Code deformation and lattice surgery are gauge fixing

Journal article (2019)

Authors

C. Vuillot QCD/Terhal Group - QuTech Advanced Research Centre , QuTech Advanced Research Centre
L. Lao Computer Engineering - EEMCS , QuTech Advanced Research Centre
D.B. Criger QCD/Terhal Group - QuTech Advanced Research Centre , Institute for Globally Distributed Open Research and Education, QuTech Advanced Research Centre
Carmen G. Almudever Computer Engineering - EEMCS , QuTech Advanced Research Centre
K.L.M. Bertels (OLD)Quantum Computer Architectures , FTQC/Bertels Lab , QuTech Advanced Research Centre
B.M. Terhal QuTech Advanced Research Centre, QCD/Terhal Group - QuTech Advanced Research Centre , QCD/Terhal Group - QuTech Advanced Research Centre
Research Group
QCD/Terhal Group (QuTech Advanced Research Centre) (TU Delft)
Copyright: © 2019 C. Vuillot, L. Lao, D.B. Criger, Carmen G. Almudever, K.L.M. Bertels, B.M. Terhal
DOI: https://doi.org/10.1088/1367-2630/ab0199
Quantum error correction Surface code Quantum stabilizer codes Quantum subsystem codes Quantum code deformation Fault-tolerant quantum computation
More Info
expand_more

Published Date

2019

Language

English

Faculty

QuTech Advanced Research Centre

Department

Quantum Computing Division

Research Group

QCD/Terhal Group

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 realized 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.Wedemonstrate the accuracy of this method numerically with examples based on the surface code, some of which are novel.