Efficient estimation of nearly sparse many-body quantum Hamiltonians

TL;DR

This paper presents a compressed sensing-based method for efficiently estimating nearly sparse many-body quantum Hamiltonians using minimal experimental configurations, applicable to complex quantum systems.

Contribution

The authors introduce a robust, scalable approach for Hamiltonian identification that significantly reduces experimental requirements for multipartite quantum systems.

Findings

Estimates Hamiltonians with O(s log(d)) configurations

Successfully simulated for three- and four-body interactions

Applied to characterize system-bath interactions

Abstract

We develop an efficient and robust approach to Hamiltonian identification for multipartite quantum systems based on the method of compressed sensing. This work demonstrates that with only O(s log(d)) experimental configurations, consisting of random local preparations and measurements, one can estimate the Hamiltonian of a d-dimensional system, provided that the Hamiltonian is nearly s-sparse in a known basis. We numerically simulate the performance of this algorithm for three- and four-body interactions in spin-coupled quantum dots and atoms in optical lattices. Furthermore, we apply the algorithm to characterize Hamiltonian fine structure and unknown system-bath interactions.