Fragility of Magic State Distillation under Imperfect Measurements

Abstract

Magic state distillation (MSD) is the leading approach to generate the non-Clifford resources required for universal fault-tolerant quantum computation. While most analyses assume ideal measurements in the distillation process, this assumption breaks down on near-term hardware where measurement fidelity remains limited and large quantum error-correcting codes are unavailable. Here we establish a general framework to analyze MSD under imperfect measurements, and reveal a sharp threshold phenomenon that differs from previous known threshold on input state error: Below a critical measurement strength, MSD loses its distillation power entirely, whereas above the threshold, the \textit{target states} are at most first-order biased and the \textit{distillation efficiency} is reduced to linear, leading to exponentially higher distillation overheads. To mitigate this fragility, we present a universal method to maximize MSD robustness against imperfect measurements by choosing stabilizer generators in standard form, which applies to all known protocols without incurring additional costs. Our work reveal fundamental constraints on MSD protocols with measurement noise and provide insights for designing practically robust distillation protocols in the near-term era of quantum hardware.