Fidelity-Driven Physically Constrained Adaptive Code Distance for Surface Codes under Biased Circuit-Level Noise

Abstract

Surface codes are leading candidates for fault-tolerant quantum computing, but conventional implementations use fixed code distances that result in conservative resource allocation during varying noise conditions. We propose a physically-constrained, fidelity-driven adaptive surface code framework that dynamically adjusts code distance at scheduled intervals to maintain target logical fidelity while minimizing resource overhead. Our approach introduces a syndrome-based logical error rate estimation algorithm using rolling-window statistics, a scheduled adaptation policy operating within pre-allocated qubit pools, and detailed modeling of adaptation latency and reconfiguration-induced errors for superconducting qubit devices. Through large-scale Monte Carlo simulations under realistic biased circuit-level noise, we demonstrate that hardware-constrained adaptive codes achieve 43-62% success rate improvements over fixed-distance strategies, reaching 72-82% success rates compared to 5̃0% for fixed approaches. Oracle adaptive strategies with perfect error knowledge achieve 91-94% success rates, indicating substantial theoretical potential. Our results show that adaptive surface codes provide significant performance improvements even under realistic hardware constraints, with oracle strategies consuming only 37% of maximum resources while achieving 86% higher success rates for shorter circuits.