Incoherent approximation for two-level system defects in quantum error correctionsimulations

Two-level system (TLS) defects are one of the dominant loss mechanisms in

superconducting-transmon processors. The frequencies of these defects can change over

time, leading to fluctuations in the qubit relaxation times [1]. Quantum error correction

(QEC) typically assumes constant physical error rates, and the impact TLS defects may

have on the code performance remains unexplored. However, including even a few TLS

defects in fully quantum QEC simulations significantly limits the codes and distances that

can be explored. The Random Phase Approximation (RPA) [2] can reduce the

computational overhead required to simulate TLS defects, assuming that the interactions

between the qubits and the defects are incoherent. We explore the validity of this

approximation for different TLS defect parameter regimes and under the repeated

measurement of the stabilizers of the code. Furthermore, we investigate the accuracy with

which the RPA captures the logical performance of small-distance codes in the presence

of TLS defects.

[1] P. V. Klimov et al., Phys. Rev. Lett. 121, 090502 (2018)

[2] J. Marshall et al., arXiv 2312.10277 (2023)