Low-overhead fault-tolerant quantum computation by gauging logical operators

TL;DR

This paper introduces a flexible, low-overhead method for fault-tolerant logical measurement in quantum error-correcting codes by gauging logical operators as symmetries, reducing qubit overhead.

Contribution

It presents a novel gauging-based measurement technique that achieves near-linear qubit overhead and adapts to arbitrary quantum codes, improving fault-tolerance efficiency.

Findings

Qubit overhead is linear in the operator weight up to polylogarithmic factors.

The gauging measurement procedure is highly flexible and adaptable.

The approach enhances the practicality of fault-tolerant quantum computation.

Abstract

Quantum computation must be performed in a fault-tolerant manner to be realizable in practice. Recent progress has uncovered quantum error-correcting codes with sparse connectivity requirements and constant qubit overhead. Existing schemes for fault-tolerant logical measurement do not always achieve low qubit overhead. Here we present a low-overhead method to implement fault-tolerant logical measurement in a quantum error-correcting code by treating the logical operator as a symmetry and gauging it. The gauging measurement procedure introduces a high degree of flexibility that can be leveraged to achieve a qubit overhead that is linear in the weight of the operator being measured up to a polylogarithmic factor. This flexibility also allows the procedure to be adapted to arbitrary quantum codes. Our results provide a new, more efficient, approach to performing fault-tolerant quantum computation, making it more tractable for near-term implementation.