Error-detection-based quantum fault tolerance against discrete Pauli noise

TL;DR

This paper rigorously proves the existence of constant noise thresholds for error-detection-based quantum fault tolerance schemes, showing they can tolerate up to approximately 0.1% noise per gate, improving understanding of quantum error resilience.

Contribution

It provides the first rigorous proof of noise thresholds for error-detection-based quantum fault tolerance schemes, which were previously only supported by numerical evidence.

Findings

Proves constant noise thresholds exist for error detection schemes

Numerical lower bound on noise threshold is approximately 0.1% per gate

Demonstrates improved fault tolerance potential over previous methods

Abstract

A quantum computer -- i.e., a computer capable of manipulating data in quantum superposition -- would find applications including factoring, quantum simulation and tests of basic quantum theory. Since quantum superpositions are fragile, the major hurdle in building such a computer is overcoming noise. Developed over the last couple of years, new schemes for achieving fault tolerance based on error detection, rather than error correction, appear to tolerate as much as 3-6% noise per gate -- an order of magnitude better than previous procedures. But proof techniques could not show that these promising fault-tolerance schemes tolerated any noise at all. With an analysis based on decomposing complicated probability distributions into mixtures of simpler ones, we rigorously prove the existence of constant tolerable noise rates ("noise thresholds") for error-detection-based schemes. Numerical calculations indicate that the actual noise threshold this method yields is lower-bounded by 0.1% noise per gate.