A Simple Proof that Toffoli and Hadamard are Quantum Universal

Details A Simple Proof that Toffoli and Hadamard are Quantum Universal A Simple Proof that Toffoli and Hadamard are Quantum Universal

2003-01-09

arxiv.org/abs/quant-ph/0301040v1

Physics

Quantum Physics

A note. 4 pages

Scientific paper

Recently Shi proved that Toffoli and Hadamard are universal for quantum computation. This is perhaps the simplest universal set of gates that one can hope for, conceptually; It shows that one only needs to add the Hadamard gate to make a 'classical' set of gates quantum universal. In this note we give a few lines proof of this fact relying on Kitaev's universal set of gates, and discuss the meaning of the result.

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