Practical Hamiltonian learning with unitary dynamics and Gibbs states

Andi Gu; Lukasz Cincio; Patrick J Coles

doi:10.1038/s41467-023-44008-1

Practical Hamiltonian learning with unitary dynamics and Gibbs states

Nat Commun. 2024 Jan 8;15(1):312. doi: 10.1038/s41467-023-44008-1.

Authors

Andi Gu^{1

2

3}, Lukasz Cincio⁴, Patrick J Coles^{4

5}

Affiliations

¹ Department of Physics, University of California, Berkeley, Berkeley, CA, USA. andigu@g.harvard.edu.
² Harvard Quantum Initiative, Harvard University, Cambridge, MA, 02138, USA. andigu@g.harvard.edu.
³ Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA. andigu@g.harvard.edu.
⁴ Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.
⁵ Normal Computing Corporation, New York, NY, USA.

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 has practical scaling for large problems: we demonstrate this with a numerical simulation of our protocol on an 80-qubit system.