100084, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100084, China
| |
Collapse
|
2
|
Liu L, Cheng X. Lifetimes and intensities study for the γ and β systems of CN radicals extending to very high vibrational state. COMPUT THEOR CHEM 2022. [DOI: 10.1016/j.comptc.2021.113582] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|
3
|
Abstract
We present a Perspective on what the future holds for full configuration interaction (FCI) theory, with an emphasis on conceptual rather than technical details. Upon revisiting the early history of FCI, a number of its key contemporary approximations are compared on as equal a footing as possible, using a recent blind challenge on the benzene molecule as a testbed [Eriksen et al., J. Phys. Chem. Lett., 2020 11, 8922]. In the process, we review the scope of applications for which FCI continues to prove indispensable, and the required traits in terms of robustness, efficacy, and reliability its modern approximations must satisfy are discussed. We close by conveying a number of general observations on the merits offered by the state-of-the-art alongside some of the challenges still faced to this day. While the field has altogether seen immense progress over the years-the past decade, in particular-it remains clear that our community as a whole has a substantial way to go in enhancing the overall applicability of near-exact electronic structure theory for systems of general composition and increasing size.
Collapse
Affiliation(s)
- Janus J Eriksen
- School of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1TS, United Kingdom
| |
Collapse
|
4
|
Chattopadhyay S. Investigation of Multiple-Bond Dissociation Using Brillouin–Wigner Perturbation with Improved Virtual Orbitals. J Phys Chem A 2020; 124:1444-1463. [DOI: 10.1021/acs.jpca.9b11522] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Sudip Chattopadhyay
- Department of Chemistry, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India
| |
Collapse
|
5
|
Cao Y, Romero J, Olson JP, Degroote M, Johnson PD, Kieferová M, Kivlichan ID, Menke T, Peropadre B, Sawaya NPD, Sim S, Veis L, Aspuru-Guzik A. Quantum Chemistry in the Age of Quantum Computing. Chem Rev 2019; 119:10856-10915. [PMID: 31469277 DOI: 10.1021/acs.chemrev.8b00803] [Citation(s) in RCA: 283] [Impact Index Per Article: 56.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
Abstract
Practical challenges in simulating quantum systems on classical computers have been widely recognized in the quantum physics and quantum chemistry communities over the past century. Although many approximation methods have been introduced, the complexity of quantum mechanics remains hard to appease. The advent of quantum computation brings new pathways to navigate this challenging and complex landscape. By manipulating quantum states of matter and taking advantage of their unique features such as superposition and entanglement, quantum computers promise to efficiently deliver accurate results for many important problems in quantum chemistry, such as the electronic structure of molecules. In the past two decades, significant advances have been made in developing algorithms and physical hardware for quantum computing, heralding a revolution in simulation of quantum systems. This Review provides an overview of the algorithms and results that are relevant for quantum chemistry. The intended audience is both quantum chemists who seek to learn more about quantum computing and quantum computing researchers who would like to explore applications in quantum chemistry.
