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Mori Y, Kawabata S, Matsuzaki Y. How to experimentally evaluate the adiabatic condition for quantum annealing. Sci Rep 2024; 14:8177. [PMID: 38589470 PMCID: PMC11001971 DOI: 10.1038/s41598-024-58286-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2023] [Accepted: 03/27/2024] [Indexed: 04/10/2024] Open
Abstract
We propose an experimental method for evaluating the adiabatic condition during quantum annealing (QA), which will be essential for solving practical problems. The adiabatic condition consists of the transition matrix element and the energy gap, and our method simultaneously provides information about these components without diagonalizing the Hamiltonian. The key idea is to measure the power spectrum of a time domain signal by adding an oscillating field during QA, and we can estimate the values of the transition matrix element and energy gap from the measurement output. Our results provides a powerful experimental basis for analyzing the performance of QA.
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Affiliation(s)
- Yuichiro Mori
- Global Research and Development Center for Business by Quantum-AI Technology (G-QuAT), National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1, Umezono, Tsukuba, Ibaraki, 305-8568, Japan.
| | - Shiro Kawabata
- Global Research and Development Center for Business by Quantum-AI Technology (G-QuAT), National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1, Umezono, Tsukuba, Ibaraki, 305-8568, Japan.
- NEC-AIST Quantum Technology Cooperative Research Laboratory, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki, 305-8568, Japan.
| | - Yuichiro Matsuzaki
- Global Research and Development Center for Business by Quantum-AI Technology (G-QuAT), National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1, Umezono, Tsukuba, Ibaraki, 305-8568, Japan.
- NEC-AIST Quantum Technology Cooperative Research Laboratory, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki, 305-8568, Japan.
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2
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Sugisaki K. Projective Measurement-Based Quantum Phase Difference Estimation Algorithm for the Direct Computation of Eigenenergy Differences on a Quantum Computer. J Chem Theory Comput 2023; 19:7617-7625. [PMID: 37874368 PMCID: PMC10653105 DOI: 10.1021/acs.jctc.3c00784] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2023] [Indexed: 10/25/2023]
Abstract
Quantum computers are capable of calculating the energy difference of two electronic states using the quantum phase difference estimation (QPDE) algorithm. The Bayesian inference-based implementations for the QPDE have been reported so far, but in this approach, the quality of the calculated energy difference depends on the input wave functions being used. Here, we report the inverse quantum Fourier transformation-based QPDE with Na of ancillary qubits, which allows us to compute the difference of eigenenergies based on the single-shot projective measurement. As proof-of-concept demonstrations, we report numerical experiments for the singlet-triplet energy difference of the hydrogen molecule and the vertical excitation energies of halogen-substituted methylenes (CHF, CHCl, CF2, CFCl, and CCl2) and formaldehyde (HCHO).
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Affiliation(s)
- Kenji Sugisaki
- Graduate
School of Science and Technology, Keio University, 7-1 Shinkawasaki, Saiwai-ku, Kawasaki, Kanagawa 212-0032, Japan
- Quantum
Computing Center, Keio University, 3-14-1 Hiyoshi,
Kohoku-ku Yokohama, Kanagawa 223-8522, Japan
- Centre
for Quantum Engineering, Research and Education
TCG Centres for Research and Education in Science and Technology, Sector V, Salt Lake, Kolkata 700091, India
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3
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Gu Y, Zhuang WF, Chai X, Liu DE. Benchmarking universal quantum gates via channel spectrum. Nat Commun 2023; 14:5880. [PMID: 37735170 PMCID: PMC10514318 DOI: 10.1038/s41467-023-41598-8] [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: 02/11/2023] [Accepted: 09/12/2023] [Indexed: 09/23/2023] Open
Abstract
Noise remains the major obstacle to scalable quantum computation. Quantum benchmarking provides key information on noise properties and is an important step for developing more advanced quantum processors. However, current benchmarking methods are either limited to a specific subset of quantum gates or cannot directly describe the performance of the individual target gate. To overcome these limitations, we propose channel spectrum benchmarking (CSB), a method to infer the noise properties of the target gate, including process fidelity, stochastic fidelity, and some unitary parameters, from the eigenvalues of its noisy channel. Our CSB method is insensitive to state-preparation and measurement errors, and importantly, can benchmark universal gates and is scalable to many-qubit systems. Unlike standard randomized schemes, CSB can provide direct noise information for both target native gates and circuit fragments, allowing benchmarking and calibration of global entangling gates and frequently used modules in quantum algorithms like Trotterized Hamiltonian evolution operator in quantum simulation.
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Affiliation(s)
- Yanwu Gu
- Beijing Academy of Quantum Information Sciences, Beijing, 100193, China.
