Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
140 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

Balancing error budget for fermionic k-RDM estimation (2312.17452v1)

Published 29 Dec 2023 in quant-ph and cond-mat.str-el

Abstract: The reduced density matrix (RDM) is crucial in quantum many-body systems for understanding physical properties, including all local physical quantity information. This study aims to minimize various error constraints that causes challenges in higher-order RDMs estimation in quantum computing. We identify the optimal balance between statistical and systematic errors in higher-order RDM estimation in particular when cumulant expansion is used to suppress the sample complexity. Furthermore, we show via numerical demonstration of quantum subspace methods for one and two dimensional Fermi Hubbard model that, biased yet efficient estimations better suppress hardware noise in excited state calculations. Our work paves a path towards cost-efficient practical quantum computing that in reality is constrained by multiple aspects of errors.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (61)
  1. Peter W Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,” SIAM review 41, 303–332 (1999).
  2. Peter W Shor, “Scheme for reducing decoherence in quantum computer memory,” Phys. Rev. A 52, R2493 (1995).
  3. Michael A Nielsen and Isaac Chuang, ‘‘Quantum computation and quantum information,”  (2002).
  4. Daniel A Lidar and Todd A Brun, Quantum error correction (Cambridge university press, 2013).
  5. Seth Lloyd, “Universal quantum simulators,” Science 273, 1073–1078 (1996).
  6. Daniel S Abrams and Seth Lloyd, “Quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors,” Physical Review Letters 83, 5162 (1999).
  7. Alán Aspuru-Guzik, Anthony D Dutoi, Peter J Love,  and Martin Head-Gordon, “Simulated quantum computation of molecular energies,” Science 309, 1704–1707 (2005).
  8. Ryan Babbush, Craig Gidney, Dominic W. Berry, Nathan Wiebe, Jarrod McClean, Alexandru Paler, Austin Fowler,  and Hartmut Neven, “Encoding electronic spectra in quantum circuits with linear t complexity,” Phys. Rev. X 8, 041015 (2018).
  9. Joonho Lee, Dominic W. Berry, Craig Gidney, William J. Huggins, Jarrod R. McClean, Nathan Wiebe,  and Ryan Babbush, “Even more efficient quantum computations of chemistry through tensor hypercontraction,” PRX Quantum 2, 030305 (2021).
  10. Nobuyuki Yoshioka, Tsuyoshi Okubo, Yasunari Suzuki, Yuki Koizumi,  and Wataru Mizukami, “Hunting for quantum-classical crossover in condensed matter problems,”  , 1–44 (2022a), arXiv:2210.14109 .
  11. Kristan Temme, Sergey Bravyi,  and Jay M. Gambetta, “Error mitigation for short-depth quantum circuits,” Phys. Rev. Lett. 119, 180509 (2017).
  12. Ying Li and Simon C Benjamin, “Efficient variational quantum simulator incorporating active error minimization,” Physical Review X 7, 021050 (2017).
  13. Bálint Koczor, “Exponential error suppression for near-term quantum devices,” Phys. Rev. X 11, 031057 (2021).
  14. William J. Huggins, Sam McArdle, Thomas E. O’Brien, Joonho Lee, Nicholas C. Rubin, Sergio Boixo, K. Birgitta Whaley, Ryan Babbush,  and Jarrod R. McClean, “Virtual distillation for quantum error mitigation,” Phys. Rev. X 11, 041036 (2021).
  15. Nobuyuki Yoshioka, Hideaki Hakoshima, Yuichiro Matsuzaki, Yuuki Tokunaga, Yasunari Suzuki,  and Suguru Endo, “Generalized quantum subspace expansion,” Phys. Rev. Lett. 129, 020502 (2022b).
  16. Zhenyu Cai, Ryan Babbush, Simon C Benjamin, Suguru Endo, William J Huggins, Ying Li, Jarrod R McClean,  and Thomas E O’Brien, “Quantum error mitigation,” Reviews of Modern Physics 95, 045005 (2023).
  17. Suguru Endo, Zhenyu Cai, Simon C Benjamin,  and Xiao Yuan, “Hybrid quantum-classical algorithms and quantum error mitigation,” Journal of the Physical Society of Japan 90, 032001 (2021).
  18. Kento Tsubouchi, Takahiro Sagawa,  and Nobuyuki Yoshioka, “Universal cost bound of quantum error mitigation based on quantum estimation theory,” Phys. Rev. Lett. 131, 210601 (2023).
  19. Ryuji Takagi, Hiroyasu Tajima,  and Mile Gu, “Universal sampling lower bounds for quantum error mitigation,” Phys. Rev. Lett. 131, 210602 (2023).
  20. Yihui Quek, Daniel Stilck França, Sumeet Khatri, Johannes Jakob Meyer,  and Jens Eisert, “Exponentially tighter bounds on limitations of quantum error mitigation,” arXiv preprint arXiv:2210.11505  (2022).
