Code deformation and lattice surgery are gauge fixing

Christophe Vuillot, Lingling Lao, Ben Criger, Carmina García Almudever, Koen Bertels, Barbara M. Terhal

Research output: Contribution to journalArticleScientificpeer-review

19 Citations (Scopus)
249 Downloads (Pure)


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.
Original languageEnglish
Article number033028
Number of pages21
JournalNew Journal of Physics
Issue number3
Publication statusPublished - 2019


  • quantum error correction
  • quantum stabilizer codes
  • quantum subsystem codes
  • surface code
  • quantum code deformation
  • fault-tolerant quantum computation


Dive into the research topics of 'Code deformation and lattice surgery are gauge fixing'. Together they form a unique fingerprint.

Cite this