Avoid state vector normalization if it worsens the round offs

[pavoljuhas]

This fixes failure of

check/pytest -n0 cirq-core/cirq/circuits/circuit_test.py::test_final_state_vector

which happened because normalization of a state vector at np.complex64
precision can subtly increase the overall round-off error.

Follow up to #6522 and #6402

[pavoljuhas]

I have got consistent failures for the cirq-core/cirq/circuits/circuit_test.py::test_final_state_vector
test on my Debian-based desktop which were bisected to #6522.
For some reason these do not show in CI runs, but it is preferable to
have passing tests in local environments too.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 97.79%. Comparing base (1bec6b5) to head (43cb287).
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Additional details and impacted files

@@           Coverage Diff           @@
##             main    #6556   +/-   ##
=======================================
  Coverage   97.79%   97.79%           
=======================================
  Files        1124     1124           
  Lines       95486    95489    +3     
=======================================
+ Hits        93376    93380    +4     
+ Misses       2110     2109    -1     

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[NoureldinYosri]

maybe we should remove it normalization then?

[pavoljuhas]

maybe we should remove it normalization then?

The normalization does help for your original round-off example in #6402.
I think the case where it worsen the outcome is for state vectors with few
nonzero elements. Here is how test_final_state_vector fails on my
desktop (the outcome may be different for other OS or CPU versions):

>>> x = np.exp(1j * np.pi/4, dtype=np.complex64)
>>> xn = x / np.linalg.norm(x)
>>> abs(x * x.conj() - 1)
5.960464477539063e-08
>>> abs(xn * xn.conj() - 1)
1.1920928955078125e-07

where the latter value for normalized xn is above the test tolerance.

With this PR the test passes and the round-off is better for #6402.