Exploring fixed points and eigenstates of quantum systems with reinforcement learning

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.

Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el); Nuclear Theory (nucl-th)

arXiv:2511.17491 [quant-ph]

(or arXiv:2511.17491v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2511.17491 Focus to learn more arXiv-issued DOI via DataCite

Phys. Rev. Research 8, 033087 (2026)

https://doi.org/10.1103/vl66-7flb Focus to learn more DOI(s) linking to related resources

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.