Boundary scattering tomography of the Bose Hubbard model on general graphs

TL;DR

This paper introduces a boundary-based tomography scheme for Bose-Hubbard quantum simulators, enabling Hamiltonian parameter estimation with limited boundary measurements, and enhances sensitivity using quantum techniques.

Contribution

It proposes a novel boundary measurement protocol for Hamiltonian tomography in Bose-Hubbard models with limited access, and demonstrates quantum-enhanced sensitivity beyond the standard quantum limit.

Findings

Boundary measurement protocol accurately estimates Hamiltonian parameters.

Quantum enhancement improves sensitivity beyond classical limits.

Method applicable to various lattice geometries and measurement constraints.

Abstract

Correlated quantum many-body phenomena in lattice models have been identified as a set of physically interesting problems that cannot be solved classically. Analog quantum simulators, in photonics and microwave superconducting circuits, have emerged as near-term platforms to address these problems. An important ingredient in practical quantum simulation experiments is the tomography of the implemented Hamiltonians -- while this can easily be performed if we have individual measurement access to each qubit in the simulator, this could be challenging to implement in many hardware platforms. In this paper, we present a scheme for tomography of quantum simulators which can be described by a Bose-Hubbard Hamiltonian while having measurement access to only some sites on the boundary of the lattice. We present an algorithm that uses the experimentally routine transmission and two-photon correlation functions, measured at the boundary, to extract the Hamiltonian parameters at the standard quantum limit. Furthermore, by building on quantum enhanced spectroscopy protocols that, we show that with the additional ability to switch on and off the on-site repulsion in the simulator, we can sense the Hamiltonian parameters beyond the standard quantum limit.