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7
votes
2answers
359 views

Could the Hadamard gate have been constructed differently with similar characteristics?

Say we had a Hadamard-like gate with the -1 in the first entry instead of the last. Let's call it $H^1$. $$H = \begin{bmatrix}1&1\\1&-1\end{bmatrix}$$ $$H^1 = \begin{bmatrix}-1&1\\1&...
13
votes
1answer
552 views

Why do we use the standard gate set that we do?

The typically used gate set for quantum computation is composed of the single qubits Cliffords (Paulis, H and S) and the controlled-NOT and/or controlled-Z. To go beyond Clifford we like to have full ...