Subsystem Spacetime Code
Abstract
Quantum error-correcting codes provide a powerful framework for analyzing and designing fault-tolerant Clifford circuits. In this work, we construct the subsystem spacetime code and use it to characterize the distances of Clifford circuits. We show that its gauge group can be explicitly constructed and classified using the masking properties of the instantaneous stabilizer groups and consists precisely of faults that are harmless to the circuit. We use this framework to identify where a dynamical code loses distance and to analyze how the fault distance changes when circuits are composed from smaller components. Our results provide a versatile tool for analyzing and designing fault-tolerant circuits, with potential applications to the construction of new dynamical codes.
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BibTeX
@misc{fu2026subsystem,
title = {{Subsystem Spacetime Code}},
author = {Esther Xiaozhen Fu and Aranya Chakraborty and Daniel Gottesman},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40357},
eprint = {2610.40357},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40357},
}
RIS
TY - UNPB
TI - Subsystem Spacetime Code
AU - Esther Xiaozhen Fu
AU - Aranya Chakraborty
AU - Daniel Gottesman
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40357
UR - https://arxiv.org/abs/2610.40357
AB - Quantum error-correcting codes provide a powerful framework for analyzing and designing fault-tolerant Clifford circuits. In this work, we construct the subsystem spacetime code and use it to characterize the distances of Clifford circuits. We show that its gauge group can be explicitly constructed and classified using the masking properties of the instantaneous stabilizer groups and consists precisely of faults that are harmless to the circuit. We use this framework to identify where a dynamical code loses distance and to analyze how the fault distance changes when circuits are composed from smaller components. Our results provide a versatile tool for analyzing and designing fault-tolerant circuits, with potential applications to the construction of new dynamical codes.
ER -