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=Θ(d) rounds, under three stated hypotheses (sector-scalar honest backbone, transcript locality, Kotecky-Preiss smallness), the channel from logical qubit to transcript is e−Θ(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 dZ≥ dmin 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×, so the theorem cannot be invoked there. Measured directly, a dZ=1 memory's record identifies its input with total variation ≥ 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±0.03 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.
Related
- Fault-tolerant execution of error-corrected quantum algorithms
- C-Phase-Aware Compilation for Efficient Fault-Tolerant Quantum Execution
- Arbitrarily Loss-Tolerant Quantum Position Verification in a Single Execution
- Below-threshold execution of fault-tolerant ripple-carry addition on a trapped-ion quantum computer
- Architecting Instruction Execution for Scalable Fault-Tolerant Quantum Computing
BibTeX
@misc{shen2026executiontranscript,
title = {{Execution-transcript privacy for fault-tolerant surface-code memories}},
author = {Jiachen Shen and Hui Zhong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09334},
eprint = {2609.09334},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09334},
}
RIS
TY - UNPB
TI - Execution-transcript privacy for fault-tolerant surface-code memories
AU - Jiachen Shen
AU - Hui Zhong
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09334
UR - https://arxiv.org/abs/2609.09334
AB - 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=Θ(d) rounds, under three stated hypotheses (sector-scalar honest backbone, transcript locality, Kotecky-Preiss smallness), the channel from logical qubit to transcript is e^−Θ(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≥ 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×, so the theorem cannot be invoked there. Measured directly, a d_Z=1 memory's record identifies its input with total variation ≥ 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±0.03 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.
ER -