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Maximum-likelihood-estimate Hamiltonian learning via efficient and robust quantum likelihood gradient
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DOI：10.1103/PhysRevResearch.5.023136.png)
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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 semidefinite 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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