  21. Nissim Ofek, Andrei Petrenko, Reinier Heeres, Philip Reinhold, Zaki Leghtas, Brian Vlastakis, Yehan Liu, Luigi Frunzio, S. M. Girvin, L. Jiang, Mazyar Mirrahimi, M. H. Devoret,  and R. J. Schoelkopf, “Extending the lifetime of a quantum bit with error correction in superconducting circuits,” Nature 536, 441–445 (2016).
  22. C. Ryan-Anderson, J. G. Bohnet, K. Lee, D. Gresh, A. Hankin, J. P. Gaebler, D. Francois, A. Chernoguzov, D. Lucchetti, N. C. Brown, T. M. Gatterman, S. K. Halit, K. Gilmore, J. A. Gerber, B. Neyenhuis, D. Hayes,  and R. P. Stutz, “Realization of real-time fault-tolerant quantum error correction,” Phys. Rev. X 11, 041058 (2021).
  23. Sebastian Krinner, Nathan Lacroix, Ants Remm, Agustin Di Paolo, Elie Genois, Catherine Leroux, Christoph Hellings, Stefania Lazar, Francois Swiadek, Johannes Herrmann, et al., “Realizing repeated quantum error correction in a distance-three surface code,” Nature 605, 669–674 (2022).
  24. VV Sivak, Alec Eickbusch, Baptiste Royer, Shraddha Singh, Ioannis Tsioutsios, Suhas Ganjam, Alessandro Miano, BL Brock, AZ Ding, Luigi Frunzio, et al., “Real-time quantum error correction beyond break-even,” Nature 616, 50–55 (2023).
  25. Neereja Sundaresan, Theodore J Yoder, Youngseok Kim, Muyuan Li, Edward H Chen, Grace Harper, Ted Thorbeck, Andrew W Cross, Antonio D Córcoles,  and Maika Takita, “Matching and maximum likelihood decoding of a multi-round subsystem quantum error correction experiment,” arXiv preprint arXiv:2203.07205  (2022).
  26. Dolev Bluvstein, Simon J Evered, Alexandra A Geim, Sophie H Li, Hengyun Zhou, Tom Manovitz, Sepehr Ebadi, Madelyn Cain, Marcin Kalinowski, Dominik Hangleiter, et al., “Logical quantum processor based on reconfigurable atom arrays,” Nature , 1–3 (2023).
  27. Google Quantum AI, “Suppressing quantum errors by scaling a surface code logical qubit,” Nature 614, 676–681 (2023).
  28. Takeshi Yanai and Garnet Kin-Lic Chan, “Canonical transformation theory from extended normal ordering,” The Journal of Chemical Physics 127, 104107 (2007), arXiv:0707.3128 .
  29. Xavier Bonet-Monroig, Ryan Babbush,  and Thomas E. O’Brien, “Nearly optimal measurement scheduling for partial tomography of quantum states,” Phys. Rev. X 10, 031064 (2020).
  30. Jordan Cotler and Frank Wilczek, “Quantum overlapping tomography,” Phys. Rev. Lett. 124, 100401 (2020).
  31. Scott Aaronson, “Shadow tomography of quantum states,” in Proceedings of the 50th annual ACM SIGACT symposium on theory of computing (2018) pp. 325–338.
  32. Hsin Yuan Huang, Richard Kueng,  and John Preskill, “Predicting many properties of a quantum system from very few measurements,” Nature Physics 16, 1050–1057 (2020), arXiv:2002.08953 .
  33. Andrew Zhao, Nicholas C. Rubin,  and Akimasa Miyake, “Fermionic Partial Tomography via Classical Shadows,” Physical Review Letters 127, 1–31 (2021), arXiv:2010.16094 .
  34. Kianna Wan, William J. Huggins, Joonho Lee,  and Ryan Babbush, “Matchgate Shadows for Fermionic Quantum Simulation,”  , 1–53 (2022), arXiv:2207.13723 .
  35. Guang Hao Low, “Classical shadows of fermions with particle number symmetry,” arXiv preprint arXiv:2208.08964  (2022).
  36. Adrian Chapman and Akimasa Miyake, “Classical simulation of quantum circuits by dynamical localization: Analytic results for pauli-observable scrambling in time-dependent disorder,” Phys. Rev. A 98, 012309 (2018).
  37. Soichiro Nishio, Yuki Oba,  and Yuki Kurashige, “Statistical errors in reduced density matrices sampled from quantum circuit simulation and the impact on multireference perturbation theory,” Physical Chemistry Chemical Physics 25, 30525–30535 (2023).
  38. See Supplementary materials (URL to be added) .
  39. David A Mazziotti, “Approximate solution for electron correlation through the use of schwinger probes,” Chemical Physics Letters 289, 419–427 (1998a).
