1
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Parajuli P, Govindarajan A, Tian L. State preparation in a Jaynes-Cummings lattice with quantum optimal control. Sci Rep 2023; 13:19924. [PMID: 37963930 PMCID: PMC10645998 DOI: 10.1038/s41598-023-47002-1] [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: 06/20/2023] [Accepted: 11/07/2023] [Indexed: 11/16/2023] Open
Abstract
High-fidelity preparation of quantum states in an interacting many-body system is often hindered by the lack of knowledge of such states and by limited decoherence times. Here, we study a quantum optimal control (QOC) approach for fast generation of quantum ground states in a finite-sized Jaynes-Cummings lattice with unit filling. Our result shows that the QOC approach can generate quantum many-body states with high fidelity when the evolution time is above a threshold time, and it can significantly outperform the adiabatic approach. We study the dependence of the threshold time on the parameter constraints and the connection of the threshold time with the quantum speed limit. We also show that the QOC approach can be robust against control errors. Our result can lead to advances in the application of the QOC to many-body state preparation.
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Affiliation(s)
- Prabin Parajuli
- School of Natural Sciences, University of California, Merced, California, 95343, USA
| | - Anuvetha Govindarajan
- School of Natural Sciences, University of California, Merced, California, 95343, USA
| | - Lin Tian
- School of Natural Sciences, University of California, Merced, California, 95343, USA.
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2
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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:e25010061. [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] [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.
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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
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3
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Lv L, Yan B, Wang H, Ma Z, Fei Y, Meng X, Duan Q. Using Variational Quantum Algorithm to Solve the LWE Problem. ENTROPY 2022; 24:1428. [PMCID: PMC9602000 DOI: 10.3390/e24101428] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2022] [Accepted: 10/02/2022] [Indexed: 05/20/2023]
Abstract
The variational quantum algorithm (VQA) is a hybrid classical–quantum algorithm. It can actually run in an intermediate-scale quantum device where the number of available qubits is too limited to perform quantum error correction, so it is one of the most promising quantum algorithms in the noisy intermediate-scale quantum era. In this paper, two ideas for solving the learning with errors problem (LWE) using VQA are proposed. First, after reducing the LWE problem into the bounded distance decoding problem, the quantum approximation optimization algorithm (QAOA) is introduced to improve classical methods. Second, after the LWE problem is reduced into the unique shortest vector problem, the variational quantum eigensolver (VQE) is used to solve it, and the number of qubits required is calculated in detail. Small-scale experiments are carried out for the two LWE variational quantum algorithms, and the experiments show that VQA improves the quality of the classical solutions.
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Affiliation(s)
- Lihui Lv
- State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, China
- Henan Key Laboratory of Network Cryptography Technology, Zhengzhou 450001, China
| | - Bao Yan
- State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, China
- Henan Key Laboratory of Network Cryptography Technology, Zhengzhou 450001, China
| | - Hong Wang
- State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, China
- Henan Key Laboratory of Network Cryptography Technology, Zhengzhou 450001, China
- Correspondence: (H.W.); (Z.M.)
| | - Zhi Ma
- State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, China
- Henan Key Laboratory of Network Cryptography Technology, Zhengzhou 450001, China
- Correspondence: (H.W.); (Z.M.)
