equal_up_to_global_phase() depends on the order of its arguments for EigenGates

[richrines1]

Description of the issue

the wrapping of the modulo operation in EigenGate._equal_up_to_global_phase_ makes it dependent on the sign of the difference between the exponents. As a result cirq.equal_up_to_global_phase() depends on the ordering of its arguments when the two gates' exponents differ by a negligible factor (see below)

i think all it would take to fix this is adding an abs() to the linked lines, e.g.:

canonical_diff = abs(exponents[0] - exponents[1]) % period
return np.isclose(canonical_diff, 0, atol=atol)

or alternatively replacing both with linalg.tolerance.near_zero_mod()

How to reproduce the issue

gate1 = cirq.Z
gate2 = cirq.Z ** (1 + 1e-10)

assert cirq.equal_up_to_global_phase(gate2, gate1, atol=1e-5)  # ok
assert cirq.equal_up_to_global_phase(gate1, gate2, atol=1e-5)  # fails

Cirq version

1.2.0.dev20230105212249

[web3quantum]

@tanujkhattar I would like to work on this issue.

[tanujkhattar]

@web3quantum Are you working on this issue? Do you have any questions or expected timeline by which you would be able to send a PR?

[siddharth-mehta]

Hi, I was planning to work on this.