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The standard universal set of gates for Clifford computation is CNOT, H and S. Are there other options, in particular, gate sets that don't use the S gate?

If yes, what are some examples?

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1 Answer 1

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  • You can choose $CZ$ and/or $CNOT$ gate.
  • You can choose $\sqrt{X}$ and/or $S$.
  • Any extension of a generator set is also a generator.
  • You may find useful to introduce the Pauli operators $X, Y, Z$.
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  • $\begingroup$ How does one define extension? For example $S = \sqrt{Z}$ multiplied by itself to give $Z$ or $\sqrt{X}$ multiplied by itself to get $X$ is not sufficient to generate all Clifford gates, correct? $\endgroup$
    – Cairo
    Commented May 19 at 12:24
  • $\begingroup$ $\mathcal{B} \subset \mathcal{A}$. If $\mathcal{A}$ generates the Clifford group, so does $\mathcal{B}$. $\endgroup$ Commented May 19 at 13:34

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