Collapse
Affiliation(s)
- Yudong Cao
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Jonathan Romero
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Jonathan P Olson
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Matthias Degroote
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Department of Chemistry , University of Toronto , Toronto , Ontario M5G 1Z8 , Canada.,Department of Computer Science , University of Toronto , Toronto , Ontario M5G 1Z8 , Canada
| | - Peter D Johnson
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Mária Kieferová
- Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States.,Department of Physics and Astronomy , Macquarie University , Sydney , NSW 2109 , Australia.,Institute for Quantum Computing and Department of Physics and Astronomy , University of Waterloo , Waterloo , Ontario N2L 3G1 , Canada
| | - Ian D Kivlichan
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Department of Physics , Harvard University , Cambridge , Massachusetts 02138 , United States
| | - Tim Menke
- Department of Physics , Harvard University , Cambridge , Massachusetts 02138 , United States.,Research Laboratory of Electronics , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States.,Department of Physics , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States
| | - Borja Peropadre
- Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Nicolas P D Sawaya
- Intel Laboratories , Intel Corporation , Santa Clara , California 95054 United States
| | - Sukin Sim
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Libor Veis
- J. Heyrovský Institute of Physical Chemistry , Academy of Sciences of the Czech Republic v.v.i. , Doleǰskova 3 , 18223 Prague 8, Czech Republic
| | - Alán Aspuru-Guzik
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States.,Department of Chemistry , University of Toronto , Toronto , Ontario M5G 1Z8 , Canada.,Department of Computer Science , University of Toronto , Toronto , Ontario M5G 1Z8 , Canada.,Canadian Institute for Advanced Research , Toronto , Ontario M5G 1Z8 , Canada.,Vector Institute for Artificial Intelligence , Toronto , Ontario M5S 1M1 , Canada
| |
Collapse
|
6
|
Li Z, Liu X, Wang H, Ashhab S, Cui J, Chen H, Peng X, Du J. Quantum Simulation of Resonant Transitions for Solving the Eigenproblem of an Effective Water Hamiltonian. PHYSICAL REVIEW LETTERS 2019; 122:090504. [PMID: 30932514 DOI: 10.1103/physrevlett.122.090504] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2018] [Revised: 02/04/2019] [Indexed: 06/09/2023]
Abstract
It is difficult to calculate the energy levels and eigenstates of a large physical system on a classical computer because of the exponentially growing size of the Hilbert space. In this work, we experimentally demonstrate a quantum algorithm which could solve this problem via simulated resonant transitions. Using a four-qubit quantum simulator in which two qubits are used as ancillas for control and measurement, we obtain the energy spectrum of a 2-qubit low-energy effective Hamiltonian of the water molecule. The simulated transitions allow the state of the quantum simulator to transform and access large regions of the Hilbert space, including states that have no overlap with the initial state. Furthermore, we make use of this algorithm to efficiently prepare specific eigenstates on the simulator according to the measured eigenenergies.
Collapse
Affiliation(s)
- Zhaokai Li
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China (USTC), Hefei 230026, China
- CAS Key Laboratory of Microscale Magnetic Resonance, USTC, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, USTC, Hefei 230026, China
| | - Xiaomei Liu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China (USTC), Hefei 230026, China
- CAS Key Laboratory of Microscale Magnetic Resonance, USTC, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, USTC, Hefei 230026, China
| | - Hefeng Wang
- Department of Applied Physics, School of Science, Xi'an Jiaotong University and Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, Xi'an, 710049, China
| | - Sahel Ashhab
- Qatar Environment and Energy Research Institute, Hamad Bin Khalifa University, Qatar Foundation, Doha, Qatar
| | - Jiangyu Cui
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China (USTC), Hefei 230026, China
- CAS Key Laboratory of Microscale Magnetic Resonance, USTC, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, USTC, Hefei 230026, China
| | - Hongwei Chen
- High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031, China
| | - Xinhua Peng
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China (USTC), Hefei 230026, China
- CAS Key Laboratory of Microscale Magnetic Resonance, USTC, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, USTC, Hefei 230026, China
| | - Jiangfeng Du
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China (USTC), Hefei 230026, China
- CAS Key Laboratory of Microscale Magnetic Resonance, USTC, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, USTC, Hefei 230026, China
| |
Collapse
