Adversarial quantum circuit learning for pure state approximation
This work addresses quantum state approximation for applications like quantum state tomography, but it is incremental as it adapts existing adversarial learning concepts to quantum computing.
The authors tackled the problem of approximating an unknown quantum pure state by developing an adversarial algorithm that can run on near-term quantum computers, using two parametrized circuits optimized with resilient backpropagation and a heuristic based on bipartite entanglement entropy for stopping.
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.