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The resulting generalised stabiliser formalism \u2013 denoted the XP stabiliser formalism \u2013 allows for a wider range of states and codespaces to be represented. We describe the states which arise in the formalism, and demonstrate an equivalence between XP stabiliser states and 'weighted hypergraph states' \u2013 a generalisation of both hypergraph and weighted graph states. Given an arbitrary set of XP operators, we present algorithms for determining the codespace and logical operators for an XP code. Finally, we consider whether measurements of XP operators on XP codes can be classically simulated.<\/jats:p>","DOI":"10.22331\/q-2022-09-22-815","type":"journal-article","created":{"date-parts":[[2022,9,22]],"date-time":"2022-09-22T15:25:34Z","timestamp":1663860334000},"page":"815","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":24,"title":["The XP Stabiliser Formalism: a Generalisation of the Pauli Stabiliser Formalism with Arbitrary Phases"],"prefix":"10.22331","volume":"6","author":[{"given":"Mark A.","family":"Webster","sequence":"first","affiliation":[{"name":"Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney, NSW 2006, Australia"},{"name":"Sydney Quantum Academy, Sydney, NSW, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Benjamin J.","family":"Brown","sequence":"additional","affiliation":[{"name":"Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney, NSW 2006, Australia"},{"name":"Niels Bohr International Academy, Niels Bohr Institute, Blegdamsvej 17, University of Copenhagen, 2100 Copenhagen, Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stephen D.","family":"Bartlett","sequence":"additional","affiliation":[{"name":"Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney, NSW 2006, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2022,9,22]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Scott Aaronson and Daniel Gottesman. 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