Toric-code logical bit leaks to a strip only past a width threshold
Original title: How wide must an eavesdropper be? Leakage of a toric-code logical bit to a strip and the Nishimori point
An emulated strip adversary on two IBM Heron processors at distance 3 and 5 showed the predicted jump at width three.
A paper proves that, for any region and any Pauli noise, an observer’s optimal advantage on a toric-code logical bit equals 1 minus twice the failure probability of maximum-likelihood decoding confined to that region. A region missing one column learns nothing at any noise level, while a spanning region is protected by noise only at large distance. Under i.i.d. noise a two-row strip matches one row, but below threshold an eavesdropper’s needed width grows only as ln d. On two IBM Heron processors at distance 3 and 5, an emulated strip adversary showed the predicted jump at width three.
Unconfirmed: Hardware results use an emulated strip adversary on distance-3 and distance-5 devices, not a deployed quantum computer attack.
- The strip’s operational threshold is identified with the Nishimori point of the random-bond Ising model.
- A Walsh-Hadamard transfer matrix up to width 16 locates that point to within a few thousandths.
- Non-uniform qubit errors let a trained attacker use a second row that uniform noise makes useless.
- The authors turn the results into rules for partitioned decoding and multiplexed readout.
From the original article
1 min read at arxiv.orgFault-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.
By Konstantinos Karagiannis · arxiv.org
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