Discovering highly efficient low-weight quantum error-correcting codes
  with reinforcement learning
Authors: name: Austin Yubo He, name: Zi-Wen Liu

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.