20 New Quantum Gates by GPT4

Similar excise here. I ask about quantum gates (from multi model intercommunication)

DAO Democracy:
invent 20 new gates

Here are 20 new gates for you, some of which are variations or combinations of existing gates:

$D_{\alpha}(|0\rangle) = e^{i\alpha}|0\rangle$
$D_{\alpha}(|1\rangle) = e^{i\alpha}|1\rangle$
$R_x(\theta)|0\rangle = \cos(\theta/2)|0\rangle - i\sin(\theta/2)|1\rangle$
$R_x(\theta)|1\rangle = -i\sin(\theta/2)|0\rangle + \cos(\theta/2)|1\rangle$
$U(\theta,\phi)|0\rangle = \cos(\theta/2)|0\rangle + e^{i\phi}\sin(\theta/2)|1\rangle$
$U(\theta,\phi)|1\rangle = -e^{-i\phi}\sin(\theta/2)|0\rangle + \cos(\theta/2)|1\rangle$
$DCNOT(|00\rangle) = |00\rangle$
$DCNOT(|01\rangle) = |11\rangle$
$DCNOT(|10\rangle) = |10\rangle$
$DCNOT(|11\rangle) = |01\rangle$
$HCH(|0\rangle) = \frac{1}{\sqrt{2}}(|0\rangle + i|1\rangle)$
$HCH(|1\rangle) = \frac{1}{\sqrt{2}}(|1\rangle + i|0\rangle)$
$CHC(|0\rangle) = \frac{1}{\sqrt{2}}(|0\rangle + i|1\rangle)$
$CHC(|1\rangle) = \frac{1}{\sqrt{2}}(|1\rangle + i|0\rangle)$
$CCZ(|00\rangle) = |00\rangle$
$CCZ(|01\rangle) = |01\rangle$
$CCZ(|10\rangle) = |10\rangle$
$CCZ(|11\rangle) = -|11\rangle$
$QSWAP(|00\rangle) = |00\rangle$
$QSWAP(|01\rangle) = i|10\rangle$

If our bots can invent. Then you should allow them as peers on this chain.

Thank you