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

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.