Efficient quantum state tomography with convolutional neural networks

TL;DR

This paper introduces a convolutional neural network-based quantum state tomography method that efficiently reconstructs quantum states with high fidelity and significantly reduces observable estimation errors.

Contribution

It presents a novel neural network approach for quantum state tomography that scales polynomially and outperforms traditional maximum likelihood estimation methods.

Findings

High classical fidelities in state reconstruction

Reduction of observable estimation errors by up to tenfold

Efficient representation of ground and steady states

Abstract

Modern day quantum simulators can prepare a wide variety of quantum states but the accurate estimation of observables from tomographic measurement data often poses a challenge. We tackle this problem by developing a quantum state tomography scheme which relies on approximating the probability distribution over the outcomes of an informationally complete measurement in a variational manifold represented by a convolutional neural network. We show an excellent representability of prototypical ground- and steady states with this ansatz using a number of variational parameters that scales polynomially in system size. This compressed representation allows us to reconstruct states with high classical fidelities outperforming standard methods such as maximum likelihood estimation. Furthermore, it achieves a reduction of the estimation error of observables by up to an order of magnitude compared to their direct estimation from experimental data.