Quantum Many-body Simulations from a Reinforcement-Learned Exponential Ansatz

Abstract: Solving for the many-body wavefunction represents a significant challenge on both classical and quantum devices because of the exponential scaling of the Hilbert space with system size. While the complexity of the wavefunction can be reduced through conventional ans\"{a}tze (e.g., the coupled cluster ansatz), it can still grow rapidly with system size even on quantum devices. An exact, universal two-body exponential ansatz for the many-body wavefunction has been shown to be generated from the solution of the contracted Schr\"odinger equation (CSE), and recently, this ansatz has been implemented without classical approximation on quantum simulators and devices for the scalable simulation of many-body quantum systems. Here we combine the solution of the CSE with a form of artificial intelligence known as reinforcement learning (RL) to generate highly compact circuits that implement this ansatz without sacrificing accuracy. As a natural extension of CSE, we reformulate the wavefunction update as a Markovian decision process and train the agent to select the optimal actions at each iteration based upon only the current CSE residual. Compact circuits with high accuracy are achieved for H3 and H4 molecules over a range of molecular geometries.