- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review A

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Variational quantum simulation of the critical Ising model with symmetry averaging

Troy J. Sewell1,2,3,*, Ning Bao4, and Stephen P. Jordan5,3

  • 1Joint Center for Quantum Information and Computer Science, College Park, Maryland 20742, USA
  • 2Department of Physics, University of Maryland, College Park, Maryland 20742, USA
  • 3University of Maryland Institute for Advanced Computer Studies, College Park, Maryland 20742, USA
  • 4Computational Science Initiative, Brookhaven National Laboratory, Upton, New York 11973, USA
  • 5Microsoft, Redmond, Washington 98052, USA

  • *tjsewell@umd.edu
PDF

Phys. Rev. A 107, 042620 – Published 26 April, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.042620

Abstract

Here we investigate the use of deep multiscale entanglement renormalization ansatz (DMERA) circuits as a variational ansatz. We use the exactly solvable one-dimensional critical transverse-field Ising model as a test bed. Numerically exact simulation of the quantum circuit ansatz can in this case be carried out to hundreds of qubits by exploiting efficient classical algorithms for simulating matchgate circuits. We find that, for this system, the DMERA strongly outperforms a standard quantum approximate optimization algorithm (QAOA)–style ansatz, and that a major source of systematic error in correlation functions approximated using the DMERA is the breaking of the translational and Kramers-Wannier symmetries of the transverse-field Ising model. We are able to reduce this error by up to four orders of magnitude by symmetry averaging, without incurring additional cost in qubits or circuit depth. We propose that this technique for mitigating systematic error could be applied to noisy intermediate-scale quantum (NISQ) simulations of physical systems with other symmetries.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (33)

  1. G. Vidal, Class of Quantum Many-Body States That Can Be Efficiently Simulated, Phys. Rev. Lett. 101, 110501 (2008).
  2. G. Evenbly and G. Vidal, Algorithms for entanglement renormalization, Phys. Rev. B 79, 144108 (2009).
  3. G. Evenbly and G. Vidal, Quantum criticality with the multi-scale entanglement renormalization ansatz, in Strongly Correlated Systems, edited by A. Avella and F. Mancini, Springer Series in Solid-State Sciences Vol. 176 (Springer, Berlin, Heidelberg, 2013), pp. 99–130.
  4. G. Evenbly and S. R. White, Entanglement Renormalization and Wavelets, Phys. Rev. Lett. 116, 140403 (2016).
  5. J. Haegeman, B. Swingle, M. Walter, J. Cotler, G. Evenbly, and V. B. Scholz, Rigorous Free-Fermion Entanglement Renormalization from Wavelet Theory, Phys. Rev. X 8, 011003 (2018).
  6. F. Witteveen, V. Scholz, B. Swingle, and M. Walter, Quantum circuit approximations and entanglement renormalization for the Dirac field in 1+1 dimensions, Commun. Math. Phys. 389, 75 (2022).
  7. I. H. Kim and B. Swingle, Robust entanglement renormalization on a noisy quantum computer, arXiv:1711.07500.
  8. J. Preskill, Quantum computing in the NISQ era and beyond, Quantum 2, 79 (2018).
  9. T. J. Sewell and S. P. Jordan, Preparing renormalization group fixed points on NISQ hardware, arXiv:2109.09787.
  10. 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).
  11. J. Tilly, H. Chen, S. Cao, D. Picozzi, K. Setia, Y. Li, E. Grant, L. Wossnig, I. Rungger, G. H. Booth, and J. Tennyson, The variational quantum eigensolver: A review of methods and best practices, Phys. Rep. 986, 1 (2022).
  12. J. R. McClean, J. Romero, R. Babbush, and A. Aspuru-Guzik, The theory of variational hybrid quantum-classical algorithms, New J. Phys. 18, 023023 (2016).
  13. Q. Miao and T. Barthel, A quantum-classical eigensolver using multiscale entanglement renormalization, arXiv:2108.13401.
  14. T. J. Osborne and A. Stottmeister, Quantum simulation of conformal field theory, arXiv:2109.14214.
  15. K. Seki, T. Shirakawa, and S. Yunoki, Symmetry-adapted variational quantum eigensolver, Phys. Rev. A 101, 052340 (2020).
  16. T. Tsuchimochi, M. Taii, T. Nishimaki, and S. L. Ten-no, Adaptive construction of shallower quantum circuits with quantum spin projection for fermionic systems, arXiv:2205.07097.
  17. R. Jozsa and A. Miyake, Matchgates and classical simulation of quantum circuits, Proc. R. Soc. A 464, 3089 (2008).
  18. S. Bravyi, Lagrangian representation for linear optics, Quantum Inf. Comput. 5, 216 (2005).
  19. N. Schuch and B. Bauer, Matrix product state algorithms for gaussian fermionic states, Phys. Rev. B 100, 245121 (2019).
  20. A. Jahn, M. Gluza, F. Pastawski, and J. Eisert, Holography and criticality in matchgate tensor networks, Sci. Adv. 5, eaaw0092 (2019).
  21. D. Radicevic, Spin structures and exact dualities in low dimensions, arXiv:1809.07757.
  22. K. Temme, S. Bravyi, and J. Gambetta, Error Mitigation for Short-Depth Quantum Circuits, Phys. Rev. Lett. 119, 180509 (2017).
  23. S. Hadfield, Z. Wang, B. O'Gorman, E. Rieffel, D. Venturelli, and R. Biswas, From the quantum approximate optimization algorithm to a quantum alternating operator ansatz, Algorithms 12, 34 (2019).
  24. E. Farhi, J. Goldstone, and S. Gutmann, A quantum approximate optimization algorithm, arXiv:1411.4028.
  25. W. W. Ho and T. H. Hsieh, Efficient variational simulation of non-trivial quantum states, SciPost Phys. 6, 029 (2019).
  26. D. Zhu, S. Johri, N. M. Linke, K. A. Landsman, C. H. Alderete, N. H. Nguyen, A. Y. Matsuura, T. H. Hsieh, and C. Monroe, Generation of thermofield double states and critical ground states with a quantum computer, in Proceedings of the National Academy of Sciences (2020), Vol. 117.
  27. E. Farhi, D. Gamarnik, and S. Gutmann, The quantum approximate optimization algorithm needs to see the whole graph: Worst case examples, arXiv:2004.09002.
  28. G. K. Brennen, P. Rohde, B. C. Sanders, and S. Singh, Multiscale quantum simulation of quantum field theory using wavelets, Phys. Rev. A 92, 032315 (2015).
  29. M. Bagherimehrab, Y. R. Sanders, D. W. Berry, G. K. Brennen, and B. C. Sanders, Nearly optimal quantum algorithm for generating the ground state of a free quantum field theory, PRX Quantum 3, 020364 (2022).
  30. F. Witteveen and M. Walter, Bosonic entanglement renormalization circuits from wavelet theory, SciPost Phys. 10, 143 (2021).
  31. T. J. Osborne and A. Stottmeister, Conformal field theory from lattice fermions, Commun. Math. Phys. 398, 219 (2023).
  32. S. Bravyi and D. Gosset, Complexity of quantum impurity problems, Commun. Math. Phys. 356, 451 (2017).
  33. B. G. Swingle and Y. Wang, Recovery map for fermionic Gaussian channels, J. Math. Phys. 60, 072202 (2019).

Outline

Information

Phys. Rev. A 107, 042620– Published 26 April, 2023
  • Received 28 October 2022
  • Accepted 28 March 2023
Article part of CHORUS
Crossmark - Check for updates button

©2023 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation