Color code thresholds under circuit-level noise beyond the Pauli framework

TL;DR

This paper extends the analysis of quantum error correction thresholds for color codes beyond traditional Pauli noise models by incorporating more realistic non-Pauli errors using tensor network simulations, revealing deviations from simplified models.

Contribution

It introduces a method to estimate color code thresholds under non-Pauli noise models using tensor networks, surpassing the limitations of Pauli approximations.

Findings

Non-Pauli noise models increase error rates compared to Pauli twirling.

Tensor network simulations accurately estimate thresholds for codes up to distance 7.

Coherent over-rotations cause higher error rates than predicted by Pauli twirling.

Abstract

A quantum error correction code is assessed over its ability to correct errors in noisy quantum circuits. This task requires extensive simulations of faulty quantum circuits, which are often made tractable by considering stochastic Pauli noise models, as they are compatible with efficient classical simulation techniques. However, such noise models do not fully capture the variety of physical error mechanisms encountered in realistic quantum platforms. In this work, we extend circuit-level noise modeling beyond the Pauli framework by estimating the threshold of the color code under more general noise models. Specifically, we consider two representative non-Pauli error channels: a systematic $X$-rotation model that introduces coherent over-rotations, and an amplitude damping channel that captures relaxation processes. These models are incorporated at the circuit level into color code circuits using a Tree Tensor Network ansatz. Our simulations demonstrate that tensor network simulations enable accurate threshold estimation under non-Pauli noise for color codes up to distance $d=7$ (73 qubits). Comparing our results with the Pauli twirling approximations of the noise models, we find that coherent over-rotations yield systematically higher error rates, deviating from the Pauli twirling approximation as the code distance increases.