Exact and Efficient Stabilizer Simulation of Thermal-Relaxation Noise for Quantum Error Correction

TL;DR

This paper introduces an exact, stabilizer-compatible model for simulating thermal relaxation noise in quantum error correction, improving accuracy over traditional approximations and enabling better decoder training.

Contribution

It develops a fully positive decomposition of thermal relaxation noise into Clifford operations for T2 ≤ T1 and proposes an approximate model with higher fidelity and reduced negativity.

Findings

The model accurately captures thermal relaxation effects in large surface and bicycle codes.

The decomposition is positive when T2 ≤ T1, enabling efficient simulation.

The approximate channel reduces negativity and improves fidelity over PTA.

Abstract

Stabilizer-based simulation of quantum error-correcting codes typically relies on the Pauli-twirling approximation (PTA) to render non-Clifford noise classically tractable, but PTA can distort the behavior of physically relevant channels such as thermal relaxation. Physically accurate noise simulation is needed to train decoders and understand the noise suppression capabilities of quantum error correction codes. In this work, we develop an exact and stabilizer-compatible model of qubit thermal relaxation noise and show that the combined amplitude damping and dephasing channel admits a fully positive probability decomposition into Clifford operations and reset whenever $T_2 \leqslant T_1$. For $T_2 > T_1$, the resulting decomposition is negative, but allows a smaller sampling overhead versus independent channels. We further introduce an approximated error channel with reset that removes the negativity of the decomposition while achieving higher channel fidelity to the true thermal relaxation than PTA, and extend our construction to finite temperature relaxation. We apply the exact combined model to investigate large surface codes and bivariate bicycle codes on superconducting platforms with realistic thermal relaxation error. The differing logical performances across code states further indicate that noise-model-informed decoders will be essential for accurately capturing thermal-noise structure in future fault-tolerant architectures.