Add tolerance to modulus check in `has_stabilizer_effect`

[ACE07-Sev]

Is your feature request related to a use case or problem? Please explain

This issue happens when we have a gate with an exponent like 0.99999999 or 1.000000001 and such to return False for has_stabilizer_effect despite the difference being very negligible.

import cirq

op = cirq.XPowGate(exponent=1.00000001)
print(op._has_stabilizer_effect_()) # False

op = cirq.XPowGate(exponent=1.0)
print(op._has_stabilizer_effect_()) # True

Describe the solution you would prefer

Add rounding or tolerance to has_stabilizer_effect to allow for a more flexible handling of this case.

How urgent is this for you? Is it blocking important work?

P3 – I'm not really blocked by it; it's an idea I'm proposing based on principle

[aditikashi23]

Hi! I opened a pull request for this issue, which will hopefully be resolved! Please let me know if this solution makes sense to you. I apologize if it does not, as this is my first time contributing and I am still a student.

[pavoljuhas]

First, the _has_stabilizer_effect_ should not be used directly, as it is an internal function, but instead through the cirq.has_stabilizer_effect interface.

More importantly, would you have a concrete example, where this is a problem? The initial attempt in #7770 breaks controlled_gate_test. In general, adding a tolerance handling would make the code more complicated which should be avoided unless there is a clear justification to do so.

[ACE07-Sev]

@pavoljuhas Greetings,

Hope you're doing well. Apologies for the delay.

This is problematic when floating point errors are introduced in any extent since we're checking for absolute equality instead of approximating which is more flexible. If we do it well, I think it shouldn't make the code any more complicated.