Speed up kronecker product

[hitomitak]

Rewrote Kronecker product calculation to not use np.kron function. This is because using this numpy function for vector calculations is very computationally expensive. This PR can speed up the reconstruction time as the following image.

Experiment Environment:

• Cut random circuits of 29 and 30 qubit
• max_subcircuit_width=10, max_cut=10

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All committers have signed the CLA.

[garrison]

Thanks for this. To be honest, it's kind of disappointing that numpy's kron is not at least as efficient as the code you give when it is passed 1D arrays.

[coveralls]

Pull Request Test Coverage Report for Build 4544439588

• 0 of 1 (0.0%) changed or added relevant line in 1 file are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage remained the same at 84.778%

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Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
circuit_knitting_toolbox/circuit_cutting/wire_cutting/wire_cutting_post_processing.py	0	1	0.0%

Totals
Change from base Build 4317758493:	0.0%
Covered Lines:	1526
Relevant Lines:	1800

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💛 - Coveralls

[garrison]

I was able to reproduce this in a simple test case using numpy 1.22.2:

>>> import timeit
>>> import numpy as np
>>> a = np.random.rand(1000)
>>> b = np.random.rand(1000)
>>> timeit.timeit(lambda: np.kron(a, b), number=200)
1.302669789060019
>>> timeit.timeit(lambda: (a[:,None] * b[None,:]).reshape(a.size * b.size), number=200)
0.25691784801892936
>>> np.allclose(np.kron(a, b), (a[:,None] * b[None,:]).reshape(a.size * b.size))
True
>>> np.__version__
'1.22.2'

However, if I try on numpy 1.24.2, the performance gap closes, and the current version on main might actually be a bit faster:

>>> import timeit
>>> import numpy as np
>>> a = np.random.rand(1000)
>>> b = np.random.rand(1000)
>>> timeit.timeit(lambda: np.kron(a, b), number=200)
0.2618443979881704
>>> timeit.timeit(lambda: (a[:,None] * b[None,:]).reshape(a.size * b.size), number=200)
0.30681791296228766
>>> np.allclose(np.kron(a, b), (a[:,None] * b[None,:]).reshape(a.size * b.size))
True
>>> np.__version__
'1.24.2'

Have you tried upgrading numpy?

[garrison]

One alternative idea is to warn in this function if somebody is using an old numpy that is known to be slow.

[garrison]

My best guess is that the performance improvement is due to numpy/numpy#21354.

It might be better here to just require the first numpy release that includes that commit (1.23, I expect) as the minimum supported by the toolbox, rather than to emit a warning.

[hitomitak]

Thank you for your investigation. I was using an older version of Numpy and was not aware of the improved performance. II agree with @garrison, so I closed this PR.

[garrison]

I just tried on numpy 1.23.0, and the performance is essentially the same between those two methods. I would support modifying pyproject.toml to require numpy>=1.23.0.