Practical Black Box Hamiltonian Learning

Abstract

We study the problem of learning the parameters for the Hamiltonian of a quantum many-body system, given limited access to the system. In this work, we build upon recent approaches to Hamiltonian learning via derivative estimation. We propose a protocol that improves the scaling dependence of prior works, particularly with respect to parameters relating to the structure of the Hamiltonian (e.g., its locality $k$). Furthermore, by deriving exact bounds on the performance of our protocol, we are able to provide a precise numerical prescription for theoretically optimal settings of hyperparameters in our learning protocol, such as the maximum evolution time (when learning with unitary dynamics) or minimum temperature (when learning with Gibbs states). Thanks to these improvements, our protocol is practical for large problems: we demonstrate this with a numerical simulation of our protocol on an 80-qubit system.

32 pages, 10 figures

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• Hamiltonian and Liouvillian learning in weakly-dissipative quantum many-body systems
• Ansatz-free Hamiltonian learning with Heisenberg-limited scaling
• Hamiltonian Learning via Shadow Tomography of Pseudo-Choi States
• Learning interactions between Rydberg atoms
• Nearly query-optimal classical shadow estimation of unitary channels
• Mitigating Errors in Analog Quantum Simulation by Hamiltonian Reshaping or Hamiltonian Rescaling
• Hamiltonian Learning via Inverse Physics-Informed Neural Networks
• Quantum natural gradient with thermal-state initialization
• Learning the structure of any Hamiltonian from minimal assumptions
• Spatial Leggett-Garg inequalities
• Optimal Hamiltonian recognition of unknown quantum dynamics