Execution-transcript privacy for fault-tolerant surface-code memories

Abstract:A fault-tolerant quantum computer runs behind a telemetry stream logging syndromes, decoder actions, resets and timing separately from the answer. Can it reveal the logical input? For a distance-$d$ rotated surface-code memory on a fixed schedule of $T=\Theta(d)$ rounds, under three stated hypotheses (sector-scalar honest backbone, transcript locality, Kotecky-Preiss smallness), the channel from logical qubit to transcript is $e^{-\Theta(d)}$-close in diamond norm to one that ignores the input. A statement of this kind follows generically from correctability-privacy duality. Anisotropy does not. Each logical axis pays the distance of its own coset, so under amplitude damping the computational-basis label is governed by the code's $Z$-distance $d_Z\ge d_{\min}$ and not by the code distance. Two codes of quantum distance $1$ make the gap concrete. A phase-flip code's $X$-syndrome transcript is exactly input-independent under unobserved damping, while a repetition code leaks at first order. A matched converse identifies the records that do expose it, among them a lattice-surgery parity readout. On a 156-qubit superconducting processor our sufficient certificate misses by $21.5\times$, so the theorem cannot be invoked there. Measured directly, a $d_Z=1$ memory's record identifies its input with total variation $\ge 0.927$ under randomised, label-balanced acquisition. Holding the code fixed and varying the damping exposure reproduces the parameter-free law, with exponent $0.85\pm0.03$ against a predicted $0.86$. Randomized encoding returns the statistic to the floor at no two-qubit-gate cost. Fault tolerance does not grant transcript privacy. It relocates it, and only to the logical state, not to the circuit's identity.

Quantum Physics (quant-ph); Cryptography and Security (cs.CR)

arXiv:2609.09334 [quant-ph]

(or arXiv:2609.09334v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.09334 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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