A Simple Proof that Toffoli and Hadamard are Quantum Universal

Dorit Aharonov

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arXiv · quant-ph/0301040

A Simple Proof that Toffoli and Hadamard are Quantum Universal

Dorit Aharonov

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Abstract

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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Dorit Aharonov. 2003-01-09. A Simple Proof that Toffoli and Hadamard are Quantum Universal. https://arxiv.org/abs/quant-ph/0301040

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