Exploring fixed points and eigenstates of quantum systems with reinforcement learning

TL;DR

This paper presents a reinforcement learning algorithm that identifies fixed points and eigenstates of quantum systems, effectively handling complex many-body models and revealing hidden symmetries.

Contribution

The authors introduce a novel RL method for quantum fixed points, capable of handling many-body systems and uncovering symmetries, advancing quantum state analysis techniques.

Findings

Successfully applied to random Hamiltonians of 2-3 qubits

Effectively analyzed many-body systems up to 6 qubits

Revealed hidden symmetries in pairing models

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.