Fast fault-tolerant filtering of quantum codewords

TL;DR

This paper introduces a fast, fault-tolerant filtering method for quantum codewords that reduces measurement complexity, increases noise thresholds, and optimizes quantum error correction processes.

Contribution

It presents a novel filtering approach exploiting code structure to minimize parity check measurements, significantly enhancing fault tolerance in quantum error correction.

Findings

Increased noise threshold by an order of magnitude.

Reduced measurement steps for parity checks.

Optimized parallel logic gate network design.

Abstract

The stabilization of a quantum computer by repeated error correction can be reduced almost entirely to repeated preparation of blocks of qubits in quantum codeword states. These are multi-particle entangled states with a high degree of symmetry. The required accuracy can be achieved by measuring parity checks, using imperfect apparatus, and rejecting states which fail them. This filtering process is considered for t-error-correcting codes with t>1. It is shown how to exploit the structure of the codeword and the check matrix, so that the filter is reduced to a minimal form where each parity check need only be measured once, not > t times by the (noisy) verification apparatus. This both raises the noise threshold and also reduces the physical size of the computer. A method based on latin rectangles is proposed, which enables the most parallel version of a logic gate network to be found, for a class of networks including those used in verification. These insights allowed the noise threshold to be increased by an order of magnitude.