Hamiltonian Quantum Generative Adversarial Networks

We introduce a framework to learn quantum states using two competing quantum optimal control protocols. Inspired by the success of classical Generative Adversarial Networks (GANs) to learn high-dimensional distributions, in our proposed Hamiltonian Quantum GAN (HQuGAN), the task of learning quantum states is achieved by playing an iterative game between two competing quantum agents, a generator and a discriminator. The optimal control approach not only makes the algorithm naturally adaptable to the experimental constraints of near-term hardwares but also has the potential to provide a better convergence due to overparameterization compared to the circuit model implementations. We numerically demonstrate the capabilities of the proposed framework to learn various highly entangled many-body quantum states, using two-body Hamiltonians and under experimentally relevant constraints such as low-bandwidth control. We analyze the computational cost of implementing HQuGAN on quantum computers, and show how the framework can be extended to learn quantum dynamics.