Exploring fixed points and eigenstates of quantum systems with reinforcement learning
Year: 2026
Type: article
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 that can be exploited to restrict learning to specific symmetry sectors. Finally, we discuss the possibility of postselecting high-fidelity states even when full convergence has not been reached.
Source: Physical Review Research
DOI: 10.1103/vl66-7flb
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,625
Funders: European Commission, Agence Nationale de la Recherche, Federación Española de Enfermedades Raras, Centre National de la Recherche Scientifique, Junta de Andalucía, European Regional Development Fund, Agencia Estatal de Investigación, Institut National de Physique Nucléaire et de Physique des Particules
OpenAlex ID: W4416600005