Fixed random_circuit for large circuits

[akshayp2003]

Summary

This PR resolves the issue #6994 by the following approaches:

• Generating 4 random numbers using numpy rng and using them to form a random number of any number of bits as we want
• Using python int instead of numpy int so that there is no integer overflow due to the upper limit in numpy int

Details and comments

The issue gets resolved if we do this in the random_circuit function:

parts = rng.integers(0, 1<<16, size=4)
shift = 0
condition_int = 0
for part in parts:
     ipart = (int)(part)
     condition_int += ipart << shift
     shift += 16
op.condition = (cr, condition_int)

I have done typecasting on parts (numpy int) and created iparts (python int) so that the condition_int value is in python int. This ensures that condition_int has no upper limit like Numpy int.

We can see that for num_qubits > 63 (80 in my case) we get no error, so the issue is fixed

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[mtreinish]

Thanks for getting a start to this, I"m looking forward to having this fixed. Besides the inline comments (the algorithm will need to be updated as it's not producing correct results with this anymore). This should have a release note documenting the fix (and potential change in behavior for a fixed seed) and also some unit tests to validate the fix moving forward.

[mtreinish]

Shouldn't this be based on the number of qubits? We want to pick a random integer between 0 and 2**num_qubits as the random condition state. Right now this is hard coded as a random large integer. Also I think this can return negatives which we don't support for the value.

[akshayp2003]

Thanks for the suggestion. I agree that this should be based on the number of qubits, so I did the following:

parts = rng.integers(0, 1<<16, size=int(num_qubits/16))
shift = 0
condition_int = 0
for part in parts:
    ipart = int(part)
    condition_int += ipart << shift
    shift += 16
condition_int = condition_int<<(num_qubits%16)
value_add = rng.integers(0, 1<<(num_qubits%16))
condition_int += int(value_add)

Here, for any number of qubits this code generates a random number with maximum value of 2**num_qubits - 1. For example, if num_qubits is 70, then the loop runs 4 times generating a random number upto 2^64 and then that number is shifted bitwise by 6 bits (70-64) and another random number of 6 bits is added to it. Kindly let me know if this approach is correct.

[akshayp2003]

Hi @mtreinish, just wanted to remind you about the changes I did after your suggestion. Could you please review the code above so that I can commit the changes to the PR if the code is correct?

[mtreinish]

Sorry for the delay, that approach looks reasonable to me. Please make the changes to your PR branch and probably add some unit tests at the same time to verify that for large circuits we still can set a condition. Then I think with a release not this will be ready to go