|
7
|
Lehtola S, Tubman NM, Whaley KB, Head-Gordon M. Cluster decomposition of full configuration interaction wave functions: A tool for chemical interpretation of systems with strong correlation. J Chem Phys 2017; 147:154105. [DOI: 10.1063/1.4996044] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Susi Lehtola
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Norm M. Tubman
- University of California, Berkeley, California 94720, USA
| | | | - Martin Head-Gordon
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- University of California, Berkeley, California 94720, USA
| |
Collapse
|
8
|
Sugisaki K, Yamamoto S, Nakazawa S, Toyota K, Sato K, Shiomi D, Takui T. Quantum Chemistry on Quantum Computers: A Polynomial-Time Quantum Algorithm for Constructing the Wave Functions of Open-Shell Molecules. J Phys Chem A 2016; 120:6459-66. [DOI: 10.1021/acs.jpca.6b04932] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Kenji Sugisaki
- Department of Chemistry and
Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
| | - Satoru Yamamoto
- Department of Chemistry and
Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
| | - Shigeaki Nakazawa
- Department of Chemistry and
Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
| | - Kazuo Toyota
- Department of Chemistry and
Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
| | - Kazunobu Sato
- Department of Chemistry and
Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
| | - Daisuke Shiomi
- Department of Chemistry and
Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
| | - Takeji Takui
- Department of Chemistry and
Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
| |
Collapse
|
9
|
McClean JR, Babbush R, Love PJ, Aspuru-Guzik A. Exploiting Locality in Quantum Computation for Quantum Chemistry. J Phys Chem Lett 2014; 5:4368-80. [PMID: 26273989 DOI: 10.1021/jz501649m] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
Accurate prediction of chemical and material properties from first-principles quantum chemistry is a challenging task on traditional computers. Recent developments in quantum computation offer a route toward highly accurate solutions with polynomial cost; however, this solution still carries a large overhead. In this Perspective, we aim to bring together known results about the locality of physical interactions from quantum chemistry with ideas from quantum computation. We show that the utilization of spatial locality combined with the Bravyi-Kitaev transformation offers an improvement in the scaling of known quantum algorithms for quantum chemistry and provides numerical examples to help illustrate this point. We combine these developments to improve the outlook for the future of quantum chemistry on quantum computers.
Collapse
Affiliation(s)
- Jarrod R McClean
- †Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Ryan Babbush
- †Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Peter J Love
- ‡Department of Physics, Haverford College, Haverford, Pennsylvania 19041, United States
| | - Alán Aspuru-Guzik
- †Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, United States
| |
Collapse
|
10
|
Peruzzo A, McClean J, Shadbolt P, Yung MH, Zhou XQ, Love PJ, Aspuru-Guzik A, O’Brien JL. A variational eigenvalue solver on a photonic quantum processor. Nat Commun 2014. [DOI: 10.1038/ncomms5213 (2014)] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/18/2023] Open
|
11
|
A variational eigenvalue solver on a photonic quantum processor. Nat Commun 2014; 5:4213. [PMID: 25055053 PMCID: PMC4124861 DOI: 10.1038/ncomms5213] [Citation(s) in RCA: 538] [Impact Index Per Article: 53.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2013] [Accepted: 05/27/2014] [Indexed: 01/13/2023] Open
Abstract
Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the physical dimension grows exponentially, finding the eigenvalues of certain operators is one such intractable problem and remains a fundamental challenge. The quantum phase estimation algorithm efficiently finds the eigenvalue of a given eigenvector but requires fully coherent evolution. Here we present an alternative approach that greatly reduces the requirements for coherent evolution and combine this method with a new approach to state preparation based on ansätze and classical optimization. We implement the algorithm by combining a highly reconfigurable photonic quantum processor with a conventional computer. We experimentally demonstrate the feasibility of this approach with an example from quantum chemistry—calculating the ground-state molecular energy for He–H+. The proposed approach drastically reduces the coherence time requirements, enhancing the potential of quantum resources available today and in the near future. Quantum computers promise to efficiently solve problems that would be practically impossible with a normal computer. Peruzzo et al. develop a variational computation approach that uses any available quantum resources and, with a photonic quantum processing unit, find the ground-state molecular energy of He–H+.
