On a recipe for quantum graphical languages
arXiv:2008.04193 · doi:10.4230/LIPIcs.ICALP.2020.118
Abstract
Different graphical calculi have been proposed to represent quantum computation. First the ZX- calculus [4], followed by the ZW-calculus [12] and then the ZH-calculus [1]. We can wonder if new Z*-calculi will continue to be proposed forever. This article answers negatively. All those language share a common core structure we call Z*-algebras. We classify Z*-algebras up to isomorphism in two dimensional Hilbert spaces and show that they are all variations of the aforementioned calculi. We do the same for linear relations and show that the calculus of [2] is essentially the unique one.
References in corpus (7)
- Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus
- The ZX calculus is a language for surface code lattice surgery
- Interacting Hopf Algebras
- ZH: A Complete Graphical Calculus for Quantum Computations Involving Classical Non-linearity
- The algebra of entanglement and the geometry of composition
- Completeness of the ZX-calculus for Pure Qubit Clifford+T Quantum Mechanics
- Bialgebra structures of 2-associative algebras