Hamiltonian Quantum Generative Adversarial Networks

TL;DR

This paper introduces Hamiltonian Quantum Generative Adversarial Networks (HQuGANs), a quantum machine learning framework that uses optimal control and game theory to generate complex quantum states efficiently under realistic hardware constraints.

Contribution

The paper presents a novel quantum generative model based on Hamiltonian control and game theory, with new cost functions and convergence acceleration methods.

Findings

Successfully learned highly entangled quantum states

Demonstrated adaptability to experimental hardware constraints

Analyzed computational costs and extended to quantum dynamics learning

Abstract

We propose Hamiltonian Quantum Generative Adversarial Networks (HQuGANs), to learn to generate unknown input quantum states using two competing quantum optimal controls. The game-theoretic framework of the algorithm is inspired by the success of classical generative adversarial networks in learning high-dimensional distributions. The quantum optimal control approach not only makes the algorithm naturally adaptable to the experimental constraints of near-term hardware, but also offers a more natural characterization of overparameterization compared to the circuit model. We numerically demonstrate the capabilities of the proposed framework to learn various highly entangled many-body quantum states, using simple two-body Hamiltonians and under experimentally relevant constraints such as low-bandwidth controls. We analyze the computational cost of implementing HQuGANs on quantum computers and show how the framework can be extended to learn quantum dynamics. Furthermore, we introduce a new cost function that circumvents the problem of mode collapse that prevents convergence of HQuGANs and demonstrate how to accelerate the convergence of them when generating a pure state.