Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
144 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Evaluating a quantum-classical quantum Monte Carlo algorithm with Matchgate shadows (2404.18303v2)

Published 28 Apr 2024 in quant-ph and physics.chem-ph

Abstract: Solving the electronic structure problem of molecules and solids to high accuracy is a major challenge in quantum chemistry and condensed matter physics. The rapid emergence and development of quantum computers offer a promising route to systematically tackle this problem. Recent work by Huggins et al.[1] proposed a hybrid quantum-classical quantum Monte Carlo (QC-QMC) algorithm using Clifford shadows to determine the ground state of a Fermionic Hamiltonian. This approach displayed inherent noise resilience and the potential for improved accuracy compared to its purely classical counterpart. Nevertheless, the use of Clifford shadows introduces an exponentially scaling post-processing cost. In this work, we investigate an improved QC-QMC scheme utilizing the recently developed Matchgate shadows technique [2], which removes the aforementioned exponential bottleneck. We observe from experiments on quantum hardware that the use of Matchgate shadows in QC-QMC is inherently noise robust. We show that this noise resilience has a more subtle origin than in the case of Clifford shadows. Nevertheless, we find that classical post-processing, while asymptotically efficient, requires hours of runtime on thousands of classical CPUs for even the smallest chemical systems, presenting a major challenge to the scalability of the algorithm.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (40)
  1. X. Lin, X. Li, and X. Lin, A review on applications of computational methods in drug screening and design, Molecules 25, 1375 (2020).
  2. S. Hammes-Schiffer and G. Galli, Integration of theory and experiment in the modelling of heterogeneous electrocatalysis, Nature Energy 6, 700 (2021).
  3. W. Kohn, A. D. Becke, and R. G. Parr, Density functional theory of electronic structure, Journal of Physical Chemistry 100, 12974 (1996).
  4. T. Helgaker, P. Jorgensen, and J. Olsen, Molecular electronic-structure theory (John Wiley & Sons, 2013).
  5. B. M. Austin, D. Y. Zubarev, and W. A. Lester Jr, Quantum monte carlo and related approaches, Chemical Reviews 112, 263 (2012).
  6. M. Troyer and U.-J. Wiese, Computational complexity and fundamental limitations to fermionic quantum monte carlo simulations, Physical Review Letters 94, 170201 (2005).
  7. J. P. Misiewicz and F. A. Evangelista, Implementation of the projective quantum eigensolver on a quantum computer, arXiv preprint arXiv:2310.04520 10.48550/arXiv.2310.04520 (2023).
  8. S. E. Smart and D. A. Mazziotti, Accelerated convergence of contracted quantum eigensolvers through a quasi-second-order, locally parameterized optimization, Journal of Chemical Theory and Computation 18, 5286 (2022).
  9. H.-Y. Huang, R. Kueng, and J. Preskill, Predicting many properties of a quantum system from very few measurements, Nature Physics 16, 1050 (2020).
  10. X. Xu and Y. Li, Quantum-assisted monte carlo algorithms for fermions, Quantum 7, 1072 (2023).
  11. A. Montanaro and S. Stanisic, Accelerating variational quantum monte carlo using the variational quantum eigensolver, arXiv preprint arXiv:2307.07719 10.48550/arXiv.2307.07719 (2023).
  12. G. Mazzola, Quantum computing for chemistry and physics applications from a monte carlo perspective, The Journal of Chemical Physics 160 (2024).
  13. A. Zhao, N. C. Rubin, and A. Miyake, Fermionic partial tomography via classical shadows, Physical Review Letters 127, 110504 (2021).
  14. D. E. Koh and S. Grewal, Classical shadows with noise, Quantum 6, 776 (2022).
  15. A. Zhao and A. Miyake, Group-theoretic error mitigation enabled by classical shadows and symmetries, arXiv preprint arXiv:2310.03071 10.48550/arXiv.2310.03071 (2023).
  16. B. Wu and D. E. Koh, Error-mitigated fermionic classical shadows on noisy quantum devices, npj Quantum Information 10, 39 (2024).
