# Improving application performance with biased distributions of quantum states

arXiv: https://arxiv.org/abs/2107.07642 · HTML: https://mlsanity.com/paper/2107.07642/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 57 references that are in the map.
- First posted on arXiv 15 Jul 2021.

## Builds on (most cited first, 7 of 7)

- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Active learning machine learns to create new quantum experiments](https://mlsanity.com/paper/1706.00868/) (2017)
- [Classification and reconstruction of optical quantum states with deep neural networks](https://mlsanity.com/paper/2012.02185/) (2020)
- [Machine learning assisted quantum state estimation](https://mlsanity.com/paper/2003.03441/) (2020)
- [1-bit Matrix Completion: PAC-Bayesian Analysis of a Variational Approximation](https://mlsanity.com/paper/1604.04191/) (2016)
- [On the experimental feasibility of quantum state reconstruction via machine learning](https://mlsanity.com/paper/2012.09432/) (2020)
- [Dirichlet draws are sparse with high probability](https://mlsanity.com/paper/1301.4917/) (2013)

## Built on by (most cited first, 1 of 1)

- [Dimension-adaptive machine-learning-based quantum state reconstruction](https://mlsanity.com/paper/2205.05804/) (2022)

## Abstract (arXiv)

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.