Adversarial quantum circuit learning for pure state approximation

TL;DR

This paper introduces an adversarial quantum circuit learning algorithm for approximating unknown pure quantum states, suitable for near-term quantum computers, with potential applications in quantum state tomography.

Contribution

It develops a novel adversarial learning framework for pure state approximation that can be implemented on near-term quantum devices, advancing quantum state modeling techniques.

Findings

Resilient backpropagation algorithms effectively optimize the circuits.

The bipartite entanglement entropy serves as a practical stopping criterion.

Numerical simulations validate the approach's effectiveness.

Abstract

Adversarial learning is one of the most successful approaches to modelling high-dimensional probability distributions from data. The quantum computing community has recently begun to generalize this idea and to look for potential applications. In this work, we derive an adversarial algorithm for the problem of approximating an unknown quantum pure state. Although this could be done on universal quantum computers, the adversarial formulation enables us to execute the algorithm on near-term quantum computers. Two parametrized circuits are optimized in tandem: One tries to approximate the target state, the other tries to distinguish between target and approximated state. Supported by numerical simulations, we show that resilient backpropagation algorithms perform remarkably well in optimizing the two circuits. We use the bipartite entanglement entropy to design an efficient heuristic for the stopping criterion. Our approach may find application in quantum state tomography.