To be confirmed: Inconsistency in controlled gate unitary between v0.8.2 and v0.9.1

[Kee-Wang]

I found the unitary after applying .cotrolled() on rz behaves differently for version v0.8.2 and v0.9.1 which causes trouble.

The simplest code that that reproduce this issue on my computer is:

import cirq
import numpy as np

rz = cirq.rz(np.pi)
crz= rz.controlled()
u = cirq.unitary(crz)
print(u)

If I run this on v0.8.2, I got

[[0.-1.j 0.+0.j 0.+0.j 0.+0.j]
 [0.+0.j 0.-1.j 0.+0.j 0.+0.j]
 [0.+0.j 0.+0.j 0.-1.j 0.+0.j]
 [0.+0.j 0.+0.j 0.+0.j 0.+1.j]]

If I run with v0.9.1, I got

[[1.+0.j 0.+0.j 0.+0.j 0.+0.j]
 [0.+0.j 1.+0.j 0.+0.j 0.+0.j]
 [0.+0.j 0.+0.j 0.-1.j 0.+0.j]
 [0.+0.j 0.+0.j 0.+0.j 0.+1.j]]

Can anyone else reproduce this issue?

The former converted the control into CZPowGate and the later is simply a controlled version of ZPowGate.

If I understand it correctly, controlled ZPowGate is turned into CZPowGate only when at least the global shift of ZPowGate is 0, as shown here, but the phase of a Rz is -0.5 not 0 so it should never be turned into a CZPowGate, is that right?

What is even more confusing is that I did not see any changes of controlled method for version v0.8.2 and v0.9.1 so I would naively believe they should behave the same.

[smitsanghavi]

Just to confirm, the latter behavior is correct as we should not be converting rz.controlled to CZPowGate. The behavior change you mention above was intentional, #3113.

Is the main question that v0.8.2 and v0.9.1 have identical code for this part?

[Kee-Wang]

Just to confirm, the latter behavior is correct as we should not be converting rz.controlled to CZPowGate. The behavior change you mention above was intentional, #3113.

Is the main question that v0.8.2 and v0.9.1 have identical code for this part?

Thanks for the confirmation. Are you asking if I used the same Python code I showed above, but with different Cirq versions? Then yes I did. I ran the identical Python code with different Cirq versions.

Also would you agree with the following sum up for the people who might get confused by definitions of gates?
The cirq.rz(theta).controlled() is implemented in:

1. v0.8.2 as:

[[1,0,0,0]
 [0,1,0,0],
 [0,0,1,0],
 [0,0,0,g]]

where g = exp(i·theta). This is implemented via CZPowGate.

2. v0.9.1 as:

[[1,0,0,0]
 [0,1,0,0],
 [0,0,a,0],
 [0,0,0,b]]

where a = e^{i·theta/2} and b = e^{- i·theta/2}. This is implemented via a controlled method of ZPowGate.

The update of definition for the rz.controlled from v0.8.2 to v0.9.1 was intentional since the later is the correct one.

[smitsanghavi]

That's correct. I'll close the issue for now, please reopen if any of your questions were unanswered.