# Reinforcement Learning in Different Phases of Quantum Control

## TL;DR

This paper demonstrates that reinforcement learning can effectively find high-fidelity quantum control protocols in complex many-body systems, performing comparably to optimal control methods and revealing a phase transition in protocol space.

## Contribution

The study introduces RL techniques for quantum state control, showing their ability to discover near-optimal protocols in complex quantum systems and uncovering a phase transition in control landscape.

## Key findings

- RL achieves high-fidelity control comparable to optimal methods
- Quantum control exhibits a spin-glass-like phase transition
- RL can find near-optimal protocols even in glassy phases

## Abstract

The ability to prepare a physical system in a desired quantum state is central to many areas of physics such as nuclear magnetic resonance, cold atoms, and quantum computing. Yet, preparing states quickly and with high fidelity remains a formidable challenge. In this work we implement cutting-edge Reinforcement Learning (RL) techniques and show that their performance is comparable to optimal control methods in the task of finding short, high-fidelity driving protocol from an initial to a target state in non-integrable many-body quantum systems of interacting qubits. RL methods learn about the underlying physical system solely through a single scalar reward (the fidelity of the resulting state) calculated from numerical simulations of the physical system. We further show that quantum state manipulation, viewed as an optimization problem, exhibits a spin-glass-like phase transition in the space of protocols as a function of the protocol duration. Our RL-aided approach helps identify variational protocols with nearly optimal fidelity, even in the glassy phase, where optimal state manipulation is exponentially hard. This study highlights the potential usefulness of RL for applications in out-of-equilibrium quantum physics.