The ZX-calculus is complete for the single-qubit Clifford+T group

  title={The ZX-calculus is complete for the single-qubit Clifford+T group},
  author={Miriam Backens},
The ZX-calculus is a graphical calculus for reasoning about pure state qubit quantum mechanics. It is complete for pure qubit stabilizer quantum mechanics, meaning any equality involving only stabilizer operations that can be derived using matrices can also be derived pictorially. Stabilizer operations include the unitary Clifford group, as well as preparation of qubits in the state |0>, and measurements in the computational basis. For general pure state qubit quantum mechanics, the ZX-calculus… Expand
38 Citations
The ZX Calculus is incomplete for Clifford+T quantum mechanics
  • 4
  • PDF
Completeness and the ZX-calculus
  • 12
  • PDF
ZX-Rules for 2-Qubit Clifford+T Quantum Circuits
  • 19
  • PDF
Completeness of the ZX-calculus for Pure Qubit Clifford+T Quantum Mechanics
  • 17
  • PDF
Completeness of the ZX-calculus
  • 2
  • Highly Influenced
  • PDF
ZX-calculus for the working quantum computer scientist
  • 3
  • PDF
ZX-Calculus: Cyclotomic Supplementarity and Incompleteness for Clifford+T Quantum Mechanics
  • 21
  • PDF
Completeness of the ZX-Calculus
  • 9
  • PDF


The ZX−calculus is complete for stabilizer quantum mechanics
  • 117
  • PDF
Interacting Quantum Observables: Categorical Algebra and Diagrammatics
  • 291
  • PDF
Representation of Quantum Circuits with Clifford and $\pi/8$ Gates
  • 38
  • Highly Influential
  • PDF
On universal and fault-tolerant quantum computing: a novel basis and a new constructive proof of universality for Shor's basis
  • 84
  • PDF
Interacting Quantum Observables
  • 194
  • Highly Influential
  • PDF
The ZX calculus is incomplete for quantum mechanics
  • 35
  • PDF