The Gauge Theory of Measurement-Based Quantum Computation

Gabriel Wong; Robert Raussendorf; Bartlomiej Czech

doi:10.22331/q-2024-07-04-1397

The Gauge Theory of Measurement-Based Quantum Computation

Gabriel Wong^1,2, Robert Raussendorf^3,4, and Bartlomiej Czech⁵

¹Center for Mathematical Sciences and Applications, Harvard University, Cambridge, MA 02138, USA
²Mathematical Institute, University of Oxford Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, United Kingdom
³Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany
⁴Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, Canada
⁵Institute for Advanced Study, Tsinghua University, Beijing 100084, China

Published:	2024-07-04, volume 8, page 1397
Eprint:	arXiv:2207.10098v2
Doi:	https://doi.org/10.22331/q-2024-07-04-1397
Citation:	Quantum 8, 1397 (2024).

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Abstract

Measurement-Based Quantum Computation (MBQC) is a model of quantum computation, which uses local measurements instead of unitary gates. Here we explain that the MBQC procedure has a fundamental basis in an underlying gauge theory. This perspective provides a theoretical foundation for global aspects of MBQC. The gauge transformations reflect the freedom of formulating the same MBQC computation in different local reference frames. The main identifications between MBQC and gauge theory concepts are: (i) the computational output of MBQC is a holonomy of the gauge field, (ii) the adaptation of measurement basis that remedies the inherent randomness of quantum measurements is effected by gauge transformations. The gauge theory of MBQC also plays a role in characterizing the entanglement structure of symmetry-protected topologically (SPT) ordered states, which are resources for MBQC. Our framework situates MBQC in a broader context of condensed matter and high energy theory.

Featured image: The fibre bundle, which underlies the gauge symmetry of Measurement-Based Quantum Computation.

Popular summary

Measurement-Based Quantum Computation (MBQC) is a formalism for carrying out quantum computations by measurements alone. Individual runs of the same MBQC computation can look very different but produce the same computational outcome. Here we explain that this equivalence reflects the same type of symmetry, which allows us to shift the value of the electric potential — that is, gauge symmetry. This offers a versatile perspective on MBQC, which is more accessible and portable for high energy and condensed matter theorists.

► BibTeX data

@article{Wong2024gaugetheoryof,
  doi = {10.22331/q-2024-07-04-1397},
  url = {https://doi.org/10.22331/q-2024-07-04-1397},
  title = {The {G}auge {T}heory of {M}easurement-{B}ased {Q}uantum {C}omputation},
  author = {Wong, Gabriel and Raussendorf, Robert and Czech, Bartlomiej},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1397},
  month = jul,
  year = {2024}
}

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