Collapse
|
12
|
|
13
|
Veeraraghavan S, Mazziotti DA. Global solutions of restricted open-shell Hartree-Fock theory from semidefinite programming with applications to strongly correlated quantum systems. J Chem Phys 2014; 140:124106. [DOI: 10.1063/1.4868242] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
|
14
|
Puzzarini C, Gauss J. Quantum-chemical determination of Born–Oppenheimer breakdown parameters for rotational constants: the open-shell species CN, CO+ and BO. Mol Phys 2013. [DOI: 10.1080/00268976.2013.797614] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Cristina Puzzarini
- Dipartimento di Chimica ‘Giacomo Ciamician’, Università di Bologna , Via Selmi 2, Bologna, I-40126, Italy
| | - Jürgen Gauss
- Institut für Physikalische Chemie, Universität Mainz , Mainz, D-55099, Germany
| |
Collapse
|
15
|
Kou Z, Shen J, Xu E, Li S. Hybrid coupled cluster methods based on the split virtual orbitals: barrier heights of reactions and spectroscopic constants of open-shell diatomic molecules. J Phys Chem A 2013; 117:626-32. [PMID: 23270485 DOI: 10.1021/jp309218q] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
We report an efficient implementation of the coupled cluster (CC) singles, doubles, and a hybrid treatment of triples based on the split virtual orbitals (SVO-CCSD(T)-h) method [J. Chem. Phys.2012, 136, 044101]. In this approach, virtual orbitals are split into two subsets, and correspondingly triple excitations are divided into active and inactive subsets. The active triple excitations are treated with the CCSDt (CC singles, doubles, and active triples) method, while the inactive triple excitations are treated with the CCSD(T) (CC singles, doubles, and perturbative triples) method. In the present work, the use of semicanonical molecular orbitals allows the CCSD(T)-like equations in SVO-CCSD(T)-h to be solved without iteration. As a result, the present SVO-CCSD(T)-h scheme does not need a large disk space to store the large number of triple excitation amplitudes, which is required by the original scheme. Test applications indicate that the present method can give results almost identical to those of the original scheme. The present method is then applied to investigate the reaction barriers for a number of simple reactions and spectroscopic constants including the equilibrium bond lengths and vibrational frequencies in several open-shell diatomic molecules. The SVO-CCSD(T)-h method is demonstrated to provide a significant improvement upon the CCSD(T) method in many cases.
Collapse
Affiliation(s)
- Zhuangfei Kou
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing 210093, People's Republic of China
| | | | | | | |
Collapse
|
16
|
Cremer D. From configuration interaction to coupled cluster theory: The quadratic configuration interaction approach. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2013. [DOI: 10.1002/wcms.1131] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
|
17
|
Lu D, Xu N, Xu B, Li Z, Chen H, Peng X, Xu R, Du J. Experimental study of quantum simulation for quantum chemistry with a nuclear magnetic resonance simulator. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2012; 370:4734-4747. [PMID: 22946038 DOI: 10.1098/rsta.2011.0360] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Quantum computers have been proved to be able to mimic quantum systems efficiently in polynomial time. Quantum chemistry problems, such as static molecular energy calculations and dynamical chemical reaction simulations, become very intractable on classical computers with scaling up of the system. Therefore, quantum simulation is a feasible and effective approach to tackle quantum chemistry problems. Proof-of-principle experiments have been implemented on the calculation of the hydrogen molecular energies and one-dimensional chemical isomerization reaction dynamics using nuclear magnetic resonance systems. We conclude that quantum simulation will surpass classical computers for quantum chemistry in the near future.
Collapse
Affiliation(s)
- Dawei Lu
- Hefei National Laboratory for Physical Sciences at Microscale, and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | | | | | | | | | | | | | | |
Collapse
|
18
|
Cleland D, Booth GH, Overy C, Alavi A. Taming the First-Row Diatomics: A Full Configuration Interaction Quantum Monte Carlo Study. J Chem Theory Comput 2012; 8:4138-52. [DOI: 10.1021/ct300504f] [Citation(s) in RCA: 71] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Deidre Cleland
- Department
of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K
| | - George H. Booth
- Department
of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K
| | - Catherine Overy
- Department
of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K
| | - Ali Alavi
- Department
of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K
| |
Collapse
|
19
|
de Lima Batista AP, Sampaio de Oliveira-Filho AG, Ornellas FR. Excited Electronic States, Transition Probabilities, and Radiative Lifetimes of CAs: A Theoretical Contribution and Challenge to Experimentalists. J Phys Chem A 2011; 115:8399-405. [DOI: 10.1021/jp204497p] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
|
20
|
Du J, Xu N, Peng X, Wang P, Wu S, Lu D. NMR implementation of a molecular hydrogen quantum simulation with adiabatic state preparation. PHYSICAL REVIEW LETTERS 2010; 104:030502. [PMID: 20366636 DOI: 10.1103/physrevlett.104.030502] [Citation(s) in RCA: 83] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2009] [Indexed: 05/29/2023]
Abstract
It is difficult to simulate quantum systems on classical computers, while quantum computers have been proved to be able to efficiently perform such kinds of simulations. We report an NMR implementation simulating the hydrogen molecule (H2) in a minimal basis to obtain its ground-state energy. Using an iterative NMR interferometer to measure the phase shift, we achieve a 45-bit estimation of the energy value. The efficiency of the adiabatic state preparation is also experimentally tested with various configurations of the same molecule.
