arXiv:2611.13174 · v1
How wide must an eavesdropper be? Leakage of a toric-code logical bit to a strip and the Nishimori point
摘要
Fault-tolerant quantum computers hand pieces of each logical qubit to separate decoder modules and shared readout lines. How much does a piece reveal? We prove that for any region and any Pauli noise, including correlated noise, an observer's optimal advantage in learning a logical bit is exactly 1 - 2 P_fail, where P_fail is the failure probability of maximum-likelihood decoding confined to that region. Two lessons follow. Geometry, not noise, provides the protection: a region that misses a single column of the code learns exactly nothing at any noise level, while a region that spans the code is protected by noise only at impractical distances (d > 350 for one row at a 10^-3 flip rate). And width is a poor guide to risk: under i.i.d. noise a two-row strip learns exactly as little as one row, yet below threshold an eavesdropper needs a width growing only as ln d. Through the identity, the strip's operational threshold is the Nishimori point of the random-bond Ising model, and a Walsh-Hadamard transfer matrix up to width 16 locates it to within a few thousandths. On two IBM Heron processors (d = 3, 5), an emulated strip adversary shows the predicted jump at width three, and non-uniform qubit errors let a trained attacker profit from the second row that uniform noise makes useless. We turn these results into design rules for partitioned decoding and multiplexed readout. Code and data are included.
作者备注：19 pages, 4 figures, 11 tables. Code, data, IBM Quantum shot records, transpiled circuits and calibration snapshots in ancillary files. Prepared with AI assistance; see "Use of AI tools"