Geometrical Approach to Logical Qubit Fidelities of Neutral Atom CSS Codes

TL;DR

This paper uses a geometrical and statistical approach to predict error rate thresholds for neutral atom quantum computers implementing topological quantum error correction codes, accounting for realistic error sources.

Contribution

It introduces a novel mapping of QEC codes to a lattice gauge theory with disorder to estimate error thresholds without optimal decoding.

Findings

Predicted error rate thresholds for neutral atom quantum computers.

Quantified bounds on experimental parameters affecting fidelity.

Analyzed impact of decay, leakage, and atom loss on QEC performance.

Abstract

Encoding quantum information in a quantum error correction (QEC) code enhances protection against errors. Imperfection of quantum devices due to decoherence effects will limit the fidelity of quantum gate operations. In particular, neutral atom quantum computers will suffer from correlated errors because of the finite lifetime of the Rydberg states that facilitate entanglement. Predicting the impact of such errors on the performance of topological QEC codes is important in understanding and characterising the fidelity limitations of a real quantum device. Mapping a QEC code to a $\mathbb{Z}_2$ lattice gauge theory with disorder allows us to use Monte Carlo techniques to calculate upper bounds on error rates without resorting to an optimal decoder. In this Article, we adopt this statistical mapping to predict error rate thresholds for neutral atom architecture, assuming radiative decay to the computational basis, leakage and atom loss as the sole error sources. We quantify this error rate threshold $p_\text{th}$ and bounds on experimental constraints, given any set of experimental parameters.