Efficient Simulation of Leakage Errors in Quantum Error Correcting Codes Using Tensor Network Methods

TL;DR

This paper introduces a tensor network-based simulation method for leakage errors in quantum error correcting codes, enabling efficient analysis of large systems and realistic noise models without approximations.

Contribution

The authors develop a novel tensor network approach using MPS to simulate leakage errors in QECCs efficiently, capturing realistic noise and removal strategies for large-scale systems.

Findings

Leakage removal significantly improves code performance.

The method accurately models leakage in large qubit systems.

Large code distances benefit from effective leakage mitigation.

Abstract

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 $3\times d$ 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.