Approximate Message Passing for Quantum State Tomography

TL;DR

This paper introduces the use of approximate message passing (AMP) algorithms for efficient low-rank quantum state tomography, significantly reducing reconstruction error and demonstrating practical applicability on IBM quantum devices.

Contribution

It adapts AMP algorithms for quantum state tomography, providing asymptotic optimality and improved accuracy over existing methods for low-rank states.

Findings

AMP reduces reconstruction error by over an order of magnitude.

Experimental validation on IBM Kingston shows practical effectiveness.

Device noise impacts fidelity predictions but AMP remains robust.

Abstract

Quantum state tomography (QST) is an indispensable tool for characterizing many-body quantum systems. However, due to the exponential scaling of the cost of the protocol with system size, many approaches have been developed for quantum states with specific structure, such as low-rank states. In this paper, we show how approximate message passing (AMP), an algorithmic framework for sparse signal recovery, can be used to perform low-rank QST. AMP provides asymptotically optimal performance guarantees for large sparse recovery problems, which suggests its utility for QST. We discuss the design challenges that come with applying AMP to QST, and show that by properly designing the AMP algorithm, we can reduce the reconstruction error by over an order of magnitude compared to existing approaches to low-rank QST. We also performed tomographic experiments on IBM Kingston and considered the effect of device noise on the reliability of the predicted fidelity of state preparation. Our work advances the state of low-rank QST and may be applicable to other quantum tomography protocols.