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3 votes

general way to decompose a CZ gate on $n$-qubit system

You can meet in the middle, use CXSWAPs instead of full swaps, and pipeline the CXSWAPs, to reduce the depth from $6n \pm O(1)$ to $n \pm O(1)$.
Craig Gidney's user avatar
  • 37.7k
2 votes
Accepted

How to prove the inclusion relation $\text{Im} (\rho) \subseteq \text{Im} (\rho[X] \otimes \rho[Y])$ about density operators?

Let's consider some examples first to see what we're talking about: Start thinking about a simple case: what does this mean if $\sqrt2|\Psi\rangle=|00\rangle+|11\rangle\in\mathbb{C}^2\otimes\mathbb{C}...
glS's user avatar
  • 25.4k

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