High threshold codes for neutral atom qubits with biased erasure errors

TL;DR

This paper investigates biased erasure errors in neutral atom qubits, demonstrating a higher fault-tolerance threshold for quantum error correction using the XZZX surface code and proposing a measurement-based approach optimized for this noise.

Contribution

It introduces a new noise model for neutral atom qubits, analyzes its impact on error correction thresholds, and proposes a hybrid-fusion measurement-based construction tailored for this noise.

Findings

Threshold of 8.2% for two-qubit gate errors with biased erasures

Higher threshold of 10.3% using the hybrid-fusion construction

Improved fault-tolerance without bias-preserving gates

Abstract

The requirements for fault-tolerant quantum error correction can be simplified by leveraging structure in the noise of the underlying hardware. In this work, we identify a new type of structured noise motivated by neutral atom qubits, biased erasure errors, which arises when qubit errors are dominated by detectable leakage from only one of the computational states of the qubit. We study the performance of this model using gate-level simulations of the XZZX surface code. Using the predicted erasure fraction and bias of metastable $^{171}$Yb qubits, we find a threshold of 8.2% for two-qubit gate errors, which is 1.9 times higher than the threshold for unbiased erasures, and 7.5 times higher than the threshold for depolarizing errors. Surprisingly, the improved threshold is achieved without bias-preserving controlled-not gates, and instead results from the lower noise entropy in this model. We also introduce an XZZX cluster state construction for measurement-based error correction, hybrid-fusion, that is optimized for this noise model. By combining fusion operations and deterministic entangling gates, this construction preserves the intrinsic symmetry of the XZZX code, leading to a higher threshold of 10.3% and enabling the use of rectangular codes with fewer qubits. We discuss a potential physical implementation using a single plane of atoms and moveable tweezers.