| | - Yangyang Fei
- State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, China
- Henan Key Laboratory of Network Cryptography Technology, Zhengzhou 450001, China
| | - Xiangdong Meng
- State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, China
- Henan Key Laboratory of Network Cryptography Technology, Zhengzhou 450001, China
| | - Qianheng Duan
- State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, China
- Henan Key Laboratory of Network Cryptography Technology, Zhengzhou 450001, China
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4
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Fixed-point oblivious quantum amplitude-amplification algorithm. Sci Rep 2022; 12:14339. [PMID: 35995929 PMCID: PMC9395401 DOI: 10.1038/s41598-022-15093-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2022] [Accepted: 06/17/2022] [Indexed: 11/24/2022] Open
Abstract
The quantum amplitude amplification algorithms based on Grover’s rotation operator need to perform phase flips for both the initial state and the target state. When the initial state is oblivious, the phase flips will be intractable, and we need to adopt oblivious amplitude amplification algorithm to handle. Without knowing exactly how many target items there are, oblivious amplitude amplification also suffers the “soufflé problem”, in which iterating too little “undercooks” the state and too much “overcooks” the state, both resulting in a mostly non-target final state. In this work, we present a fixed-point oblivious quantum amplitude-amplification (FOQA) algorithm by introducing damping based on methods proposed by A. Mizel. Moreover, we construct the quantum circuit to implement our algorithm under the framework of duality quantum computing. Our algorithm can avoid the “soufflé problem”, meanwhile keep the square speedup of quantum search, serving as a subroutine to improve the performance of quantum algorithms containing oblivious amplitude amplification procedure.
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5
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Quantum Simulation of Pseudo-Hermitian-φ-Symmetric Two-Level Systems. ENTROPY 2022; 24:e24070867. [PMID: 35885090 PMCID: PMC9323109 DOI: 10.3390/e24070867] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/20/2022] [Revised: 06/17/2022] [Accepted: 06/22/2022] [Indexed: 01/14/2023]
Abstract
Non-Hermitian (NH) quantum theory has been attracting increased research interest due to its featured properties, novel phenomena, and links to open and dissipative systems. Typical NH systems include PT-symmetric systems, pseudo-Hermitian systems, and their anti-symmetric counterparts. In this work, we generalize the pseudo-Hermitian systems to their complex counterparts, which we call pseudo-Hermitian-φ-symmetric systems. This complex extension adds an extra degree of freedom to the original symmetry. On the one hand, it enlarges the non-Hermitian class relevant to pseudo-Hermiticity. On the other hand, the conventional pseudo-Hermitian systems can be understood better as a subgroup of this wider class. The well-defined inner product and pseudo-inner product are still valid. Since quantum simulation provides a strong method to investigate NH systems, we mainly investigate how to simulate this novel system in a Hermitian system using the linear combination of unitaries in the scheme of duality quantum computing. We illustrate in detail how to simulate a general P-pseudo-Hermitian-φ-symmetric two-level system. Duality quantum algorithms have been recently successfully applied to similar types of simulations, so we look forward to the implementation of available quantum devices.
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6
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Dai J, Krems RV. Quantum Gaussian process model of potential energy surface for a polyatomic molecule. J Chem Phys 2022; 156:184802. [PMID: 35568545 DOI: 10.1063/5.0088821] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
With gates of a quantum computer designed to encode multi-dimensional vectors, projections of quantum computer states onto specific qubit states can produce kernels of reproducing kernel Hilbert spaces. We show that quantum kernels obtained with a fixed ansatz implementable on current quantum computers can be used for accurate regression models of global potential energy surfaces (PESs) for polyatomic molecules. To obtain accurate regression models, we apply Bayesian optimization to maximize marginal likelihood by varying the parameters of the quantum gates. This yields Gaussian process models with quantum kernels. We illustrate the effect of qubit entanglement in the quantum kernels and explore the generalization performance of quantum Gaussian processes by extrapolating global six-dimensional PESs in the energy domain.
