Gate inconsistencies between versions when using controlled interface

It seems there is a (unintentional?) change to what the controlled interface does before and after the 8179aa2d678bcce480c0ce14bd2852068657abf6 commit in certain cases, possibly related to how the global phase is handled.

Running the following circuit (and inspecting the states at each moment):

q0 = cirq.GridQubit(0, 0)
q1 = cirq.GridQubit(0, 1)
q2 = cirq.GridQubit(0, 2)
circuit = cirq.Circuit()
circuit.append(cirq.X(q0))
circuit.append(cirq.rx(1).controlled()(q0,q1))
circuit.append(cirq.rx(1).controlled()(q1,q2))
simulator = cirq.Simulator()
for i, step in enumerate(simulator.simulate_moment_steps(circuit))
    temp = np.around(step.state_vector(), 3)
    print('state at step %d: %s %s' % (i, temp[temp != 0], temp.nonzero()))

gives the following output before the 8179aa2d678bcce480c0ce14bd2852068657abf6 commit

state at step 0: [1.+0.j] (array([4]),)
state at step 1: [0.878+0.j    0.   -0.479j] (array([4, 6]),)
state at step 2: [ 0.878+0.j     0.   -0.421j -0.23 +0.j   ] (array([4, 6, 7]),)

and this output after:

state at step 0: [1.+0.j] (array([4]),)
state at step 1: [0.878+0.j    0.   -0.479j] (array([4, 6]),)
state at step 2: [ 0.77-0.421j  0.  -0.421j -0.23+0.j   ] (array([4, 6, 7]),)

The output I would expect to see is the former one, as it matches other implementations of the same circuit.

[dabacon]

What is happening here is that the current code constructs a CXPowGate, but uses the global phase of the gate. Since Rx gates have global phase, that phase ends up in the “identity” part of the gate. That is not at all what users expect, they expect that the gate is a CRx gate. I think the solution here is if the global shift is not 0, use the old way to construct a controlled not.

Alternatively we could add CR* Gates. This is one of the “features” on the roadmap that needs to be decided, so I think for now the “don’t do it when the shift doesn’t work” is the right path

@smitsanghavi or @Strilanc any comments since you were involved in the bug leading up to this change.

[Strilanc]

The bug is that the code is not checking the global phase (self._global_phase_shift) before performing the substitution.