[Submitted on 21 Nov 2025] (cross-list from quant-ph)
Exploring fixed points and eigenstates of quantum systems with reinforcement learning
María Laura Olivera-Atencio🇪🇸 · Jesús Casado-Pascual🇪🇸 · Denis Lacroix🇫🇷
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.
- Comments:
- 19 pages, 11 figures
- Subjects:
- Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el); Nuclear Theory (nucl-th)
- arXiv:
- 2511.17491 [pdf]