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Affiliation(s)
- J Dai
- Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Z1, CanadaStewart Blusson Quantum Matter Institute, Vancouver, British Columbia V6T 1Z4, Canada
| | - R V Krems
- Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Z1, CanadaStewart Blusson Quantum Matter Institute, Vancouver, British Columbia V6T 1Z4, Canada
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7
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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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8
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Pivoluska M, Plesch M. Implementation of quantum compression on IBM quantum computers. Sci Rep 2022; 12:5841. [PMID: 35393490 PMCID: PMC8991190 DOI: 10.1038/s41598-022-09881-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2022] [Accepted: 03/28/2022] [Indexed: 11/09/2022] Open
Abstract
Advances in development of quantum computing processors brought ample opportunities to test the performance of various quantum algorithms with practical implementations. In this paper we report on implementations of quantum compression algorithm that can efficiently compress unknown quantum information. We restricted ourselves to compression of three pure qubits into two qubits, as the complexity of even such a simple implementation is barely within the reach of today's quantum processors. We implemented the algorithm on IBM quantum processors with two different topological layouts-a fully connected triangle processor and a partially connected line processor. It turns out that the incomplete connectivity of the line processor affects the performance only minimally. On the other hand, it turns out that the transpilation, i.e. compilation of the circuit into gates physically available to the quantum processor, crucially influences the result. We also have seen that the compression followed by immediate decompression is, even for such a simple case, on the edge or even beyond the capabilities of currently available quantum processors.
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Affiliation(s)
- Matej Pivoluska
- Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 841 04, Bratislava, Slovak Republic.,Institute of Computer Science, Masaryk University, Šumavská 416, 602 00, Brno, Czech Republic
| | - Martin Plesch
- Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 841 04, Bratislava, Slovak Republic. .,Institute of Computer Science, Masaryk University, Šumavská 416, 602 00, Brno, Czech Republic.
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9
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Benfenati F, Mazzola G, Capecci C, Barkoutsos PK, Ollitrault PJ, Tavernelli I, Guidoni L. Improved Accuracy on Noisy Devices by Nonunitary Variational Quantum Eigensolver for Chemistry Applications. J Chem Theory Comput 2021; 17:3946-3954. [PMID: 34077220 DOI: 10.1021/acs.jctc.1c00091] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We propose a modification of the Variational Quantum Eigensolver algorithm for electronic structure optimization using quantum computers, named nonunitary Variational Quantum Eigensolver (nu-VQE), in which a nonunitary operator is combined with the original system Hamiltonian leading to a new variational problem with a simplified wave function ansatz. In the present work, as nonunitary operator, we use the Jastrow factor, inspired from classical Quantum Monte Carlo techniques for simulation of strongly correlated electrons. The method is applied to prototypical molecular Hamiltonians for which we obtain accurate ground-state energies with shallower circuits, at the cost of an increased number of measurements. Finally, we also show that this method achieves an important error mitigation effect that drastically improves the quality of the results for VQE optimizations on today's noisy quantum computers. The absolute error in the calculated energy within our scheme is 1 order of magnitude smaller than the corresponding result using traditional VQE methods, with the same circuit depth.
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Affiliation(s)
- Francesco Benfenati
- Dipartimento di Scienze Fisiche e Chimiche, Università degli Studi dell'Aquila, Coppito, L'Aquila 67100, Italy.,Multiverse Computing, Donostia-San Sebastián 20014, Spain
| | | | - Chiara Capecci
- Dipartimento di Scienze Fisiche e Chimiche, Università degli Studi dell'Aquila, Coppito, L'Aquila 67100, Italy.,Dipartimento di Fisica, Sapienza Università di Roma, Roma 00185, Italy
| | | | | | | | - Leonardo Guidoni
- Dipartimento di Scienze Fisiche e Chimiche, Università degli Studi dell'Aquila, Coppito, L'Aquila 67100, Italy
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10
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Pan CY, Hao M, Barraza N, Solano E, Albarrán-Arriagada F. Experimental semi-autonomous eigensolver using reinforcement learning. Sci Rep 2021; 11:12241. [PMID: 34112819 PMCID: PMC8192530 DOI: 10.1038/s41598-021-90534-7] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2020] [Accepted: 03/22/2021] [Indexed: 11/09/2022] Open
Abstract
The characterization of observables, expressed via Hermitian operators, is a crucial task in quantum mechanics. For this reason, an eigensolver is a fundamental algorithm for any quantum technology. In this work, we implement a semi-autonomous algorithm to obtain an approximation of the eigenvectors of an arbitrary Hermitian operator using the IBM quantum computer. To this end, we only use single-shot measurements and pseudo-random changes handled by a feedback loop, reducing the number of measures in the system. Due to the classical feedback loop, this algorithm can be cast into the reinforcement learning paradigm. Using this algorithm, for a single-qubit observable, we obtain both eigenvectors with fidelities over 0.97 with around 200 single-shot measurements. For two-qubits observables, we get fidelities over 0.91 with around 1500 single-shot measurements for the four eigenvectors, which is a comparatively low resource demand, suitable for current devices. This work is useful to the development of quantum devices able to decide with partial information, which helps to implement future technologies in quantum artificial intelligence.
