Fault-Tolerant Quantum Computation with Adversarial Errors
Abstract
We prove a fault-tolerance theorem for quantum computation against adversarial noise. For every quantum circuit on N̅ logical qudits of depth T̅, we construct a fault-tolerant circuit on N=poly(N̅) physical qudits of depth T̅·N̅o(1), which is robust against an adversary who may arbitrarily choose and corrupt an almost-linear number N1−o(1) of physical qudits at each time step. This robustness significantly improves upon prior fault-tolerance theorems, which assumed corruptions were either local and stochastic, or else only act on a polynomially vanishing fraction of qudits. Our fault-tolerance scheme addresses a key bottleneck towards constructing quantum PCPs via the circuit-to-Hamiltonian mapping of Anshu, Breuckmann, and Nguyen (STOC'24). More fundamentally, our result demonstrates that fault-tolerant quantum computation remains possible under noise models that are global, worst-case, and non-Markovian over the full duration of the computation, directly countering concerns that correlated noise could fundamentally undermine quantum fault tolerance. Our construction is based on a new family of subsystem product codes we develop, which have large dimension and distance along with low-weight parity-checks, and which support transversal non-Clifford gates. We show how to perform single-shot fault-tolerant error correction on these codes using a Floquet-like procedure based on the local testability of classical tensor codes. We then obtain a universal fault-tolerance scheme using repeated code switching in a hypercubic qudit architecture. Finally, we recursively compose our scheme with itself to reduce an initially exponential qudit dimension down to a constant.
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BibTeX
@misc{breuckmann2026faulttolerant,
title = {{Fault-Tolerant Quantum Computation with Adversarial Errors}},
author = {Nikolas P. Breuckmann and Louis Golowich and Umesh Vazirani},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.16857},
eprint = {2608.16857},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.16857},
}
RIS
TY - UNPB
TI - Fault-Tolerant Quantum Computation with Adversarial Errors
AU - Nikolas P. Breuckmann
AU - Louis Golowich
AU - Umesh Vazirani
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2608.16857
UR - https://arxiv.org/abs/2608.16857
AB - We prove a fault-tolerance theorem for quantum computation against adversarial noise. For every quantum circuit on N̅ logical qudits of depth T̅, we construct a fault-tolerant circuit on N=poly(N̅) physical qudits of depth T̅·N̅^o(1), which is robust against an adversary who may arbitrarily choose and corrupt an almost-linear number N^1−o(1) of physical qudits at each time step. This robustness significantly improves upon prior fault-tolerance theorems, which assumed corruptions were either local and stochastic, or else only act on a polynomially vanishing fraction of qudits. Our fault-tolerance scheme addresses a key bottleneck towards constructing quantum PCPs via the circuit-to-Hamiltonian mapping of Anshu, Breuckmann, and Nguyen (STOC'24). More fundamentally, our result demonstrates that fault-tolerant quantum computation remains possible under noise models that are global, worst-case, and non-Markovian over the full duration of the computation, directly countering concerns that correlated noise could fundamentally undermine quantum fault tolerance. Our construction is based on a new family of subsystem product codes we develop, which have large dimension and distance along with low-weight parity-checks, and which support transversal non-Clifford gates. We show how to perform single-shot fault-tolerant error correction on these codes using a Floquet-like procedure based on the local testability of classical tensor codes. We then obtain a universal fault-tolerance scheme using repeated code switching in a hypercubic qudit architecture. Finally, we recursively compose our scheme with itself to reduce an initially exponential qudit dimension down to a constant.
ER -