Convergence of reconstructed density matrix to a pure state using maximal entropy approach

TL;DR

This paper introduces a maximal entropy-based method for reconstructing pure quantum states from incomplete measurements, offering a practical alternative to traditional quantum state tomography for noisy intermediate-scale quantum devices.

Contribution

It proposes a novel maximal entropy approach for pure state reconstruction from pairwise measurements, improving quantum state inference in NISQ devices.

Findings

Reconstructed density matrix converges to a pure state.

Method effectively estimates quantum states with incomplete data.

Potential applications in quantum error mitigation.

Abstract

Impressive progress has been made in the past decade in the study of technological applications of varied types of quantum systems. With industry giants like IBM laying down their roadmap for scalable quantum devices with more than 1000-qubits by the end of 2023, efficient validation techniques are also being developed for testing quantum processing on these devices. The characterization of a quantum state is done by experimental measurements through the process called quantum state tomography (QST) which scales exponentially with the size of the system. However, QST performed using incomplete measurements is aptly suited for characterizing these quantum technologies especially with the current nature of noisy intermediate-scale quantum (NISQ) devices where not all mean measurements are available with high fidelity. We, hereby, propose an alternative approach to QST for the complete reconstruction of the density matrix of a quantum system in a pure state for any number of qubits by applying the maximal entropy formalism on the pairwise combinations of the known mean measurements. This approach provides the best estimate of the target state when we know the complete set of observables which is the case of convergence of the reconstructed density matrix to a pure state. Our goal is to provide a practical inference of a quantum system in a pure state that can find its applications in the field of quantum error mitigation on a real quantum computer that we intend to investigate further.