{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,12]],"date-time":"2026-04-12T03:10:38Z","timestamp":1775963438440,"version":"3.50.1"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>The ZX-calculus is a powerful framework for reasoning in quantum computing.\nIt provides in particular a compact representation of matrices of interests. A\npeculiar property of the ZX-calculus is the absence of a formal sum allowing\nthe linear combinations of arbitrary ZX-diagrams. The universality of the\nformalism guarantees however that for any two ZX-diagrams, the sum of their\ninterpretations can be represented by a ZX-diagram. We introduce a general,\ninductive definition of the addition of ZX-diagrams, relying on the\nconstruction of controlled diagrams. Based on this addition technique, we\nprovide an inductive differentiation of ZX-diagrams.\n  Indeed, given a ZX-diagram with variables in the description of its angles,\none can differentiate the diagram according to one of these variables.\nDifferentiation is ubiquitous in quantum mechanics and quantum computing (e.g.\nfor solving optimization problems). Technically, differentiation of ZX-diagrams\nis strongly related to summation as witnessed by the product rules.\n  We also introduce an alternative, non inductive, differentiation technique\nrather based on the isolation of the variables. Finally, we apply our results\nto deduce a diagram for an Ising Hamiltonian.<\/jats:p>","DOI":"10.46298\/lmcs-20(2:10)2024","type":"journal-article","created":{"date-parts":[[2024,5,20]],"date-time":"2024-05-20T21:05:05Z","timestamp":1716239105000},"source":"Crossref","is-referenced-by-count":2,"title":["Addition and Differentiation of ZX-diagrams"],"prefix":"10.46298","volume":"Volume 20, Issue 2","author":[{"given":"Emmanuel","family":"Jeandel","sequence":"first","affiliation":[]},{"given":"Simon","family":"Perdrix","sequence":"additional","affiliation":[]},{"given":"Margarita","family":"Veshchezerova","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2024,5,20]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/13625\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/13625\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,20]],"date-time":"2024-05-20T21:05:05Z","timestamp":1716239105000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/11049"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,20]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-20(2:10)2024","relation":{"has-preprint":[{"id-type":"arxiv","id":"2202.11386v3","asserted-by":"subject"},{"id-type":"arxiv","id":"2202.11386v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2202.11386","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2202.11386","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,5,20]]},"article-number":"11049"}}