Collapse
Affiliation(s)
- Jiangfeng Du
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China.
| | | | | | | | | | | |
Collapse
|
21
|
Li X, Gour JR, Paldus J, Piecuch P. On the significance of quadruply excited clusters in coupled-cluster calculations for the low-lying states of BN and C2. Chem Phys Lett 2008. [DOI: 10.1016/j.cplett.2008.07.004] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
|
22
|
Rolik Z, Szabados Á, Surján PR. A sparse matrix based full-configuration interaction algorithm. J Chem Phys 2008; 128:144101. [DOI: 10.1063/1.2839304] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
|
23
|
Wang H, Kais S, Aspuru-Guzik A, Hoffmann MR. Quantum algorithm for obtaining the energy spectrum of molecular systems. Phys Chem Chem Phys 2008; 10:5388-93. [DOI: 10.1039/b804804e] [Citation(s) in RCA: 84] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
|
24
|
Southern J, Pitt-Francis J, Whiteley J, Stokeley D, Kobashi H, Nobes R, Kadooka Y, Gavaghan D. Multi-scale computational modelling in biology and physiology. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2008; 96:60-89. [PMID: 17888502 PMCID: PMC7112301 DOI: 10.1016/j.pbiomolbio.2007.07.019] [Citation(s) in RCA: 91] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Recent advances in biotechnology and the availability of ever more powerful computers have led to the formulation of increasingly complex models at all levels of biology. One of the main aims of systems biology is to couple these together to produce integrated models across multiple spatial scales and physical processes. In this review, we formulate a definition of multi-scale in terms of levels of biological organisation and describe the types of model that are found at each level. Key issues that arise in trying to formulate and solve multi-scale and multi-physics models are considered and examples of how these issues have been addressed are given for two of the more mature fields in computational biology: the molecular dynamics of ion channels and cardiac modelling. As even more complex models are developed over the coming few years, it will be necessary to develop new methods to model them (in particular in coupling across the interface between stochastic and deterministic processes) and new techniques will be required to compute their solutions efficiently on massively parallel computers. We outline how we envisage these developments occurring.
Collapse
Affiliation(s)
- James Southern
- Fujitsu Laboratories of Europe Ltd, Hayes Park Central, Hayes End Road, Hayes, Middlesex UB4 8FE, UK.
| | | | | | | | | | | | | | | |
Collapse
|
25
|
Shao Y, Molnar LF, Jung Y, Kussmann J, Ochsenfeld C, Brown ST, Gilbert ATB, Slipchenko LV, Levchenko SV, O'Neill DP, DiStasio RA, Lochan RC, Wang T, Beran GJO, Besley NA, Herbert JM, Lin CY, Van Voorhis T, Chien SH, Sodt A, Steele RP, Rassolov VA, Maslen PE, Korambath PP, Adamson RD, Austin B, Baker J, Byrd EFC, Dachsel H, Doerksen RJ, Dreuw A, Dunietz BD, Dutoi AD, Furlani TR, Gwaltney SR, Heyden A, Hirata S, Hsu CP, Kedziora G, Khalliulin RZ, Klunzinger P, Lee AM, Lee MS, Liang W, Lotan I, Nair N, Peters B, Proynov EI, Pieniazek PA, Rhee YM, Ritchie J, Rosta E, Sherrill CD, Simmonett AC, Subotnik JE, Woodcock HL, Zhang W, Bell AT, Chakraborty AK, Chipman DM, Keil FJ, Warshel A, Hehre WJ, Schaefer HF, Kong J, Krylov AI, Gill PMW, Head-Gordon M. Advances in methods and algorithms in a modern quantum chemistry program package. Phys Chem Chem Phys 2006; 8:3172-91. [PMID: 16902710 DOI: 10.1039/b517914a] [Citation(s) in RCA: 2126] [Impact Index Per Article: 118.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
Advances in theory and algorithms for electronic structure calculations must be incorporated into program packages to enable them to become routinely used by the broader chemical community. This work reviews advances made over the past five years or so that constitute the major improvements contained in a new release of the Q-Chem quantum chemistry package, together with illustrative timings and applications. Specific developments discussed include fast methods for density functional theory calculations, linear scaling evaluation of energies, NMR chemical shifts and electric properties, fast auxiliary basis function methods for correlated energies and gradients, equation-of-motion coupled cluster methods for ground and excited states, geminal wavefunctions, embedding methods and techniques for exploring potential energy surfaces.
