Latent Space Purification via Neural Density Operators

TL;DR

This paper introduces a neural network-based method for representing and purifying quantum mixed states using a restricted Boltzmann machine, enabling effective quantum state tomography with competitive fidelities.

Contribution

It proposes a novel neural density operator model that can purify mixed quantum states via latent space, advancing quantum state representation techniques.

Findings

Successfully performed quantum state tomography on entangled photon states.

Achieved fidelities comparable to standard quantum tomography methods.

Demonstrated the model's capability to encode mixed states in a neural network framework.

Abstract

Machine learning is actively being explored for its potential to design, validate, and even hybridize with near-term quantum devices. A central question is whether neural networks can provide a tractable representation of a given quantum state of interest. When true, stochastic neural networks can be employed for many unsupervised tasks, including generative modeling and state tomography. However, to be applicable for real experiments such methods must be able to encode quantum mixed states. Here, we parametrize a density matrix based on a restricted Boltzmann machine that is capable of purifying a mixed state through auxiliary degrees of freedom embedded in the latent space of its hidden units. We implement the algorithm numerically and use it to perform tomography on some typical states of entangled photons, achieving fidelities competitive with standard techniques.