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Affiliation(s)
- C-Y Pan
- International Center in Quantum Artificial Intelligence for Science and Technology (QuArtist) and Physics Department, Shanghai University, Shanghai, 200444, China
| | - M Hao
- International Center in Quantum Artificial Intelligence for Science and Technology (QuArtist) and Physics Department, Shanghai University, Shanghai, 200444, China
| | - N Barraza
- International Center in Quantum Artificial Intelligence for Science and Technology (QuArtist) and Physics Department, Shanghai University, Shanghai, 200444, China
| | - E Solano
- International Center in Quantum Artificial Intelligence for Science and Technology (QuArtist) and Physics Department, Shanghai University, Shanghai, 200444, China. .,Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080, Bilbao, Spain. .,IKERBASQUE, Basque Foundation for Science, Plaza Euskadi 5, 48009, Bilbao, Spain. .,Kipu Quantum, Kurwenalstrasse 1, 80804, Munich, Germany.
| | - F Albarrán-Arriagada
- International Center in Quantum Artificial Intelligence for Science and Technology (QuArtist) and Physics Department, Shanghai University, Shanghai, 200444, China.
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11
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Hu Z, Liu X, Tian M, Ma Y, Jin B, Gao W, Cui G, Guo J, Huang L. Recent progress and new perspectives for diterpenoid biosynthesis in medicinal plants. Med Res Rev 2021; 41:2971-2997. [PMID: 33938025 DOI: 10.1002/med.21816] [Citation(s) in RCA: 28] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2020] [Revised: 04/09/2021] [Accepted: 04/19/2021] [Indexed: 12/25/2022]
Abstract
Diterpenoids, including more than 18,000 compounds, represent an important class of metabolites that encompass both phytohormones and some industrially relevant compounds. These molecules with complex, diverse structures and physiological activities, have high value in the pharmaceutical industry. Most medicinal diterpenoids are extracted from plants. Major advances in understanding the biosynthetic pathways of these active compounds are providing unprecedented opportunities for the industrial production of diterpenoids by metabolic engineering and synthetic biology. Here, we summarize recent developments in the field of diterpenoid biosynthesis from medicinal herbs. An overview of the pathways and known biosynthetic enzymes is presented. In particular, we look at the main findings from the past decade and review recent progress in the biosynthesis of different groups of ringed compounds. We also discuss diterpenoid production using synthetic biology and metabolic engineering strategies, and draw on new technologies and discoveries to bring together many components into a useful framework for diterpenoid production.
