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A Simple Proof that Toffoli and Hadamard are Quantum Universal
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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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Cited by 4 Pith papers
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Quantum Error Correction Exploiting Quantum Spatial Distribution and Gauge Symmetry
Gauge symmetry combined with quantum spatial distribution in a 3+2 particle stabilizer code corrects unified decoherence and dephasing noise while enabling local implementations of error detection, Hadamard, Toffoli, ...
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