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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.<\/jats:p>","DOI":"10.22331\/q-2024-07-04-1397","type":"journal-article","created":{"date-parts":[[2024,7,4]],"date-time":"2024-07-04T14:19:52Z","timestamp":1720102792000},"page":"1397","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":3,"title":["The Gauge Theory of Measurement-Based Quantum Computation"],"prefix":"10.22331","volume":"8","author":[{"given":"Gabriel","family":"Wong","sequence":"first","affiliation":[{"name":"Center for Mathematical Sciences and Applications, Harvard University, Cambridge, MA 02138, USA"},{"name":"Mathematical Institute, University of Oxford Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, United Kingdom"}]},{"given":"Robert","family":"Raussendorf","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Theoretische Physik, Leibniz Universit\u00e4t Hannover, Appelstra\u00dfe 2, 30167 Hannover, Germany"},{"name":"Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, Canada"}]},{"given":"Bartlomiej","family":"Czech","sequence":"additional","affiliation":[{"name":"Institute for Advanced Study, Tsinghua University, Beijing 100084, China"}]}],"member":"9598","published-online":{"date-parts":[[2024,7,4]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"R. 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