  40. F. Colmenero and C. Valdemoro, “Approximating q-order reduced density matrices in terms of the lower-order ones. ii. applications,” Phys. Rev. A 47, 979–985 (1993).
  41. Hiroshi Nakatsuji and Koji Yasuda, “Direct determination of the quantum-mechanical density matrix using the density equation,” Phys. Rev. Lett. 76, 1039–1042 (1996a).
  42. Koji Yasuda and Hiroshi Nakatsuji, “Direct determination of the quantum-mechanical density matrix using the density equation. ii.” Phys. Rev. A 56, 2648–2657 (1997a).
  43. Jarrod R. McClean, Mollie E. Kimchi-Schwartz, Jonathan Carter,  and Wibe A. de Jong, “Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states,” Physical Review A 95 (2017).
  44. Nobuyuki Yoshioka, Wataru Mizukami,  and Franco Nori, “Solving quasiparticle band spectra of real solids using neural-network quantum states,” Communications Physics 4, 0–7 (2021), arXiv:2010.01358 .
  45. Nobuyuki Yoshioka, Takeshi Sato, Yuya O. Nakagawa, Yu Ya Ohnishi,  and Wataru Mizukami, “Variational quantum simulation for periodic materials,” Physical Review Research 4, 1–8 (2022c), arXiv:2008.09492 .
  46. Mario Motta, William Kirby, Ieva Liepuoniute, Kevin J Sung, Jeffrey Cohn, Antonio Mezzacapo, Katherine Klymko, Nam Nguyen, Nobuyuki Yoshioka,  and Julia E Rice, “Subspace methods for electronic structure simulations on quantum computers,” arXiv preprint arXiv:2312.00178  (2023).
  47. Valerio Magnasco, “Chapter 1 - mathematical foundations and approximation methods,” in Elementary Molecular Quantum Mechanics (Second Edition), edited by Valerio Magnasco (Elsevier, Oxford, 2013) second edition ed., pp. 3–68.
  48. Ethan N. Epperly, Lin Lin,  and Yuji Nakatsukasa, “A theory of quantum subspace diagonalization,”   (2021), arXiv:2110.07492 [quant-ph] .
  49. Toma ž Prosen, “Ergodic properties of a generic nonintegrable quantum many-body system in the thermodynamic limit,” Phys. Rev. E 60, 3949–3968 (1999).
  50. Soumya Bera, Giuseppe De Tomasi, Felix Weiner,  and Ferdinand Evers, “Density propagator for many-body localization: Finite-size effects, transient subdiffusion, and exponential decay,” Phys. Rev. Lett. 118, 196801 (2017).
  51. Adhip Agarwala and Diptiman Sen, “Effects of interactions on periodically driven dynamically localized systems,” Phys. Rev. B 95, 014305 (2017).
  52. Giuseppe De Tomasi, “Algebraic many-body localization and its implications on information propagation,” Phys. Rev. B 99, 054204 (2019).
  53. Alexander M Dalzell, Nicholas Hunter-Jones,  and Fernando GSL Brandão, “Random quantum circuits transform local noise into global white noise,” arXiv preprint arXiv:2111.14907  (2021).
  54. William J. Huggins, Kianna Wan, Jarrod McClean, Thomas E. O’Brien, Nathan Wiebe,  and Ryan Babbush, “Nearly optimal quantum algorithm for estimating multiple expectation values,” Phys. Rev. Lett. 129, 240501 (2022).
  55. Joran van Apeldoorn, Arjan Cornelissen, András Gilyén,  and Giacomo Nannicini, “Quantum tomography using state-preparation unitaries,” in Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) (SIAM, 2023) pp. 1265–1318.
  56. Irma Avdic and David A Mazziotti, “Fewer measurements from shadow tomography with n𝑛nitalic_n-representability conditions,” arXiv preprint arXiv:2312.11715  (2023).
  57. C. Valdemoro, “Theory and methodology of the contracted schrödinger equation,” in Reduced‐Density‐Matrix Mechanics: With Application to Many‐Electron Atoms and Molecules (John Wiley & Sons, Ltd, 2007) Chap. 7, pp. 119–164, https://onlinelibrary.wiley.com/doi/pdf/10.1002/9780470106600.ch7 .
  58. Hiroshi Nakatsuji and Koji Yasuda, ‘‘Direct determination of the quantum-mechanical density matrix using the density equation,” Phys. Rev. Lett. 76, 1039–1042 (1996b).
  59. Koji Yasuda and Hiroshi Nakatsuji, “Direct determination of the quantum-mechanical density matrix using the density equation. ii.” Phys. Rev. A 56, 2648–2657 (1997b).
  60. David A. Mazziotti, “Contracted schrödinger equation: Determining quantum energies and two-particle density matrices without wave functions,” Phys. Rev. A 57, 4219–4234 (1998b).
  61. Ryogo Kubo, “Generalized cumulant expansion method,” Journal of the Physical Society of Japan 17, 1100–1120 (1962).

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