Fault-tolerant Quantum Error Correction Using a Linear Array of Emitters

TL;DR

This paper introduces a fault-tolerant quantum error correction scheme using a linear array of emitters and delay lines, demonstrating how increasing emitters reduces logical error rates and analyzing the error thresholds and overhead.

Contribution

It presents a novel linear-array architecture for fault-tolerant quantum error correction that leverages emitter-photon interactions and delay lines, with detailed error analysis.

Findings

Logical error rate decreases with more emitters.

Error suppression feasible with current delay line technology.

Error scaling improves from exponential to quadratic with emitter number.

Abstract

We propose a fault-tolerant quantum error correction architecture consisting of a linear array of emitters and delay lines. In our scheme, a resource state for fault-tolerant quantum computation is generated by letting the emitters interact with a stream of photons and their neighboring emitters. Depending on the number of emitters $n_e$, we study the effect of delay line errors in two regimes: when $n_e$ is a small constant of order unity and when $n_e$ scales with the code distance. Between these two regimes, the logical error rate steadily decreases as $n_e$ increases, from a scaling of $\exp(-c\eta^{-1/2})$ to $\exp(-c'\eta^{-1})$, where $\eta$ is the error rate per unit length in the delay line, for some constants $c,c'>0$. We also carry out a detailed study of the break-even point and the fault-tolerance overhead. These studies suggest that the multi-emitter architecture, using the state-of-the-art delay lines, can be used to demonstrate error suppression, assuming other sources of errors are sufficiently small.