Error Thresholds for Abelian Quantum Double Models: Increasing the bit-flip Stability of Topological Quantum Memory

TL;DR

This paper demonstrates that topological quantum memories using qudits have higher error thresholds and increased resilience to noise compared to qubit-based systems, potentially improving quantum error correction.

Contribution

It provides numerical evidence that abelian quantum double models with qudits have higher error thresholds, approaching the hashing bound, enhancing quantum memory stability.

Findings

Qudit-based topological quantum memories exhibit higher error thresholds.

Error thresholds approach the hashing bound.

Qudit systems offer increased noise resilience for quantum error correction.

Abstract

Current approaches for building quantum computing devices focus on two-level quantum systems which nicely mimic the concept of a classical bit, albeit enhanced with additional quantum properties. However, rather than artificially limiting the number of states to two, the use of d-level quantum systems (qudits) could provide advantages for quantum information processing. Among other merits, it has recently been shown that multi-level quantum systems can offer increased stability to external disturbances - a key problem in current technologies. In this study we demonstrate that topological quantum memories built from qudits, also known as abelian quantum double models, exhibit a substantially increased resilience to noise. That is, even when taking into account the multitude of errors possible for multi-level quantum systems, topological quantum error correction codes employing qudits can sustain a larger error rate than their two-level counterparts. In particular, we find strong numerical evidence that the thresholds of these error-correction codes are given by the hashing bound. Considering the significantly increased error thresholds attained, this might well outweigh the added complexity of engineering and controlling higher dimensional quantum systems.