Leakage errors, in which a qubit is excited to a level outside the qubit
subspace, represent a significant obstacle in the development of robust quantum
computers. We present a computationally efficient simulation methodology for
studying leakage errors in quantum error correcting codes (QECCs) using tensor
network methods, specifically Matrix Product States (MPS). Our approach enables
the simulation of various leakage processes, including thermal noise and
coherent errors, without approximations (such as the Pauli twirling
approximation) that can lead to errors in the estimation of the logical error
rate. We apply our method to two QECCs: the one-dimensional (1D) repetition
code and a thin 3×d surface code. By leveraging the small amount of
entanglement generated during the error correction process, we are able to
study large systems, up to a few hundred qudits, over many code cycles. We
consider a realistic noise model of leakage relevant to superconducting qubits
to evaluate code performance and a variety of leakage removal strategies. Our
numerical results suggest that appropriate leakage removal is crucial,
especially when the code distance is large.Comment: 14 pages, 12 figure