Fault Tolerance in Parity-State Linear Optical Quantum Computing

TL;DR

This paper analyzes the noise threshold and resource needs for a linear optical quantum computing scheme using parity-state encoding, demonstrating significant resource savings at the expense of a slightly lower noise threshold.

Contribution

It introduces a combined analytical and numerical approach to evaluate a parity-state encoding scheme with error correction, showing substantial resource efficiency improvements.

Findings

Achieves approximately 1000x resource savings compared to previous schemes.

Uses parity-state encoding at the lowest level of concatenation for error correction.

Finds a trade-off between resource efficiency and noise threshold.

Abstract

We use a combination of analytical and numerical techniques to calculate the noise threshold and resource requirements for a linear optical quantum computing scheme based on parity-state encoding. Parity-state encoding is used at the lowest level of code concatenation in order to efficiently correct errors arising from the inherent nondeterminism of two-qubit linear-optical gates. When combined with teleported error-correction (using either a Steane or Golay code) at higher levels of concatenation, the parity-state scheme is found to achieve a saving of approximately three orders of magnitude in resources when compared to a previous scheme, at a cost of a somewhat reduced noise threshold.