Machine learning pipeline for quantum state estimation with incomplete measurements

TL;DR

This paper presents a machine learning pipeline capable of estimating quantum states from incomplete measurement data, demonstrating robustness and improved accuracy over existing methods, especially for large quantum systems.

Contribution

Introduces a novel machine learning pipeline that handles missing measurements in quantum state estimation without needing separate models for each missing measurement.

Findings

Outperforms previous ML-based quantum state estimation methods in fidelity.

Effective with both noiseless and noisy measurement data.

Scales efficiently to large quantum systems.

Abstract

Two-qubit systems typically employ 36 projective measurements for high-fidelity tomographic estimation. The overcomplete nature of the 36 measurements suggests possible robustness of the estimation procedure to missing measurements. In this paper, we explore the resilience of machine-learning-based quantum state estimation techniques to missing measurements by creating a pipeline of stacked machine learning models for imputation, denoising, and state estimation. When applied to simulated noiseless and noisy projective measurement data for both pure and mixed states, we demonstrate quantum state estimation from partial measurement results that outperforms previously developed machine-learning-based methods in reconstruction fidelity and several conventional methods in terms of resource scaling. Notably, our developed model does not require training a separate model for each missing measurement, making it potentially applicable to quantum state estimation of large quantum systems where preprocessing is computationally infeasible due to the exponential scaling of quantum system dimension.