Gradient-descent methods for scalable quantum detector tomography

TL;DR

This paper introduces a gradient descent-based method for quantum detector tomography that outperforms traditional convex optimization in speed and fidelity, applicable to phase insensitive and potentially phase sensitive detectors.

Contribution

The authors develop a scalable gradient descent approach for quantum detector tomography, improving efficiency and accuracy over existing convex optimization techniques.

Findings

Achieves higher or comparable fidelity faster than constrained convex optimization.

Effective in noisy environments with limited probe states.

Extensible to phase sensitive detectors via parametrization on the complex Stiefel manifold.

Abstract

We present a technique for performing quantum detector tomography (QDT) of phase insensitive quantum detectors, a category under which many detectors of interest fall under, using gradient descent-based optimization to learn the positive operator-valued measure (POVM) that best describes the data collected using the detector under study. We numerically benchmark our method against constrained convex optimization (CCO) and show that it reaches higher or comparable reconstruction fidelity in much less time even in the presence of noise and limited probe state resources. We also present a possible extension of our approach to the phase sensitive case via a parametrization of POVMs on the complex Stiefel manifold which enables gradient based optimization restricted to this manifold.