{"paper":{"title":"ZX-Flow: A Flexible Criterion for Deterministic Computation with ZX-Diagrams","arxiv_id":"2603.09580","primary_cat":"quant-ph","submitted_at":"2026-03-10T12:26:09+00:00","version_compiled":"v2"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v2","sentences":[{"i":0,"p":1.0,"id":"s0","own":false,"role":"background","text":"Flow criteria are used to efficiently extract computations, either in the form of measurement patterns or quantum circuits, from ZX-diagrams.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.05,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":1.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":1,"p":0.85,"id":"s1","own":false,"role":"background","text":"Existing criteria such as causal flow, generalised flow, and Pauli flow, were all originally formulated for graph states, so they require ZX-diagrams to be in a very particular graph-state-like form.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.04,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.2,"role_probabilities":{"gap":0.12,"method":0.0,"result":0.0,"background":0.85,"limitation":0.03,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":2,"p":0.71,"id":"s2","own":false,"role":"background","text":"This form is easily broken by applying basic ZX rules and makes establishing some desirable properties very complicated.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.09,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.23,"method":0.0,"result":0.0,"background":0.71,"limitation":0.06,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":3,"p":1.0,"id":"s3","own":true,"role":"contribution","text":"Here, we introduce a new \"ZX-native\" flow criterion called ZX-flow, formulated using a new type of decoration of a ZX-diagram we call Pauli semiwebs.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.21,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":1.0,"interpretation":0.0}},{"i":4,"p":0.89,"id":"s4","own":false,"role":"background","text":"These are a generalisation of Pauli webs, which have recently been used extensively in reasoning about fault-tolerant computations in the ZX-calculus.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.1,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.12,"role_probabilities":{"gap":0.0,"method":0.02,"result":0.0,"background":0.89,"limitation":0.0,"future_work":0.0,"contribution":0.09,"interpretation":0.0}},{"i":5,"p":0.98,"id":"s5","own":true,"role":"result","text":"We show that ZX-flow is straightforwardly preserved by all Clifford rewrites and furthermore that a ZX-diagram has ZX-flow if and only if it is Clifford-equivalent to a graph-like ZX-diagram with Pauli flow.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.41,"quantitative":false,"quantitative_p":0.21,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.98,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.02,"interpretation":0.0}},{"i":6,"p":0.8,"id":"s6","own":true,"role":"result","text":"Finally, we show that any diagram with ZX-flow can be readily interpreted either as a deterministic measurement-based computation or as a Clifford isometry followed by a sequence of Pauli exponentials.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.33,"quantitative":false,"quantitative_p":0.07,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.8,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.04,"interpretation":0.16}},{"i":7,"p":0.46,"id":"s7","own":true,"role":"result","text":"The latter can then be efficiently extracted to a quantum 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