Reinforcement Learning Assisted Quantum Simulation of Many-Body Excited States and Real-Time Dynamics

TL;DR

This paper extends reinforcement learning quantum algorithms to efficiently simulate excited states and real-time dynamics of many-fermion systems, achieving high accuracy with fewer operators.

Contribution

It generalizes the RL-CQE algorithm to excited states and dynamics, introducing scalable state representations and demonstrating improved robustness and efficiency.

Findings

Achieved chemical accuracy with minimal operator counts

Extended sign-free qubit operator equivalence to excited states

Demonstrated robustness across various bond lengths

Abstract

The computation of electronic excited states and real-time quantum dynamics of many-fermion systems is among the most promising applications of near-term quantum computing. In this work, we generalize the reinforcement learning contracted quantum eigensolver (RL-CQE), previously developed for ground-state problems, to electronic excited states and real-time quantum dynamics, in which a deep Q-network agent adaptively selects the two-body operators at each iteration, yielding more compact ans\"{a}tze and improved robustness with respect to critical hyperparameters. A key feature of the algorithm is a scalable state representation based on the ACSE residuals, whose dimension grows with the one-particle basis but remains independent of the number of targeted excited states. We also verify the equivalence of sign-free qubit operators in the excited-state setting, extending a result previously established for ground-state problems. Our RL-CQE for time evolution derives from a constant-scaling ansatz that represents the wave function with a fixed number of unitary transformations independent of simulation time $t$, enabled by the shared unitary structure of the purified ensemble treatment of excited states. Benchmarks on chemical systems demonstrate chemical accuracy with minimal operator counts across a range of bond lengths.