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Practical Hamiltonian learning with unitary dynamics and Gibbs states

Journal Article · · Nature Communications
 [1];  [2];  [3]
  1. University of California, Berkeley, CA (United States); Harvard Univ., Cambridge, MA (United States); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
  2. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
  3. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Normal Computing Corporation, New York, NY (United States)

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.

Research Organization:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program
Grant/Contract Number:
89233218CNA000001
OSTI ID:
2475600
Alternate ID(s):
OSTI ID: 2470488
Report Number(s):
LA-UR-22-26209
Journal Information:
Nature Communications, Vol. 15, Issue 1; ISSN 2041-1723
Publisher:
Nature Publishing GroupCopyright Statement
Country of Publication:
United States
Language:
English

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