Fault-Tolerant Quantum Computation with Adversarial Errors

• URL: http://arxiv.org/abs/2608.16857v1
• Date: Mon, 17 Aug 2026 17:40:14 GMT
• Title: Fault-Tolerant Quantum Computation with Adversarial Errors
• Abstract summary: We prove a fault-tolerance theorem for quantum computation against adversarial noise.<n>For every quantum circuit on $barN$ logical qudits depth $barT$, we construct a fault-tolerant circuit.<n>Our result demonstrates that fault-tolerant quantum computation remains possible under noise models that are global, worst-case, and non-Markovian.
• Score: 5.5438676149999075
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We prove a fault-tolerance theorem for quantum computation against adversarial noise. For every quantum circuit on $\bar{N}$ logical qudits of depth $\bar{T}$, we construct a fault-tolerant circuit on $N=\text{poly}(\bar{N})$ physical qudits of depth $\bar{T}\cdot\bar{N}^{o(1)}$, 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.

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