- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Demonstrating quantum computation for quasiparticle band structures

Takahiro Ohgoe1, Hokuto Iwakiri2, Masaya Kohda2, Kazuhide Ichikawa1, Yuya O. Nakagawa2, Hubert Okadome Valencia2, and Sho Koh2

  • 1Panasonic Holdings Corporation, 1006 Kadoma, Kadoma City, Osaka 571-8508, Japan
  • 2QunaSys Inc., Aqua Hakusan Building 9F, 1-13-7 Hakusan, Bunkyo, Tokyo 113-0001, Japan

PDF

Phys. Rev. Research 6, L022022 – Published 25 April, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L022022

Abstract

Understanding and predicting the properties of solid-state materials from first principles has been a great challenge for decades. Owing to the recent advances in quantum technologies, quantum computations offer a promising way to achieve this goal. Here, we demonstrate the first-principles calculation of a quasiparticle band structure on actual quantum computers. This is achieved by hybrid quantum-classical algorithms in conjunction with qubit-reduction and error-mitigation techniques. Our demonstration will pave the way to practical applications of quantum computers.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (46)

  1. P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136, B864 (1964).
  2. W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140, A1133 (1965).
  3. M. S. Hybertsen and S. G. Louie, First-principles theory of quasiparticles: Calculation of band gaps in semiconductors and insulators, Phys. Rev. Lett. 55, 1418 (1985).
  4. J. McClain, Q. Sun, G. K.-L. Chan, and T. C. Berkelbach, Gaussian-based coupled-cluster theory for the ground-state and band structure of solids, J. Chem. Theory Comput. 13, 1209 (2017).
  5. A. Dittmer, R. Izsák, F. Neese, and D. Maganas, Accurate band gap predictions of semiconductors in the framework of the similarity transformed equation of motion coupled cluster theory, Inorg. Chem. 58, 9303 (2019).
  6. X. Wang and T. C. Berkelbach, Excitons in solids from periodic equation-of-motion coupled-cluster theory, J. Chem. Theory Comput. 16, 3095 (2020).
  7. A. Gallo, F. Hummel, A. Irmler, and A. Grüneis, A periodic equation-of-motion coupled-cluster implementation applied to F-centers in alkaline earth oxides, J. Chem. Phys. 154, 064106 (2021).
  8. M. F. Lange and T. C. Berkelbach, On the relation between equation-of-motion coupled-cluster theory and the GW approximation, J. Chem. Theory Comput. 14, 4224 (2018).
  9. A. Y. Kitaev, Quantum measurements and the Abelian stabilizer problem, arXiv:quant-ph/9511026.
  10. R. Cleve, A. Ekert, C. Macchiavello, and M. Mosca, Quantum algorithms revisited, Proc. R. Soc. London, Ser. A 454, 339 (1998).
  11. A. Aspuru-Guzik, A. D. Dutoi, P. J. Love, and M. Head-Gordon, Simulated quantum computation of molecular energies, Science 309, 1704 (2005).
  12. A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O'Brien, A variational eigenvalue solver on a photonic quantum processor, Nat. Commun. 5, 4213 (2014).
  13. A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta, Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets, Nature (London) 549, 242 (2017).
  14. A. Kandala, K. Temme, A. D. Córcoles, A. Mezzacapo, J. M. Chow, and J. M. Gambetta, Error mitigation extends the computational reach of a noisy quantum processor, Nature (London) 567, 491 (2019).
  15. J. Preskill, Quantum computing in the NISQ era and beyond, Quantum 2, 79 (2018).
  16. J. Liu, L. Wan, Z. Li, and J. Yang, Simulating periodic systems on a quantum computer using molecular orbitals, J. Chem. Theory Comput. 16, 6904 (2020).
  17. F. T. Cerasoli, K. Sherbert, J. Sławińska, and M. Buongiorno Nardelli, Quantum computation of silicon electronic band structure, Phys. Chem. Chem. Phys. 22, 21816 (2020).
  18. K. Mizuta, M. Fujii, S. Fujii, K. Ichikawa, Y. Imamura, Y. Okuno, and Y. O. Nakagawa, Deep variational quantum eigensolver for excited states and its application to quantum chemistry calculation of periodic materials, Phys. Rev. Res. 3, 043121 (2021).
  19. Y. Fan, J. Liu, Z. Li, and J. Yang, Equation-of-motion theory to calculate accurate band structures with a quantum computer, J. Phys. Chem. Lett. 12, 8833 (2021).
  20. N. Yoshioka, T. Sato, Y. O. Nakagawa, Y.-Y. Ohnishi, and W. Mizukami, Variational quantum simulation for periodic materials, Phys. Rev. Res. 4, 013052 (2022).