  17. M. Motta and S. Zhang, Ab initio computations of molecular systems by the auxiliary-field quantum monte carlo method, Wiley Interdisciplinary Reviews: Computational Molecular Science 8, e1364 (2018).
  18. S. Zhang, 15 auxiliary-field quantum monte carlo for correlated electron systems, Emergent Phenomena in Correlated Matter  (2013).
  19. A. Mahajan and S. Sharma, Taming the sign problem in auxiliary-field quantum monte carlo using accurate wave functions, Journal of Chemical Theory and Computation 17, 4786 (2021).
  20. J. Helsen and M. Walter, Thrifty shadow estimation: Reusing quantum circuits and bounding tails, Physical Review Letters 131, 240602 (2023).
  21. S. Aaronson and D. Gottesman, Improved simulation of stabilizer circuits, Physical Review A 70, 052328 (2004).
  22. E. Tang, A quantum-inspired classical algorithm for recommendation systems, in Proceedings of the 51st annual ACM SIGACT symposium on theory of computing (2019) pp. 217–228.
  23. G. H. Low, Classical shadows of fermions with particle number symmetry, arXiv preprint arXiv:2208.08964 10.48550/arXiv.2208.08964 (2022).
  24. B. O’Gorman, Fermionic tomography and learning, arXiv preprint arXiv:2207.14787  (2022).
  25. E. Wigner and P. Jordan, Über das paulische äquivalenzverbot, Z. Phys 47, 46 (1928).
  26. Y. Zhou and Q. Liu, Performance analysis of multi-shot shadow estimation, Quantum 7, 1044 (2023).
  27. B. Huang, M. Govoni, and G. Galli, Simulating the electronic structure of spin defects on quantum computers, PRX Quantum 3, 010339 (2022).
  28. H. Q. Pham, R. Ouyang, and D. Lv, Scalable quantum monte carlo with direct-product trial wave functions, arXiv preprint arXiv:2306.15186 10.48550/arXiv.2306.15186 (2023).
  29. A. Mahajan and S. Sharma, Efficient local energy evaluation for multi-slater wave functions in orbital space quantum monte carlo, The Journal of Chemical Physics 153, https://doi.org/10.1063/5.0025055 (2020).
  30. R. J. Anderson, T. Shiozaki, and G. H. Booth, Efficient and stochastic multireference perturbation theory for large active spaces within a full configuration interaction quantum monte carlo framework, The Journal of Chemical Physics 152, 10.1063/1.5140086 (2020).
  31. G. Mazzola and G. Carleo, Exponential challenges in unbiasing quantum monte carlo algorithms with quantum computers, arXiv preprint arXiv:2205.09203 10.48550/arXiv.2205.09203 (2022).
  32. J. Hubbard, Calculation of partition functions, Physical Review Letters 3, 77 (1959).
  33. R. Stratonovich, On a method of calculating quantum distribution functions, in Soviet Physics Doklady, Vol. 2 (1957) p. 416.
  34. H. F. Trotter, On the product of semi-groups of operators, Proceedings of the American Mathematical Society 10, 545 (1959).
  35. M. Suzuki, Relationship between d-dimensional quantal spin systems and (d+1)-dimensional ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations, Progress of theoretical physics 56, 1454 (1976).
  36. D. J. Thouless, Stability conditions and nuclear rotations in the hartree-fock theory, Nuclear Physics 21, 225 (1960).
  37. D. Thouless, Vibrational states of nuclei in the random phase approximation, Nuclear Physics 22, 78 (1961).
  38. H. Zhu, Multiqubit clifford groups are unitary 3-designs, Physical Review A 96, 062336 (2017).
  39. A. Zhao, Fermionic classical shadows, https://github.com/zhao-andrew/symmetry-adjusted-classical-shadows (2023).
  40. Q. Sun and G. K.-L. Chan, Quantum embedding theories, Accounts of Chemical Research 49, 2705 (2016).
Citations (7)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets