Fix zero-operand gates and instructions

[jakelishman]

Summary

A few checks in different places didn't account for zero-operand gates
being possible. In most uses, there never would be anything useful
here, but it can occasionally be useful to create a "global-phase"
instruction, especially if this is later going to have controls applied
to it. This is well-formed within the Qiskit data model; spectator
qubits implicitly undergo the identity, so this corresponds to the
global phase being multiplied by the identity on all qubits.

Details and comments

This came up in #8236. This PR doesn't add the requested gate, it just removes the roadblocks from a user-defined definition - such a gate should already be representable in the Gate.definition form, but due to the bugs fixed here, would fail in weird ways.

There's probably more places where this edge case will slip through and make a mess that I didn't catch here, but this makes everything I could immediately think of work - transpilation at pre-defined levels, gate control, conversion to Operator, etc.

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[coveralls]

Pull Request Test Coverage Report for Build 3350717692

• 12 of 13 (92.31%) changed or added relevant lines in 4 files are covered.
• 3 unchanged lines in 1 file lost coverage.
• Overall coverage increased (+0.04%) to 84.451%

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Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
qiskit/circuit/controlledgate.py	7	8	87.5%

Files with Coverage Reduction	New Missed Lines	%
qiskit/pulse/library/waveform.py	3	91.49%

Totals
Change from base Build 3348990138:	0.04%
Covered Lines:	62173
Relevant Lines:	73620

---

💛 - Coveralls

[Cryoris]

It feels a little weird to add a controlled global phase this way but if it's required that's fine by me. So this is to add a global phase on the entire circuit right? If we need a relative phase we could also do something like

phase = QuantumCircuit(1, global_phase=phase)
phase.control(...)

[jakelishman]

The example you gave is similar to what's being asked for in the linked issue, yeah. It's possible to get around that by other means, but these fixes here are stuff that should work anyway. It's a bit awkward that you need to use a create a full QuantumCircuit to apply a true global phase, and it's awkward that at the moment you somewhat arbitrarily need to apply it to one-or-more qubits, when our rules of "spectator qubits implicitly undergo the identity" should mean that you only need to apply it to zero.

Basically: there's ways to get the desired effect in the linked issue, but this stuff should work anyway, and a very basic "global phase" gate seems like a convenient utility definition we could supply.

[jakelishman]

I've fixed the merge conflict and added an extra test for Erick.

[Cryoris]

Overall LGTM, but now something like

my_cx = ControlledGate(
    name="cx?", 
    num_qubits=2, 
    params=[],
    num_ctrl_qubits=2, # same as num_qubits!
)

is technically a valid input right? Could we add a test to ensure this breaks as expected?

Also in the class docstring is still says that

            CircuitError: If ``num_ctrl_qubits`` >= ``num_qubits``.

maybe

            CircuitError: If ``num_ctrl_qubits + base_gate.num_qubits`` >= ``num_qubits``.

would be more accurate? 🙂

[jakelishman]

Oh, good idea on the last part - that's the constraint that actually should be implemented. We did need the case of num_qubits == num_ctrl_qubits to be allowed so that something like ControlledGate(base_gate=GlobalPhaseGate(pi)) could succeed, but you're right it should still error out for things like base_gate=XGate(). (Of course, the potential GlobalPhaseGate().control() would actually just return PhaseGate(), but the point stands that the ControlledGate constructor should be able to take it.)

[jakelishman]

Done in af1abf0.