How are 2 qubit Controlled Z gates (1 control / 1 target) typically implemented? Do we seek physical realizations of this gate, or have an alternate decomposition?

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    $\begingroup$ This will generally be hardware dependent. Do you have a specific platform in mind? $\endgroup$ – Niel de Beaudrap Aug 22 at 23:37
  • $\begingroup$ No - I was curious if there was a typical realization with CNOTs / Pauli gates. I'd also be interested on which platforms CZs can be directly implemented. $\endgroup$ – C. Kang Aug 23 at 17:21

On IBM QX architectures, the only entangling gate is the controlled not (CX), so controlled Z gates with control qubit $n$ and target qubit $m$ are decomposed into $CZ^n_m = H_m CX^n_m H_m$.

Although this is QX-specific, it demonstrates a principle that will likely hold on any architecture -- That the general method is to use a similarity transform to rotate Z onto the most conducive rotation axis for the hardware, perform that rotation, and rotate Z back into place.


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