aiqbench analysis
This research extends ZX calculus—a graphical language for quantum circuits—into the domain of gauge theory by linking it to two-dimensional Yang-Mills models via Hopf Frobenius algebras. By unifying these frameworks through topological quantum field theory diagrammatics, the work establishes a theoretical bridge that could facilitate future applications in low-dimensional gravity research.
A ribbon ZX calculus for gauge theory
arXiv:2606.13551v1 Announce Type: cross Abstract: ZX calculus provides a graphical formalism for reasoning about quantum processes, built from two interacting Frobenius algebras associated with the Z and X bases of a qubit. While it has found widespread application in quantum information and computing, its relationship to quantum field theory has only recently begun to be explored. In this work, we further develop this connection by providing a generalization of ZX calculus to two-dimensional Yang Mills theory with a compact gauge group. The key observation is that both frameworks can be organized around the Hopf Frobenius algebraic structure associated with a group algebra, which can in turn be described by the diagrammatics of two dimensional topological quantum field theory. Given the well known relationship between gauge theory and gravity in two and three dimensions, our work paves the way for applications of ZX to low dimensional gravity.
Abstract:ZX calculus provides a graphical formalism for reasoning about quantum processes, built from two interacting Frobenius algebras associated with the Z and X bases of a qubit. While it has found widespread application in quantum information and computing, its relationship to quantum field theory has only recently begun to be explored. In this work, we further develop this connection by providing a generalization of ZX calculus to two-dimensional Yang Mills theory with a compact gauge group. The key observation is that both frameworks can be organized around the Hopf Frobenius algebraic structure associated with a group algebra, which can in turn be described by the diagrammatics of two dimensional topological quantum field theory. Given the well known relationship between gauge theory and gravity in two and three dimensions, our work paves the way for applications of ZX to low dimensional gravity.
High Energy Physics - Theory (hep-th); Other Condensed Matter (cond-mat.other); Mathematical Physics (math-ph); Quantum Physics (quant-ph)
arXiv:2606.13551 [hep-th]
(or arXiv:2606.13551v1 [hep-th] for this version)
https://doi.org/10.48550/arXiv.2606.13551 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 248 words
