Automatic spin-chain learning to explore the quantum speed limit

TL;DR

This paper demonstrates how reinforcement learning can discover optimal quantum state transfer schemes in spin chains, surpassing existing speed limits while maintaining high fidelity, thus advancing quantum control methods.

Contribution

It introduces a reinforcement learning framework for quantum state transfer, achieving faster schemes than known quantum speed limits in both time-independent and time-dependent Hamiltonian scenarios.

Findings

RL finds faster transfer schemes with high fidelity.

RL outperforms existing quantum speed limit schemes.

Deep Q-learning effectively solves quantum control problems.

Abstract

One of the ambitious goals of artificial intelligence is to build a machine that outperforms human intelligence, even if limited knowledge and data are provided. Reinforcement Learning (RL) provides one such possibility to reach this goal. In this work, we consider a specific task from quantum physics, i.e. quantum state transfer in a one-dimensional spin chain. The mission for the machine is to find transfer schemes with fastest speeds while maintaining high transfer fidelities. The first scenario we consider is when the Hamiltonian is time-independent. We update the coupling strength by minimizing a loss function dependent on both the fidelity and the speed. Compared with a scheme proven to be at the quantum speed limit for the perfect state transfer, the scheme provided by RL is faster while maintaining the infidelity below $5\times 10^{-4}$. In the second scenario where a time-dependent external field is introduced, we convert the state transfer process into a Markov decision process that can be understood by the machine. We solve it with the deep Q-learning algorithm. After training, the machine successfully finds transfer schemes with high fidelities and speeds, which are faster than previously known ones. These results show that Reinforcement Learning can be a powerful tool for quantum control problems.