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Affiliation(s)
- Zhimin Hu
- State Key Laboratory of Dao-di Herbs, National Resource Center for Chinese Materia Medica, China Academy of Chinese Medical Sciences, Beijing, China
| | - Xiuyu Liu
- State Key Laboratory of Dao-di Herbs, National Resource Center for Chinese Materia Medica, China Academy of Chinese Medical Sciences, Beijing, China.,School of Pharmaceutical Sciences, Henan University of Chinese Medicine, Zhengzhou, Henan Province, China
| | - Mei Tian
- State Key Laboratory of Dao-di Herbs, National Resource Center for Chinese Materia Medica, China Academy of Chinese Medical Sciences, Beijing, China
| | - Ying Ma
- State Key Laboratory of Dao-di Herbs, National Resource Center for Chinese Materia Medica, China Academy of Chinese Medical Sciences, Beijing, China
| | - Baolong Jin
- State Key Laboratory of Dao-di Herbs, National Resource Center for Chinese Materia Medica, China Academy of Chinese Medical Sciences, Beijing, China
| | - Wei Gao
- School of Pharmaceutical, Sciences, Capital Medical University, Beijing, China
| | - Guanghong Cui
- State Key Laboratory of Dao-di Herbs, National Resource Center for Chinese Materia Medica, China Academy of Chinese Medical Sciences, Beijing, China
| | - Juan Guo
- State Key Laboratory of Dao-di Herbs, National Resource Center for Chinese Materia Medica, China Academy of Chinese Medical Sciences, Beijing, China
| | - Luqi Huang
- State Key Laboratory of Dao-di Herbs, National Resource Center for Chinese Materia Medica, China Academy of Chinese Medical Sciences, Beijing, China
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12
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Smart SE, Mazziotti DA. Quantum Solver of Contracted Eigenvalue Equations for Scalable Molecular Simulations on Quantum Computing Devices. PHYSICAL REVIEW LETTERS 2021; 126:070504. [PMID: 33666467 DOI: 10.1103/physrevlett.126.070504] [Citation(s) in RCA: 30] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/21/2020] [Revised: 10/02/2020] [Accepted: 01/05/2021] [Indexed: 06/12/2023]
Abstract
The accurate computation of ground and excited states of many-fermion quantum systems is one of the most consequential, contemporary challenges in the physical and computational sciences whose solution stands to benefit significantly from the advent of quantum computing devices. Existing methodologies using phase estimation or variational algorithms have potential drawbacks such as deep circuits requiring substantial error correction or nontrivial high-dimensional classical optimization. Here, we introduce a quantum solver of contracted eigenvalue equations, the quantum analog of classical methods for the energies and reduced density matrices of ground and excited states. The solver does not require deep circuits or difficult classical optimization and achieves an exponential speed-up over its classical counterpart. We demonstrate the algorithm though computations on both a quantum simulator and two IBM quantum processing units.
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Affiliation(s)
- Scott E Smart
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
| | - David A Mazziotti
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
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13
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Universal quantum simulation of single-qubit nonunitary operators using duality quantum algorithm. Sci Rep 2021; 11:3960. [PMID: 33597681 PMCID: PMC7889913 DOI: 10.1038/s41598-021-83521-5] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2020] [Accepted: 02/04/2021] [Indexed: 11/25/2022] Open
Abstract
Quantum information processing enhances human’s power to simulate nature in quantum level and solve complex problem efficiently. During the process, a series of operators is performed to evolve the system or undertake a computing task. In recent year, research interest in non-Hermitian quantum systems, dissipative-quantum systems and new quantum algorithms has greatly increased, which nonunitary operators take an important role in. In this work, we utilize the linear combination of unitaries technique for nonunitary dynamics on a single qubit to give explicit decompositions of the necessary unitaries, and simulate arbitrary time-dependent single-qubit nonunitary operator F(t) using duality quantum algorithm. We find that the successful probability is not only decided by F(t) and the initial state, but also is inversely proportional to the dimensions of the used ancillary Hilbert subspace. In a general case, the simulation can be achieved in both eight- and six-dimensional Hilbert spaces. In phase matching conditions, F(t) can be simulated by only two qubits. We illustrate our method by simulating typical non-Hermitian systems and single-qubit measurements. Our method can be extended to high-dimensional case, such as Abrams–Lloyd’s two-qubit gate. By discussing the practicability, we expect applications and experimental implementations in the near future.
