Solving for the many-body wave function 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 wave function can be reduced through conventional Ansätze (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 wave function has been shown to be generated from the solution of the contracted Schrödinger 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 to generate highly compact circuits that implement this Ansatz without sacrificing accuracy. As a natural extension of the CSE, we reformulate the wave-function 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 ${\mathrm{H}}_3$ and ${\mathrm{H}}_4$ molecules over a range of molecular geometries.

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• Machine learning
• Quantum computing models
• Density matrix methods
• Electron-correlation calculations