Code Deformation and Lattice Surgery Are Gauge Fixing

TL;DR

This paper unifies lattice surgery and code deformation under the gauge fixing framework, providing a rigorous method for fault-tolerance in quantum error correction with practical examples.

Contribution

It shows that lattice surgery and code deformation are special cases of gauge fixing, offering a new, unified perspective and testing approach for fault-tolerant quantum operations.

Findings

Gauge fixing encompasses lattice surgery and code deformation.

Numerical validation confirms the method's accuracy.

Some examples based on the surface code are novel.

Abstract

The large-scale execution of quantum algorithms requires basic quantum operations to be implemented fault-tolerantly. The most popular technique for accomplishing this, using the devices that can be realised in the near term, uses stabilizer codes which can be embedded in a planar layout. The set of fault-tolerant operations which can be executed in these systems using unitary gates is typically very limited. This has driven the development of measurement-based schemes for performing logical operations in these codes, known as lattice surgery and code deformation. In parallel, gauge fixing has emerged as a measurement-based method for performing universal gate sets in subsystem stabilizer codes. In this work, we show that lattice surgery and code deformation can be expressed as special cases of gauge fixing, permitting a simple and rigorous test for fault-tolerance together with simple guiding principles for the implementation of these operations. We demonstrate the accuracy of this method numerically with examples based on the surface code, some of which are novel.