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing, 100084, China.
| | - Wei-Feng Zhuang
- Beijing Academy of Quantum Information Sciences, Beijing, 100193, China
| | - Xudan Chai
- Beijing Academy of Quantum Information Sciences, Beijing, 100193, China
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing, 100084, China
| | - Dong E Liu
- Beijing Academy of Quantum Information Sciences, Beijing, 100193, China.
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing, 100084, China.
- Frontier Science Center for Quantum Information, Beijing, 100184, China.
- Hefei National Laboratory, Hefei, 230088, China.
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4
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Gu Y, Ma Y, Forcellini N, Liu DE. Noise-Resilient Phase Estimation with Randomized Compiling. PHYSICAL REVIEW LETTERS 2023; 130:250601. [PMID: 37418736 DOI: 10.1103/physrevlett.130.250601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2022] [Accepted: 06/01/2023] [Indexed: 07/09/2023]
Abstract
We develop an error mitigation method for the control-free phase estimation. We prove a theorem that under the first-order correction, the phases of a unitary operator are immune to the noise channels with only Hermitian Kraus operators, and therefore, certain benign types of noise for phase estimation are identified. By further incorporating the randomized compiling protocol, we can convert the generic noise in the phase estimation circuits into stochastic Pauli noise, which satisfies the condition of our theorem. Thus, we achieve a noise-resilient phase estimation without any quantum resource overhead. The simulated experiments show that our method can significantly reduce the estimation error of the phases by up to 2 orders of magnitude. Our method paves the way for the utilization of quantum phase estimation before the advent of fault-tolerant quantum computers.
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Affiliation(s)
- Yanwu Gu
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Yunheng Ma
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Nicolò Forcellini
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Dong E Liu
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
- Frontier Science Center for Quantum Information, Beijing 100184, China
- Hefei National Laboratory, Hefei 230088, China
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5
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Asthana A, Kumar A, Abraham V, Grimsley H, Zhang Y, Cincio L, Tretiak S, Dub PA, Economou SE, Barnes E, Mayhall NJ. Quantum self-consistent equation-of-motion method for computing molecular excitation energies, ionization potentials, and electron affinities on a quantum computer. Chem Sci 2023; 14:2405-2418. [PMID: 36873839 PMCID: PMC9977410 DOI: 10.1039/d2sc05371c] [Citation(s) in RCA: 14] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2022] [Accepted: 01/26/2023] [Indexed: 01/30/2023] Open
Abstract
Near-term quantum computers are expected to facilitate material and chemical research through accurate molecular simulations. Several developments have already shown that accurate ground-state energies for small molecules can be evaluated on present-day quantum devices. Although electronically excited states play a vital role in chemical processes and applications, the search for a reliable and practical approach for routine excited-state calculations on near-term quantum devices is ongoing. Inspired by excited-state methods developed for the unitary coupled-cluster theory in quantum chemistry, we present an equation-of-motion-based method to compute excitation energies following the variational quantum eigensolver algorithm for ground-state calculations on a quantum computer. We perform numerical simulations on H2, H4, H2O, and LiH molecules to test our quantum self-consistent equation-of-motion (q-sc-EOM) method and compare it to other current state-of-the-art methods. q-sc-EOM makes use of self-consistent operators to satisfy the vacuum annihilation condition, a critical property for accurate calculations. It provides real and size-intensive energy differences corresponding to vertical excitation energies, ionization potentials and electron affinities. We also find that q-sc-EOM is more suitable for implementation on NISQ devices as it is expected to be more resilient to noise compared with the currently available methods.
