arXiv:2405.10896quant-ph
ZX-calculus is Complete for Finite-Dimensional Hilbert Spaces
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Abstract
The ZX-calculus is a graphical language for reasoning about quantum computing and quantum information theory. As a complete graphical language, it incorporates a set of axioms rich enough to derive any equation of the underlying formalism. While completeness of the ZX-calculus has been established for qubits and the Clifford fragment of prime-dimensional qudits, universal completeness beyond two-level systems has remained unproven until now. In this paper, we present a proof establishing the completeness of finite-dimensional ZX-calculus, incorporating only the mixed-dimensional Z-spider and the qudit X-spider as generators. Our approach builds on the completeness of another graphical language, the finite-dimensional ZW-calculus, with direct translations between these two calculi. By proving its completeness, we lay a solid foundation for the ZX-calculus as a versatile tool not only for quantum computation but also for various fields within finite-dimensional quantum theory.
IANAP so got curious about how ZX Calculus related to Feynman Diagrams (if at all) Search landed on this neat summary [^1] (2024) from the lab(?) which also has a link to the original paper [^2] [1]: https://www.quantinuum.com/blog/quantinuum-scientists-have-p... [2]…
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