Code deformation and lattice surgery are gauge fixing

Journal Article (2019)
Author(s)

C. Vuillot (TU Delft - QCD/Terhal Group, TU Delft - QuTech Advanced Research Centre)

Lingling Lao (TU Delft - QuTech Advanced Research Centre, TU Delft - Computer Engineering)

D.B. Criger (TU Delft - QuTech Advanced Research Centre, TU Delft - QCD/Terhal Group, Institute for Globally Distributed Open Research and Education)

Carmina Almudever (TU Delft - Computer Engineering, TU Delft - QuTech Advanced Research Centre)

K Bertels (TU Delft - FTQC/Bertels Lab, TU Delft - QuTech Advanced Research Centre, TU Delft - (OLD)Quantum Computer Architectures)

B.M. Terhal (TU Delft - QCD/Terhal Group, TU Delft - Quantum Computing, TU Delft - QuTech Advanced Research Centre)

Research Group
QCD/Terhal Group
Copyright
© 2019 C. Vuillot, L. Lao, D.B. Criger, Carmen G. Almudever, K.L.M. Bertels, B.M. Terhal
DOI related publication
https://doi.org/10.1088/1367-2630/ab0199
More Info
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Publication Year
2019
Language
English
Copyright
© 2019 C. Vuillot, L. Lao, D.B. Criger, Carmen G. Almudever, K.L.M. Bertels, B.M. Terhal
Research Group
QCD/Terhal Group
Issue number
3
Volume number
21
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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.