Simulation of thermal-relaxation noise for quantum error correction

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-correcting codes. In this work, we develop an exact stabilizer model without variance overhead for qubit thermal-relaxation noise when T 2 ⩽ T 1 . We show that the combined amplitude damping and dephasing channel admits a fully positive Clifford and reset decomposition that enables efficiency in this regime. For T 2 > T 1 , the resulting decomposition is negative, but the same technique serves to reduce the overhead versus independent channels. We further introduce an approximated error channel with reset for the T 2 > T 1 regime 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.