Error-resilient Monte Carlo Quantum Simulation Of Imaginary Time

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Mingxia Huo¹ and Ying Li²

¹Department of Physics and Beijing Key Laboratory for Magneto-Photoelectrical Composite and Interface Science, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
²Graduate School of China Academy of Engineering Physics, Beijing 100193, China

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Abstract

Computing the ground-state properties of quantum many-body systems is a promising application of near-term quantum hardware with a potential impact in many fields. The conventional algorithm quantum phase estimation uses deep circuits and requires fault-tolerant technologies. Many quantum simulation algorithms developed recently work in an inexact and variational manner to exploit shallow circuits. In this work, we combine quantum Monte Carlo with quantum computing and propose an algorithm for simulating the imaginary-time evolution and solving the ground-state problem. By sampling the real-time evolution operator with a random evolution time according to a modified Cauchy-Lorentz distribution, we can compute the expected value of an observable in imaginary-time evolution. Our algorithm approaches the exact solution given a circuit depth increasing polylogarithmically with the desired accuracy. Compared with quantum phase estimation, the Trotter step number, i.e. the circuit depth, can be thousands of times smaller to achieve the same accuracy in the ground-state energy. We verify the resilience to Trotterisation errors caused by the finite circuit depth in the numerical simulation of various models. The results show that Monte Carlo quantum simulation is promising even without a fully fault-tolerant quantum computer.

► BibTeX data

@article{Huo2023errorresilientmonte, doi = {10.22331/q-2023-02-09-916}, url = {https://doi.org/10.22331/q-2023-02-09-916}, title = {Error-resilient {M}onte {C}arlo quantum simulation of imaginary time}, author = {Huo, Mingxia and Li, Ying}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {916}, month = feb, year = {2023}<br /> }

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Cited by

[1] Keisuke Matsumoto, Yuta Shingu, Suguru Endo, Shiro Kawabata, Shohei Watabe, Tetsuro Nikuni, Hideaki Hakoshima, and Yuichiro Matsuzaki, “Calculation of Gibbs partition function with imaginary time evolution on near-term quantum computers”, Japanese Journal of Applied Physics 61 4, 042002 (2022).

[2] Yu-Rong Shu, Shao-Kai Jian, and Shuai Yin, “Nonequilibrium Dynamics of Deconfined Quantum Critical Point in Imaginary Time”, Physical Review Letters 128 2, 020601 (2022).

[3] Pei Zeng, Jinzhao Sun, and Xiao Yuan, “Universal quantum algorithmic cooling on a quantum computer”, arXiv:2109.15304, (2021).

[4] Yifei Huang, Yuguo Shao, Weiluo Ren, Jinzhao Sun, and Dingshun Lv, “Efficient quantum imaginary time evolution by drifting real time evolution: an approach with low gate and measurement complexity”, arXiv:2203.11112, (2022).

[5] Yukun Zhang, Yifei Huang, Jinzhao Sun, Dingshun Lv, and Xiao Yuan, “Quantum Computing Quantum Monte Carlo”, arXiv:2206.10431, (2022).

[6] Zongkang Zhang, Anbang Wang, Xiaosi Xu, and Ying Li, “Measurement-efficient quantum Krylov subspace diagonalisation”, arXiv:2301.13353, (2023).

[7] Qingxing Xie, Yi Song, and Yan Zhao, “Power of Sine Hamiltonian Operator for Estimating the Eigenstate Energies on Quantum Computers”, arXiv:2209.14801, (2022).

The above citations are from SAO/NASA ADS (last updated successfully 2023-02-11 13:59:14). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2023-02-11 13:59:12).

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Source: https://quantum-journal.org/papers/q-2023-02-09-916/

Time Stamp: February 9, 2023

Time Stamp: May 31, 2023

Error-resilient Monte Carlo quantum simulation of imaginary time

Republished By Plato

Abstract

► BibTeX data

► References

Cited by

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