Qutrit ZX-calculus is Complete for Stabilizer Quantum Mechanics
arXiv:1803.00696 · doi:10.4204/EPTCS.266.3
Abstract
In this paper, we show that a qutrit version of ZX-calculus, with rules significantly different from that of the qubit version, is complete for pure qutrit stabilizer quantum mechanics, where state preparations and measurements are based on the three dimensional computational basis, and unitary operations are required to be in the generalized Clifford group. This means that any equation of diagrams that holds true under the standard interpretation in Hilbert spaces can be derived diagrammatically. In contrast to the qubit case, the situation here is more complicated due to the richer structure of this qutrit ZX-calculus.
In Proceedings QPL 2017, arXiv:1802.09737
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Cited by in corpus (7)
- Completeness for arbitrary finite dimensions of ZXW-calculus, a unifying calculus
- A Graphical Calculus for Lagrangian Relations
- The Qupit Stabiliser ZX-travaganza: Simplified Axioms, Normal Forms and Graph-Theoretic Simplification
- The Qudit ZH-Calculus: Generalised Toffoli+Hadamard and Universality
- Building Qutrit Diagonal Gates from Phase Gadgets
- ZX-calculus is Complete for Finite-Dimensional Hilbert Spaces
- A Complete and Natural Rule Set for Multi-Qutrit Clifford Circuits