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Alternative gate sets for universal Clifford computation?

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 $X, Y, Z$.
Daniele Cuomo's user avatar
1 vote

Universality of adding gate to Cliffords without inverses

Note that there are non-Clifford gates with no inverse. For example: measurement in a non-Pauli basis. Consider $M_{X+Y}$, which measures if a single qubit state is in the positive or negative ...
Craig Gidney's user avatar
  • 37.5k
1 vote
Accepted

Universality of adding gate to Cliffords without inverses

TL;DR: Yes, in a finite dimensional Hilbert space, $G^{-1}$ can be approximated to arbitrary accuracy as a finite power of $G$. If $G$ has finite order $r$, this follows from $G^{-1}=G^{r-1}$. The ...
Adam Zalcman's user avatar
  • 22.9k

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