Collapse
Affiliation(s)
- Yihan Shao
- Department of Chemistry, University of California, Berkeley, CA 94720, USA
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
Collapse
|
26
|
Aspuru-Guzik A, Dutoi AD, Love PJ, Head-Gordon M. Simulated Quantum Computation of Molecular Energies. Science 2005; 309:1704-7. [PMID: 16151006 DOI: 10.1126/science.1113479] [Citation(s) in RCA: 329] [Impact Index Per Article: 17.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
The calculation time for the energy of atoms and molecules scales exponentially with system size on a classical computer but polynomially using quantum algorithms. We demonstrate that such algorithms can be applied to problems of chemical interest using modest numbers of quantum bits. Calculations of the water and lithium hydride molecular ground-state energies have been carried out on a quantum computer simulator using a recursive phase-estimation algorithm. The recursive algorithm reduces the number of quantum bits required for the readout register from about 20 to 4. Mappings of the molecular wave function to the quantum bits are described. An adiabatic method for the preparation of a good approximate ground-state wave function is described and demonstrated for a stretched hydrogen molecule. The number of quantum bits required scales linearly with the number of basis functions, and the number of gates required grows polynomially with the number of quantum bits.
Collapse
Affiliation(s)
- Alán Aspuru-Guzik
- Department of Chemistry, University of California, Berkeley, CA, USA.
| | | | | | | |
Collapse
|
27
|
Heckert M, KÁllay ‡ M, Gauss † J. Molecular equilibrium geometries based on coupled-cluster calculations including quadruple excitations. Mol Phys 2005. [DOI: 10.1080/00268970500083416] [Citation(s) in RCA: 121] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
|
28
|
Kowalski K. Implementation of the locally renormalized CCSD(T) approaches for arbitrary reference function. J Chem Phys 2005; 123:014102. [PMID: 16035828 DOI: 10.1063/1.1944723] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Several new variants of the locally-renormalized coupled-cluster (CC) approaches that account for the effect of triples (LR-CCSD(T)) have been formulated and implemented for arbitrary reference states using the TENSOR CONTRACTION ENGINE functionality, enabling the automatic generation of an efficient parallel code. Deeply rooted in the recently derived numerator-denominator-connected (NDC) expansion for the ground-state energy [K. Kowalski and P. Piecuch, J. Chem. Phys. 122, 074107 (2005)], LR-CCSD(T) approximations use, in analogy to the completely renormalized CCSD(T) (CR-CCSD(T)) approach, the three-body moments in constructing the noniterative corrections to the energies obtained in CC calculations with singles and doubles (CCSD). In contrast to the CR-CCSD(T) method, the LR-CCSD(T) approaches discussed in this paper employ local denominators, which assure the additive separability of the energies in the noninteracting system limit when the localized occupied spin-orbitals are employed in the CCSD and LR-CCSD(T) calculations. As clearly demonstrated on several challenging examples, including breaking the bonds of the F2, N2, and CN molecules, the LR-CCSD(T) approaches are capable of providing a highly accurate description of the entire potential-energy surface (PES), while maintaining the characteristic N(7) scaling of the ubiquitous CCSD(T) approach. Moreover, as illustrated numerically for the ozone molecule, the LR-CCSD(T) approaches yield highly competitive values for a number of equilibrium properties including bond lengths, angles, and harmonic frequencies.
Collapse
Affiliation(s)
- Karol Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, Richland, Washington 99352, USA.
| |
Collapse
|