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14
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Teplukhin A, Kendrick BK, Tretiak S, Dub PA. Electronic structure with direct diagonalization on a D-wave quantum annealer. Sci Rep 2020; 10:20753. [PMID: 33247201 PMCID: PMC7695747 DOI: 10.1038/s41598-020-77315-4] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2020] [Accepted: 11/06/2020] [Indexed: 11/22/2022] Open
Abstract
Quantum chemistry is regarded to be one of the first disciplines that will be revolutionized by quantum computing. Although universal quantum computers of practical scale may be years away, various approaches are currently being pursued to solve quantum chemistry problems on near-term gate-based quantum computers and quantum annealers by developing the appropriate algorithm and software base. This work implements the general Quantum Annealer Eigensolver (QAE) algorithm to solve the molecular electronic Hamiltonian eigenvalue-eigenvector problem on a D-Wave 2000Q quantum annealer. The approach is based on the matrix formulation, efficiently uses qubit resources based on a power-of-two encoding scheme and is hardware-dominant relying on only one classically optimized parameter. We demonstrate the use of D-Wave hardware for obtaining ground and excited electronic states across a variety of small molecular systems. The approach can be adapted for use by a vast majority of electronic structure methods currently implemented in conventional quantum-chemical packages. The results of this work will encourage further development of software such as qbsolv which has promising applications in emerging quantum information processing hardware and has expectation to address large and complex optimization problems intractable for classical computers.
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Affiliation(s)
- Alexander Teplukhin
- Theoretical Division (T-1, MS B221), Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - Brian K Kendrick
- Theoretical Division (T-1, MS B221), Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.
| | - Sergei Tretiak
- Theoretical Division (T-1, MS B221), Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - Pavel A Dub
- Chemistry Division (C-IIAC, MS K558), Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.
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15
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Fei S. Entanglement in
IBMQ
superconducting quantum computer with 53 qubits. ACTA ACUST UNITED AC 2020. [DOI: 10.1002/que2.48] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Affiliation(s)
- Shao‐Ming Fei
- School of Mathematical Sciences Capital Normal University Beijing China
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Zheng C, Tian J, Li D, Wen J, Wei S, Li Y. Efficient Quantum Simulation of an Anti- P-Pseudo-Hermitian Two-Level System. ENTROPY (BASEL, SWITZERLAND) 2020; 22:E812. [PMID: 33286582 PMCID: PMC7517382 DOI: 10.3390/e22080812] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/25/2020] [Revised: 07/19/2020] [Accepted: 07/21/2020] [Indexed: 11/20/2022]
Abstract
Besides Hermitian systems, quantum simulation has become a strong tool to investigate non-Hermitian systems, such as PT-symmetric, anti-PT-symmetric, and pseudo-Hermitian systems. In this work, we theoretically investigate quantum simulation of an anti-P-pseudo-Hermitian two-level system in different dimensional Hilbert spaces. In an arbitrary phase, we find that six dimensions are the minimum to construct the anti-P-pseudo-Hermitian two-level subsystem, and it has a higher success probability than using eight dimensions. We find that the dimensions can be reduced further to four or two when the system is in the anti-PT-symmetric or Hermitian phase, respectively. Both qubit-qudit hybrid and pure-qubit systems are able to realize the simulation, enabling experimental implementations in the near future.
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Affiliation(s)
- Chao Zheng
- Department of Physics, College of Science, North China University of Technology, Beijing 100144, China; (J.T.); (D.L.)
| | - Jin Tian
- Department of Physics, College of Science, North China University of Technology, Beijing 100144, China; (J.T.); (D.L.)
| | - Daili Li
- Department of Physics, College of Science, North China University of Technology, Beijing 100144, China; (J.T.); (D.L.)
| | - Jingwei Wen
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China; (J.W.); (S.W.); (Y.L.)
| | - Shijie Wei
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China; (J.W.); (S.W.); (Y.L.)
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Yansong Li
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China; (J.W.); (S.W.); (Y.L.)
- Frontiers Science Center of Quantum Information, Beijing 100084, China
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