Out-of-control Hamiltonian Learning

2026-10-05

AI Summary

This study addresses the challenge of learning many-body Hamiltonians from dynamics on near-term analog quantum platforms with limited control. We propose a learning framework operating under a minimal-access model that circumvents the reliance of conventional algorithms on complex quantum control. Specifically, we prove that parameter reconstruction is achievable using only uniform state preparation or computational-basis operations, and employ structured polynomial system solving techniques for large-scale parameter estimation tailored to atomic and ionic analog platforms. Experimentally, we demonstrate the complete reconstruction of generic two-body local Hamiltonians and nearest-neighbor interaction parameters on Rydberg atom platforms. These results establish the feasibility of efficiently learning quantum many-body dynamics under stringent experimental constraints.

Abstract

Learning the Hamiltonian of a many-body system from its dynamics is a central task in quantum science, yet the algorithms with the strongest provable guarantees assume some level of quantum control--fast, arbitrary single-qubit gates interleaved with time evolution, and measurements in arbitrary bases--that is beyond the capabilities of near-term analog quantum simulators. Motivated by analog atom- and ion-based platforms, we study Hamiltonian learning under minimal access models. Uniform state preparation and measurements: We first consider the setting where in every experiment, one can rotate each qubit to the same state, perform short-time evolution, and measure every qubit in the same basis. Surprisingly, we show that for generic 2-local Hamiltonians on any interaction graph, all of the parameters can be reconstructed from such experiments. Computational basis state preparation and measurements: We then consider a similarly constrained setting, but where state preparation and measurement are restricted to the computational basis. For nearest-neighbor Hamiltonians with only Pauli $X/Z$ interactions, a class which captures contemporary Rydberg atom platforms, we show that over 1D and 2D rectangular lattices, all of the parameters can be reconstructed from such experiments up to unavoidable gauges. Our protocols introduce new techniques for solving structured polynomial systems over an extensive number of parameters. Taken together, our results suggest that one can learn a great deal from the dynamics of quantum many-body systems even under the most stringent experimental constraints.

Problem

• Hamiltonian learning
• many-body systems
• analog quantum simulators
• minimal access models
• state preparation and measurement

Innovation

• Hamiltonian learning
• analog quantum simulators
• minimal access models
• structured polynomial systems
• Rydberg atom platforms