Single-shot fault-tolerant quantum error correction

TL;DR

This paper demonstrates that certain topological quantum codes can achieve fault-tolerance with only a single round of local measurements, enabling faster quantum error correction and potentially constant-time logical operations.

Contribution

It introduces the concept of single-shot fault-tolerant quantum error correction using 3D gauge color codes, simplifying error detection and correction processes.

Findings

Single-shot error correction is possible with specific topological codes.

3D gauge color codes enable fault-tolerant quantum computing with constant-time logical operations.

The approach leverages self-correction and confinement phenomena in quantum Hamiltonian models.

Abstract

Conventional quantum error correcting codes require multiple rounds of measurements to detect errors with enough confidence in fault-tolerant scenarios. Here I show that for suitable topological codes a single round of local measurements is enough. This feature is generic and is related to self-correction and confinement phenomena in the corresponding quantum Hamiltonian model. 3D gauge color codes exhibit this single-shot feature, which applies also to initialization and gauge-fixing. Assuming the time for efficient classical computations negligible, this yields a topological fault-tolerant quantum computing scheme where all elementary logical operations can be performed in constant time.