`_Pauli{X,Y,Z}` maybe shouldn't be private

Unlike every other gate, with cirq.X, cirq.Y, and cirq.Z, it’s very easy to end up with an instance of a class that is not importable from top-level-cirq

x1 = cirq.X
x2 = cirq.X**0.99
type(x1)
Out[6]: cirq.ops.pauli_gates._PauliX
type(x2)
Out[7]: cirq.ops.common_gates.XPowGate

consider renaming to PauliX and exposing as cirq.PauliX

[mpharrigan]

I’d generally push back against any further consolidation into them being gate-like. I’m still not fully convinced that there shouldn’t be two separate things: X-the-gate and X-the-operator. It’s pretty rare to have a case where you want to take one thing and use it both as an operator (Hermitian) and a gate (unitary). In fact, most of the time when you have an X-the-operator, you convert to an associated gate by exp[i t X-the-operator].

The only commonality is the matrix representation, so you’d want to call cirq.unitary(X-the-gate) or cirq.unitary(X-the-operator) and get the same answer; but this also gets confusing in the latter case because you’re not requesting a unitary matrix. You really need a Hermitian matrix.

[mpharrigan]

I think it’s fine that they’re private