Resource costs for fault-tolerant linear optical quantum computing

TL;DR

This paper quantifies the high resource costs of fault-tolerant linear optical quantum computing using a surface code protocol, highlighting the significant hardware overheads and key factors affecting scalability.

Contribution

It provides a detailed resource cost analysis for LOQC with a specific surface code protocol, revealing the substantial hardware overheads compared to matter-based systems.

Findings

Resource requirements are at least five orders of magnitude higher than matter-based systems.

Resource costs increase significantly with photon loss rates above 1 in 1000.

Switch performance critically impacts resource scaling.

Abstract

Linear optical quantum computing (LOQC) seems attractively simple: information is borne entirely by light and processed by components such as beam splitters, phase shifters and detectors. However this very simplicity leads to limitations, such as the lack of deterministic entangling operations, which are compensated for by using substantial hardware overheads. Here we quantify the resource costs for full scale LOQC by proposing a specific protocol based on the surface code. With the caveat that our protocol can be further optimised, we report that the required number of physical components is at least five orders of magnitude greater than in comparable matter-based systems. Moreover the resource requirements grow higher if the per-component photon loss rate is worse than one in a thousand, or the per-component noise rate is worse than $10^{-5}$. We identify the performance of switches in the network as the single most influential factor influencing resource scaling.