Discovering highly efficient low-weight quantum error-correcting codes with reinforcement learning

TL;DR

This paper introduces a reinforcement learning-based method to discover low-weight quantum error-correcting codes, significantly reducing physical qubit overhead and advancing practical fault-tolerant quantum computing.

Contribution

It presents a novel, efficient RL approach for stabilizer code weight reduction, outperforming existing methods and enabling more feasible quantum error correction implementations.

Findings

Reinforcement learning produces low-weight codes with improved performance.

Achieves 10-100x reduction in qubit overhead for certain codes.

Extends code parameters beyond previous small-distance limitations.

Abstract

The realization of scalable fault-tolerant quantum computing is expected to hinge on quantum error-correcting codes. In the quest for more efficient quantum fault tolerance, a critical code parameter is the weight of measurements that extract information about errors to enable error correction: as higher measurement weights require higher implementation costs and introduce more errors, it is important in code design to optimize measurement weight. This underlies the surging interest in quantum low-density parity-check (qLDPC) codes, the study of which has primarily focused on the asymptotic (large-code-limit) properties. In this work, we introduce a versatile and computationally efficient approach to stabilizer code weight reduction based on reinforcement learning (RL), which produces new low-weight codes that substantially outperform the state of the art in practically relevant parameter regimes, extending significantly beyond previously accessible small distances. For example, our approach demonstrates savings in physical qubit overhead compared to existing results by 1 to 2 orders of magnitude for weight 6 codes and brings the overhead into a feasible range for near-future experiments. We also investigate the interplay between code parameters using our RL framework, offering new insights into the potential efficiency and power of practically viable coding strategies. Overall, our results demonstrate how RL can effectively advance the crucial yet challenging problem of quantum code discovery and thereby facilitate a faster path to the practical implementation of fault-tolerant quantum technologies.