Maximum-Likelihood-Estimate Hamiltonian learning via efficient and robust quantum likelihood gradient

• URL: http://arxiv.org/abs/2212.13718v2
• Date: Fri, 23 Jun 2023 11:37:18 GMT
• Title: Maximum-Likelihood-Estimate Hamiltonian learning via efficient and robust quantum likelihood gradient
• Authors: Tian-Lun Zhao, Shi-Xin Hu and Yi Zhang
• Abstract summary: We propose an efficient strategy combining maximum likelihood estimation, gradient descent, and quantum many-body algorithms. Compared with previous approaches, it also exhibits better accuracy and overall stability toward noises, fluctuations, and temperature ranges.
• Score: 4.490097334898205
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Given the recent developments in quantum techniques, modeling the physical Hamiltonian of a target quantum many-body system is becoming an increasingly practical and vital research direction. Here, we propose an efficient strategy combining maximum likelihood estimation, gradient descent, and quantum many-body algorithms. Given the measurement outcomes, we optimize the target model Hamiltonian and density operator via a series of descents along the quantum likelihood gradient, which we prove is negative semi-definite with respect to the negative-log-likelihood function. In addition to such optimization efficiency, our maximum-likelihood-estimate Hamiltonian learning respects the locality of a given quantum system, therefore, extends readily to larger systems with available quantum many-body algorithms. Compared with previous approaches, it also exhibits better accuracy and overall stability toward noises, fluctuations, and temperature ranges, which we demonstrate with various examples.

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