Physical Review Research (Jul 2024)

Hamiltonian quantum generative adversarial networks

  • Leeseok Kim,
  • Seth Lloyd,
  • Milad Marvian

DOI
https://doi.org/10.1103/PhysRevResearch.6.033019
Journal volume & issue
Vol. 6, no. 3
p. 033019

Abstract

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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 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.