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

@inproceedings{Backens2014TheZI,
title={The ZX-calculus is complete for the single-qubit Clifford+T group},
author={Miriam Backens},
year={2014}
}
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
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#### References

SHOWING 1-6 OF 6 REFERENCES
Representation of Quantum Circuits with Clifford and $\pi/8$ Gates
• Mathematics, Physics
• 2008
• 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
• Mathematics, Computer Science
• 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)
• 1999
• 84
• PDF
Interacting Quantum Observables
• Mathematics, Computer Science
• ICALP
• 2008
• 194
• Highly Influential
• PDF
The ZX calculus is incomplete for quantum mechanics
• Mathematics, Computer Science
• QPL
• 2014
• 35
• PDF