Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays

TL;DR

This paper introduces a qubit encoding and gate protocol for alkaline earth Rydberg atom arrays that converts physical errors into erasures, significantly improving fault-tolerance thresholds and logical error rates in quantum computing.

Contribution

It proposes a novel erasure conversion method for ${}^{171}$Yb neutral atom qubits, enhancing error correction efficiency and threshold in quantum computing.

Findings

98% of errors can be converted into erasures

Surface code threshold increased from 0.937% to 4.15%

Faster decrease in logical error rate near threshold

Abstract

Executing quantum algorithms on error-corrected logical qubits is a critical step for scalable quantum computing, but the requisite numbers of qubits and physical error rates are demanding for current experimental hardware. Recently, the development of error correcting codes tailored to particular physical noise models has helped relax these requirements. In this work, we propose a qubit encoding and gate protocol for ${}^{171}$Yb neutral atom qubits that converts the dominant physical errors into erasures, that is, errors in known locations. The key idea is to encode qubits in a metastable electronic level, such that gate errors predominantly result in transitions to disjoint subspaces whose populations can be continuously monitored via fluorescence. We estimate that 98% of errors can be converted into erasures. We quantify the benefit of this approach via circuit-level simulations of the surface code, finding a threshold increase from 0.937% to 4.15%. We also observe a larger code distance near the threshold, leading to a faster decrease in the logical error rate for the same number of physical qubits, which is important for near-term implementations. Erasure conversion should benefit any error correcting code, and may also be applied to design new gates and encodings in other qubit platforms.