Improving application performance with biased distributions of quantum states

TL;DR

This paper introduces a method to generate biased distributions of quantum states using Dirichlet-weighted mixtures, improving the performance of quantum state tomography and reconstruction in practical experiments.

Contribution

It analytically derives parameters for biased quantum state distributions and demonstrates their advantages in machine learning and experimental quantum state characterization.

Findings

Dirichlet-weighted mixtures match Hilbert--Schmidt distribution exactly

Improved quantum state tomography performance using biased distributions

Enhanced experimental quantum state characterization with the proposed method

Abstract

We consider the properties of a specific distribution of mixed quantum states of arbitrary dimension that can be biased towards a specific mean purity. In particular, we analyze mixtures of Haar-random pure states with Dirichlet-distributed coefficients. We analytically derive the concentration parameters required to match the mean purity of the Bures and Hilbert--Schmidt distributions in any dimension. Numerical simulations suggest that this value recovers the Hilbert--Schmidt distribution exactly, offering an alternative and intuitive physical interpretation for ensembles of Hilbert--Schmidt-distributed random quantum states. We then demonstrate how substituting these Dirichlet-weighted Haar mixtures in place of the Bures and Hilbert--Schmidt distributions results in measurable performance advantages in machine-learning-based quantum state tomography systems and Bayesian quantum state reconstruction. Finally, we experimentally characterize the distribution of quantum states generated by both a cloud-accessed IBM quantum computer and an in-house source of polarization-entangled photons. In each case, our method can more closely match the underlying distribution than either Bures or Hilbert--Schmidt distributed states for various experimental conditions.