Hamiltonian Quantum Generative Adversarial Networks

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 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 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

On the Moments of the Number of Hires in the Assistant Hiring Algorithm

We find closed-form expressions for the variance and the third moment of the number of hires in the assistant hiring algorithm, as well as asymptotic values for higher moments of this variable

On the Moments of the Number of Hires in the Assistant Hiring Algorithm

We find closed-form expressions for the variance and the third moment of the number of hires in the assistant hiring algorithm, as well as asymptotic values for higher moments of this variable