Auditing Structured Randomness for Quantum Error Correction under a Bounded Cloud Fault Model

Abstract

Cloud quantum processors compile submitted quantum error correction circuits and may colocate them with untrusted workloads. A fixed public encoder gives a fault-injection adversary a reusable target. Per-run reseeding changes the physical-to-logical fault map. Exact Haar-random encoders have exponential circuit cost. Efficient random ensembles provide average-moment guarantees and leave worst-case accepted corruption uncharacterized. We define accepted logical disturbance, an acceptance-weighted measure of harmful logical action in accepted results, and derive its exact Haar expectation. We evaluate a polynomial-cost seeded Clifford encoder family using dense linear algebra and gate-level stabilizer simulation against faults chosen before or after the encoder is known. Reseeding reduces mean accepted logical disturbance from 0.150 for faults chosen after learning each encoder to 0.020 for one fault chosen before it is known. The 86.7% reduction results from rejection. The fixed distance-three \([[5,1,3]]\) code corrects every tested weight-one Pauli, while 18.5% of sampled encoders in the selected ensemble satisfy exact quantum error correction. The measured reduction quantifies the integrity gain from reseeding and separates postselected detection from exact correction under explicit fault and attacker-knowledge models.