Related papers: Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code

URL: http://arxiv.org/abs/2510.20489v2
Date: Wed, 29 Oct 2025 06:27:33 GMT
Title: Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code
Authors: Ji-Ze Xu, Yin Zhong, Miguel A. Martin-Delgado, Hao Song, Ke Liu,
Abstract summary: Three-dimensional (3D) topological codes offer the advantage of supporting fault-tolerant implementations of non-Clifford gates.<n>We show that the 3D toric code exhibits optimal thresholds of $pX,M_th approx 11%$ and $pZ,M_th approx 2%$ against bit-flip and phase-flip errors.
Score: 3.1189678982805216
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: Three-dimensional (3D) topological codes offer the advantage of supporting fault-tolerant implementations of non-Clifford gates, yet their performance against realistic noise remains largely unexplored. In this work, we focus on the paradigmatic 3D toric code and investigate its fault-tolerance thresholds in the presence of both Pauli and measurement errors. Two randomly coupled lattice gauge models that describe the code's correctability are derived, including a random 2-form $\mathbb{Z}_2$ gauge theory. By exploiting a generalized duality technique, we show that the 3D toric code exhibits optimal thresholds of $p^{X,M}_{th} \approx 11\%$ and $p^{Z,M}_{th} \approx 2\%$ against bit-flip and phase-flip errors, respectively. These threshold values show modest reductions compared to the case of perfect measurements, establishing the robustness of the 3D toric code against measurement errors. Our results constitute a substantial advance towards assessing the practical performance of 3D topological codes. This contribution is timely and in high demand, as rapid hardware advancements are bringing complex codes into experimental reach. Moreover, our work highlights the interdisciplinary nature of fault-tolerant quantum computation and holds significant interest for quantum information science, high-energy physics, and condensed matter physics.

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