Coping with qubit leakage in topological codes

TL;DR

This paper investigates how qubit leakage affects topological quantum error correction, demonstrating that leakage causes significant errors but can be mitigated with simple additional circuitry to restore code performance.

Contribution

It analyzes the impact of leakage-induced errors on topological codes and proposes a practical circuitry solution to mitigate these effects.

Findings

Leakage causes time-correlated errors in topological codes.

A threshold error rate still exists despite leakage.

Additional circuitry restores error correction performance.

Abstract

Many physical systems considered promising qubit candidates are not, in fact, two-level systems. Such systems can leak out of the preferred computational states, leading to errors on any qubits that interact with leaked qubits. Without specific methods of dealing with leakage, long-lived leakage can lead to time-correlated errors. We study the impact of such time-correlated errors on topological quantum error correction codes, which are considered highly practical codes, using the repetition code as a representative case study. We show that, under physically reasonable assumptions, a threshold error rate still exists, however performance is significantly degraded. We then describe simple additional quantum circuitry that, when included in the error detection cycle, restores performance to acceptable levels.