Exploring fixed points and eigenstates of quantum systems with reinforcement learning

• URL: http://arxiv.org/abs/2511.17491v1
• Date: Fri, 21 Nov 2025 18:48:46 GMT
• Title: Exploring fixed points and eigenstates of quantum systems with reinforcement learning
• Authors: María Laura Olivera-Atencio, Jesús Casado-Pascual, Denis Lacroix,
• Abstract summary: We introduce a reinforcement learning algorithm designed to identify the fixed points of a given quantum operation.<n>The method iteratively constructs the unitary transformation that maps the computational basis onto the basis of fixed points.<n>In cases where the operation corresponds to a Hamiltonian evolution, this task reduces to determining the Hamiltonian eigenstates.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a reinforcement learning algorithm designed to identify the fixed points of a given quantum operation. The method iteratively constructs the unitary transformation that maps the computational basis onto the basis of fixed points through a reward-penalty scheme based on quantum measurements. In cases where the operation corresponds to a Hamiltonian evolution, this task reduces to determining the Hamiltonian eigenstates. The algorithm is first benchmarked on random Hamiltonians acting on two and three qubits and then applied to many-body systems of up to six qubits, including the transverse-field Ising model and the all-to-all pairing Hamiltonian. In both cases, the algorithm is demonstrated to perform successfully; in the pairing model, it can also reveal hidden symmetries, which can be exploited to restrict learning to specific symmetry sectors. Finally, we discuss the possibility of post-selecting high-fidelity states even when full convergence has not been reached.

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