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In this work, we introduce a graphical framework for distributed quantum computing that brings together linear optics, the ZX-calculus, and dataflow programming. Our language supports the formal analysis and optimization of distributed protocols involving both qubits and photonic modes, with explicit interfaces for classical control and feedforward, all expressed within a synchronous dataflow model with discrete-time dynamics. Within this setting, we classify entangling photonic fusion measurements, show how their induced Pauli errors can be corrected via a novel flow structure for fusion networks, and establish correctness proofs for new repeat-until-success protocols enabling arbitrary fusions. Layer by layer, we construct qubit architectures incorporating practical optical components such as beam splitters, switches, and photon sources, with graphical proofs that they are deterministic and support universal quantum computation. Together, these results establish a foundation for verifiable compilation and automated optimization in networked quantum computing.<\/jats:p>","DOI":"10.22331\/q-2026-01-19-1972","type":"journal-article","created":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T16:45:31Z","timestamp":1768841131000},"page":"1972","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["A dataflow programming framework for linear optical distributed quantum computing"],"prefix":"10.22331","volume":"10","author":[{"given":"Giovanni","family":"de Felice","sequence":"first","affiliation":[{"name":"Quantinuum, 17 Beaumont Street, Oxford, OX1 2NA, United Kingdom"}]},{"given":"Boldizs\u00e1r","family":"Po\u00f3r","sequence":"additional","affiliation":[{"name":"Quantinuum, 17 Beaumont Street, Oxford, OX1 2NA, United Kingdom"},{"name":"University of Oxford, Department of Computer Science, Oxford, OX1 3QD, United Kingdom"}]},{"given":"Cole","family":"Comfort","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris-Saclay, CNRS, ENS Paris-Saclay, Inria, Laboratoire M\u00e9thodes Formelles, 91190, Gif-sur-Yvette, France"}]},{"given":"Lia","family":"Yeh","sequence":"additional","affiliation":[{"name":"University of Cambridge, Department of Computer Science and Technology, Cambridge, CB3 0FD, United Kingdom"}]},{"given":"Mateusz","family":"Kupper","sequence":"additional","affiliation":[{"name":"Quantinuum, 17 Beaumont Street, Oxford, OX1 2NA, United Kingdom"}]},{"given":"William","family":"Cashman","sequence":"additional","affiliation":[{"name":"University of Oxford, Department of Computer Science, Oxford, OX1 3QD, United Kingdom"}]},{"given":"Bob","family":"Coecke","sequence":"additional","affiliation":[{"name":"Wolfson college, Linton Road, Oxford, OX2 6UD, United Kingdom"},{"name":"Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada"}]}],"member":"9598","published-online":{"date-parts":[[2026,1,19]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Scott Aaronson and Alex Arkhipov. 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