The ZX-calculus is incomplete for quantum mechanics
arXiv:1404.3633 · doi:10.4204/EPTCS.172.20
Abstract
We prove that the ZX-calculus is incomplete for quantum mechanics. We suggest the addition of a new 'color-swap' rule, of which currently no analytical formulation is known and which we suspect may be necessary, but not sufficient to make the ZX-calculus complete.
arXiv commentIn Proceedings QPL 2014, arXiv:1412.8102
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Cited by in corpus (23)
- Interacting Hopf Algebras
- A universal completion of the ZX-calculus
- The ZX-calculus is complete for the single-qubit Clifford+T group
- The algebra of entanglement and the geometry of composition
- Making the stabilizer ZX-calculus complete for scalars
- ZX-calculus for the working quantum computer scientist
- Interacting Hopf Algebras: the theory of linear systems
- A Simplified Stabilizer ZX-calculus
- Completeness of the ZX-Calculus
- Completeness for arbitrary finite dimensions of ZXW-calculus, a unifying calculus
- Qutrit ZX-calculus is Complete for Stabilizer Quantum Mechanics
- SZX-calculus: Scalable Graphical Quantum Reasoning
- Y-Calculus: A Language for Real Matrices Derived from the ZX-Calculus
- Shaded Tangles for the Design and Verification of Quantum Programs (Extended Abstract)
- Kindergarden quantum mechanics graduates (...or how I learned to stop gluing LEGO together and love the ZX-calculus)
- Multi-agent blind quantum computation without universal cluster states
- Shaded tangles for the design and verification of quantum circuits
- ZX-calculus is Complete for Finite-Dimensional Hilbert Spaces
- Equivalence of Local Complementation and Euler Decomposition in the Qutrit ZX-calculus
- Equivalence checking of quantum circuits via intermediary matrix product operator
- Graphical Calculi and their Conjecture Synthesis
- ZX Graphical Calculus for Continuous-Variable Quantum Processes
- ZX-Rules for 2-qubit Clifford+T Quantum Circuits