Tensor network simulator of the surface code in the presence of noisy syndromes

The performance of the surface code (SC) is usually estimated under Pauli errors, as they can be efficiently simulated using the stabilizer formalism. However, Pauli errors do not reflect the actual decoherence mechanisms that physical qubits undergo, which may negatively impact the predictions about the code performance in actual experiments. Here we present a tensor network simulator of the SC subject to arbitrary physical local noise [1], such as relaxation and dephasing, and always present ZZ interactions. Our simulation includes not only noisy data qubits, but also noisy syndrome qubits resulting in imperfect parity measurements. The simulator is exact for small surface code distances, and relies on approximate contraction techniques to extend the result to larger patches. We derive logical error rates on SC implemented in cirQED architectures.

[1] A. Darmawan, D. Poulin, PRL 119, 040502 (2017)