preprint · arXiv (Cornell University) · 2022

Quantum computing quantum Monte Carlo algorithm

Yukun Zhang, Yifei Huang, Jinzhao Sun, Dingshun Lv, Xiaoqing Yuan

Cited by 10Open access

Abstract

Quantum computing and quantum Monte Carlo (QMC) are respectively the state-of-the-art quantum and classical computing methods for understanding many-body quantum systems. Here, we propose a hybrid quantum-classical algorithm that integrates these two methods, inheriting their distinct features in efficient representation and manipulation of quantum states and overcoming their limitations. We first introduce non-stoquasticity indicators (NSIs) and their upper bounds, which measure the sign problem, the most notable limitation of QMC. We show that our algorithm could greatly mitigate the sign problem, which decreases NSIs with the assistance of quantum computing. Meanwhile, the use of quantum Monte Carlo also increases the expressivity of shallow quantum circuits, allowing more accurate computation that is conventionally achievable only with much deeper circuits. We numerically test and verify the method for the N$_2$ molecule (12 qubits) and the Hubbard model (16 qubits). Our work paves the way to solving practical problems with intermediate-scale and early-fault tolerant quantum computers, with potential applications in chemistry, condensed matter physics, materials, high energy physics, etc.

Cite this paper

APA 7

Zhang, Y., Huang, Y., Sun, J., Lv, D., & Yuan, X. (2022). Quantum computing quantum Monte Carlo algorithm. arXiv (Cornell University). https://doi.org/10.48550/arxiv.2206.10431

MLA 9

Zhang, Yukun, et al. “Quantum computing quantum Monte Carlo algorithm.” arXiv (Cornell University), 2022, https://doi.org/10.48550/arxiv.2206.10431.

Chicago

Zhang, Yukun, Yifei Huang, Jinzhao Sun, Dingshun Lv, and Xiaoqing Yuan. 2022. “Quantum computing quantum Monte Carlo algorithm.” arXiv (Cornell University). https://doi.org/10.48550/arxiv.2206.10431.

Harvard

Zhang, Y. et al. (2022) ‘Quantum computing quantum Monte Carlo algorithm’, arXiv (Cornell University). Available at: https://doi.org/10.48550/arxiv.2206.10431.

BibTeX

@misc{zhang2022quantum,
  title = {{Quantum computing quantum Monte Carlo algorithm}},
  author = {Zhang, Yukun and Huang, Yifei and Sun, Jinzhao and Lv, Dingshun and Yuan, Xiaoqing},
  journal = {arXiv (Cornell University)},
  year = {2022},
  doi = {10.48550/arxiv.2206.10431}
}

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