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Affiliation(s)
- Ayush Asthana
- Department of Chemistry, Virginia Tech Blacksburg 24061 VA USA
- Virginia Tech Center for Quantum Information Science and Engineering Blacksburg 24061 VA USA
| | - Ashutosh Kumar
- Theoretical Division, Los Alamos National Laboratory Los Alamos 87545 NM USA
| | - Vibin Abraham
- Department of Chemistry, University of Michigan Ann Arbor 48109 MI USA
| | - Harper Grimsley
- Department of Chemistry, Virginia Tech Blacksburg 24061 VA USA
- Virginia Tech Center for Quantum Information Science and Engineering Blacksburg 24061 VA USA
| | - Yu Zhang
- Theoretical Division, Los Alamos National Laboratory Los Alamos 87545 NM USA
| | - Lukasz Cincio
- Theoretical Division, Los Alamos National Laboratory Los Alamos 87545 NM USA
| | - Sergei Tretiak
- Theoretical Division, Los Alamos National Laboratory Los Alamos 87545 NM USA
- Center for Integrated Nanotechnologies, Los Alamos National Laboratory Los Alamos 87545 NM USA
| | - Pavel A Dub
- Chemistry Division, Los Alamos National Laboratory Los Alamos 87545 NM USA
| | - Sophia E Economou
- Department of Physics, Virginia Tech Blacksburg 24061 VA USA
- Virginia Tech Center for Quantum Information Science and Engineering Blacksburg 24061 VA USA
| | - Edwin Barnes
- Department of Physics, Virginia Tech Blacksburg 24061 VA USA
- Virginia Tech Center for Quantum Information Science and Engineering Blacksburg 24061 VA USA
| | - Nicholas J Mayhall
- Department of Chemistry, Virginia Tech Blacksburg 24061 VA USA
- Virginia Tech Center for Quantum Information Science and Engineering Blacksburg 24061 VA USA
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Sugisaki K, Sakai C, Toyota K, Sato K, Shiomi D, Takui T. Bayesian phase difference estimation: a general quantum algorithm for the direct calculation of energy gaps. Phys Chem Chem Phys 2021; 23:20152-20162. [PMID: 34551045 DOI: 10.1039/d1cp03156b] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
Quantum computers can perform full configuration interaction (full-CI) calculations by utilising the quantum phase estimation (QPE) algorithms including Bayesian phase estimation (BPE) and iterative quantum phase estimation (IQPE). In these quantum algorithms, the time evolution of wave functions for atoms and molecules is simulated conditionally with an ancillary qubit as the control, which make implementation to real quantum devices difficult. Also, most of the problems in chemistry discuss energy differences between two electronic states rather than total energies themselves, and thus direct calculations of energy gaps are promising for future applications of quantum computers to real chemistry problems. In the race of finding efficient quantum algorithms to solve quantum chemistry problems, we test a Bayesian phase difference estimation (BPDE) algorithm, which is a general algorithm to calculate the difference of two eigenphases of unitary operators in the several cases of the direct calculations of energy gaps between two electronic states on quantum computers, including vertical ionisation energies, singlet-triplet energy gaps, and vertical excitation energies. In the BPDE algorithm, state preparation is carried out conditionally on the ancillary qubit, and the time evolution of the wave functions in superposition of two electronic states are executed unconditionally. Based on our test, we conclude that BPDE is capable of computing the energy gap with an accuracy similar to BPE without controlled-time evolution simulations and with the smaller number of iterations in Bayesian optimisations.
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Affiliation(s)
- Kenji Sugisaki
- Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan. .,JST PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama, 332-0012, Japan.,Centre for Quantum Engineering, Research and Education (CQuERE), TCG Centres for Research and Education in Science and Technology (TCG CREST), 16th Floor, Omega, BIPL Building, Blocks EP & GP, Sector V, Salt Lake, Kolkata 700091, India
| | - Chikako Sakai
- Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan.
| | - Kazuo Toyota
- Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan.
| | - Kazunobu Sato
- Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan.
| | - Daisuke Shiomi
- Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan.
| | - Takeji Takui
- Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan. .,Research Support Department/University Research Administrator Centre, University Administration Division, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
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7
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Sugisaki K, Toyota K, Sato K, Shiomi D, Takui T. Quantum Algorithm for the Direct Calculations of Vertical Ionization Energies. J Phys Chem Lett 2021; 12:2880-2885. [PMID: 33724039 DOI: 10.1021/acs.jpclett.1c00283] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Recently, a quantum algorithm that is capable of directly calculating the energy gap between two electronic states having different spin quantum numbers without inspecting the total energy of the individual electronic states was proposed. This quantum algorithm guarantees an exponential speedup, like quantum phase estimation (QPE)-based full-CI, with much lower costs. In this work, we propose a modified quantum circuit for the direct calculations of spin state energy gaps to reduce the number of qubits and quantum gates, extending the quantum algorithm to the direct calculation of vertical ionization energies. Numerical quantum circuit simulations for the ionization of light atoms (He, Li, Be, B, C, and N) and small molecules (HF, BF, CF, CO, O2, NO, CN, F2, H2O, and NH3) revealed that the proposed quantum algorithm affords the vertical ionization energies within 0.1 eV of precision.
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Affiliation(s)
- Kenji Sugisaki
- Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
- JST PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama, 332-0012, Japan
- Centre for Quantum Engineering, Research and Education (CQuERE), TCG Centres for Research and Education in Science and Technology (TCG CREST), 16th Floor, Omega, BIPL Building, Blocks EP & GP, Sector V, Salt Lake, Kolkata 700091, India
| | - Kazuo Toyota
- Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
| | - Kazunobu Sato
- Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
| | - Daisuke Shiomi
- Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
| | - Takeji Takui
- Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
- Research Support Department/University Research Administrator Center, University Administration Division, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
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