Adjust quantum_order_finder result for power-of-two multiples of the actual order

[pavoljuhas]

Fix test failure where order of 2 for 7 is returned as 6 instead of 3:

pytest --randomly-seed=2114237555 examples/examples_test.py

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 98.66%. Comparing base (1a75d9f) to head (ef421e5).
Report is 5 commits behind head on main.

Additional details and impacted files

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  Coverage   98.66%   98.66%           
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  Files        1106     1106           
  Lines       96042    96043    +1     
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+ Hits        94758    94763    +5     
+ Misses       1284     1280    -4     

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[pavoljuhas]

This should prevent CI test failure at https://github.com/quantumlib/Cirq/actions/runs/14451987369/job/40526599449#step:8:318

[viathor]

I don't think this is the right way to fix this.

Why do you think the algorithm returns a power-of-2 multiple of the order?

Order of 2 modulo 7 is 3, so the most likely outputs from the quantum phase estimation (QPE) are 0, 1/3 and 2/3. In the first case, we return None since it's impossible to recover the order from the denominator. In the other two cases, it should be straightforward to recover the order exactly (since it's a prime number, so we cannot run into the problem where numerator and denominator have a common factor).

I have two hypotheses for why the order is erroneously determined to be 6. First, sampling from the quantum circuit actually returns an output other than the most likely one. If this is the case, we can suppress it by making the quantum register larger or by sampling twice and returning the minimum (or better yet GCD) of the two outputs. This could be controlled by a new argument, e.g. num_samples to quantum_order_finder which we'd set to 2 in the offending test.

Second, perhaps there is an off-by-one error in bit counting in the code that interprets the output register of the QPE. Here, QPE would be returning 1/3, but classical post-processing would erroneously interpret it as 1/6. I doubt this is what's happening, because in this case we'd probably see other errors.