Teacher Distillation Limits in Reinforcement Learning for Scalable Quantum Error Correction
Carlos Garcia, Tanaka Hiroshi, Rodriguez Luis
The scalability of fault-tolerant quantum computing is fundamentally bottlenecked by the real-time decoding problem, wherein quantum error correction (QEC) syndromes must be processed within microsecond latency windows to prevent the exponential accumulation of errors. Reinforcement Learning (RL) has emerged as a promising approach to discovering optimal decoding policies, yet high-capacity RL models inevitably fail to meet the stringent latency constraints of near-term superconducting and ion-trap quantum architectures. In this work, we pedagogically analyze the information-theoretic limits of policy distillation—transferring the knowledge of a slow, high-accuracy teacher decoder (e.g., Minimum Weight Perfect Matching or an over-parameterized RL agent) into a fast, lightweight student neural network. We establish analytical bounds on the distillation efficiency using the Kullback-Leibler (KL) divergence between teacher and student policies, demonstrating how the student's capacity restricts the maximum achievable logical fidelity. We present a rigorous evaluation on surface codes under circuit-level noise, revealing a fundamental trade-off between the inference latency of the student network and its asymptotic threshold. Our findings provide a theoretical framework for designing maximally efficient student decoders that operate within the strict real-time constraints of scalable quantum processors.
•Jul 21, 2026•0 citations