Deep Neural Network-assisted improvement of quantum compressed sensing tomography

TL;DR

This paper introduces a deep neural network-based post-processing method to enhance quantum state reconstruction in compressed sensing tomography, especially when data is insufficient for accurate initial results.

Contribution

It presents a novel deep learning approach for denoising and improving quantum state estimates in compressed sensing tomography, including iterative refinement and out-of-distribution robustness.

Findings

Significant improvement in reconstruction accuracy demonstrated through numerical experiments.

The denoising process enhances initial compressed sensing results.

Looping inference further refines state estimation.

Abstract

Quantum compressed sensing is the fundamental tool for low-rank density matrix tomographic reconstruction in the informationally incomplete case. We examine situations where the acquired information is not enough to allow one to obtain a precise compressed sensing reconstruction. In this scenario, we propose a Deep Neural Network-based post-processing to improve the initial reconstruction provided by compressed sensing. The idea is to treat the estimated state as a noisy input for the network and perform a deep-supervised denoising task. After the network is applied, a projection onto the space of feasible density matrices is performed to obtain an improved final state estimation. We demonstrate through numerical experiments the improvement obtained by the denoising process and exploit the possibility of looping the inference scheme to obtain further advantages. Finally, we test the resilience of the approach to out-of-distribution data.