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This research introduces Operator Score Matching, a novel framework that bypasses the computational bottlenecks of partition function calculations in quantum Hamiltonian learning. By leveraging gradient descent within operator algebras, the method enables efficient parameter recovery for complex models like the Fermi-Hubbard system using only low-temperature thermal data. This advancement significantly improves the scalability of quantum state reconstruction without relying on intractable normalization constants.
Operator Score Matching for Learning Quantum Hamiltonians
arXiv:2609.25246v1 Announce Type: new Abstract: Learning quantum Hamiltonians from low-temperature thermal state measurements is a fundamental problem in quantum physics. Scalability of existing methods is limited by the complexity of semidefinite optimization problems or partition function computation. Here, we develop a quantum analog of classical score matching method that exploits generalized notions of derivatives and integration by parts in operator algebras. We introduce a new \emph{Operator Score Matching} loss function that recovers Hamiltonian parameters by a simple gradient descent without the need to compute intractable normalization constants. Numerical experiments on the Gibbs states of the transverse-field Ising model, XXZ spin chain, Fermi-Hubbard model, and lattice $\phi^4$ theory demonstrate efficient parameter recovery using finite-depth truncations of nested commutator expansions. Our results establish Operator Score Matching as a practical, partition-function-free framework for quantum Hamiltonian learning.
Abstract:Learning quantum Hamiltonians from low-temperature thermal state measurements is a fundamental problem in quantum physics. Scalability of existing methods is limited by the complexity of semidefinite optimization problems or partition function computation. Here, we develop a quantum analog of classical score matching method that exploits generalized notions of derivatives and integration by parts in operator algebras. We introduce a new \emph{Operator Score Matching} loss function that recovers Hamiltonian parameters by a simple gradient descent without the need to compute intractable normalization constants. Numerical experiments on the Gibbs states of the transverse-field Ising model, XXZ spin chain, Fermi-Hubbard model, and lattice $\phi^4$ theory demonstrate efficient parameter recovery using finite-depth truncations of nested commutator expansions. Our results establish Operator Score Matching as a practical, partition-function-free framework for quantum Hamiltonian learning.
arXiv:2609.25246 [quant-ph]
(or arXiv:2609.25246v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2609.25246 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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