  21. D. Z. Manrique, I. T. Khan, K. Yamamoto, V. Wichitwechkarn, and D. M. Ramo, Momentum-space unitary coupled cluster and translational quantum subspace expansion for periodic systems on quantum computers, arXiv:2008.08694.
  22. K. Yamamoto, D. Z. Manrique, I. T. Khan, H. Sawada, and D. M. Ramo, Quantum hardware calculations of periodic systems with partition-measurement symmetry verification: Simplified models of hydrogen chain and iron crystals, Phys. Rev. Res. 4, 033110 (2022).
  23. K. Sherbert, F. Cerasoli, and M. Buongiorno Nardelli, A systematic variational approach to band theory in a quantum computer, RSC Adv. 11, 39438 (2021).
  24. J. R. McClean, M. E. Kimchi-Schwartz, J. Carter, and W. A. de Jong, Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states, Phys. Rev. A 95, 042308 (2017).
  25. S. Goedecker, M. Teter, and J. Hutter, Separable dual-space Gaussian pseudopotentials, Phys. Rev. B 54, 1703 (1996).
  26. S. Bravyi, J. M. Gambetta, A. Mezzacapo, and K. Temme, Tapering off qubits to simulate fermionic Hamiltonians, arXiv:1701.08213.
  27. K. M. Nakanishi, K. Fujii, and S. Todo, Sequential minimal optimization for quantum-classical hybrid algorithms, Phys. Rev. Res. 2, 043158 (2020).
  28. Rigetti Systems Aspen-M-3 Quantum Processor, https://qcs.rigetti.com/qpus.
  29. Y. Chen, M. Farahzad, S. Yoo, and T.-C. Wei, Detector tomography on IBM quantum computers and mitigation of an imperfect measurement, Phys. Rev. A 100, 052315 (2019).
  30. F. B. Maciejewski, Z. Zimborás, and M. Oszmaniec, Mitigation of readout noise in near-term quantum devices by classical post-processing based on detector tomography, Quantum 4, 257 (2020).
  31. S. Bravyi, S. Sheldon, A. Kandala, D. C. Mckay, and J. M. Gambetta, Mitigating measurement errors in multiqubit experiments, Phys. Rev. A 103, 042605 (2021).
  32. K. E. Hamilton, T. Kharazi, T. Morris, A. J. McCaskey, R. S. Bennink, and R. C. Pooser, Scalable quantum processor noise characterization, arXiv:2006.01805.
  33. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.6.L022022 for the details of quantum devices, shot allocation, readout-error mitigation, and zero-noise extrapolation, which includes Refs. [45, 46].
  34. L. F. Richardson, The approximate arithmetical solution by finite differences of physical problems involving differential equations with an application to the stress in a masonry dam, Philos. Trans. R. Soc. London A 210, 307 (1911).
  35. Y. Li and S. C. Benjamin, Efficient variational quantum simulator incorporating active error minimization, Phys. Rev. X 7, 021050 (2017).
  36. K. Temme, S. Bravyi, and J. M. Gambetta, Error mitigation for short-depth quantum circuits, Phys. Rev. Lett. 119, 180509 (2017).
  37. P. D. Nation, H. Kang, N. Sundaresan, and J. M. Gambetta, Scalable mitigation of measurement errors on quantum computers, PRX Quantum 2, 040326 (2021).
  38. S. Srinivasan, B. Pokharel, G. Quiroz, and B. Boots, Scalable measurement error mitigation via iterative Bayesian unfolding, arXiv:2210.12284.
  39. W. J. Huggins, B. A. O'Gorman, N. C. Rubin, D. R. Reichman, R. Babbush, and J. Lee, Unbiasing fermionic quantum Monte Carlo with a quantum computer, Nature (London) 603, 416 (2022).
  40. K. Kanno, M. Kohda, R. Imai, S. Koh, K. Mitarai, W. Mizukami, and Y. O. Nakagawa, Quantum-selected configuration interaction: classical diagonalization of Hamiltonians in subspaces selected by quantum computers, arXiv:2302.11320.
  41. Y. Suzuki, Y. Kawase, Y. Masumura, Y. Hiraga, M. Nakadai, J. Chen, K. M. Nakanishi, K. Mitarai, R. Imai, Shiro Tamiya et al., qulacs: a fast and versatile quantum circuit simulator for research purpose, Quantum 5, 559 (2021).
  42. quri parts (2022), https://github.com/QunaSys/quri-parts.
  43. Q. Sun, X. Zhang, S. Banerjee et al., Recent developments in the pyscf program package, J. Chem. Phys. 153, 024109 (2020).
  44. J. R. McClean, N. C. Rubin, K. J. Sung et al., openfermion: the electronic structure package for quantum computers, Quantum Sci. Technol. 5, 034014 (2020).
  45. Amazon Web Services, Amazon Braket, https://aws.amazon.com/braket/.
  46. V. Verteletskyi, T. Yen, and A. F. Izmaylov, Measurement optimization in the variational quantum eigensolver using a minimum clique cover, J. Chem. Phys. 152, 124114 (2020).

Outline

Information

Phys. Rev. Research 6, L022022– Published 25 April, 2024
  • Received 27 July 2023
  • Accepted 14 March 2024
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation