Make ancilla for BiQubitsMixer sided too.

[fdmalone]

Similar fix as #6312 and fixes quantumlib/Qualtran#389

[tanujkhattar]

@fdmalone I'm still interested in getting an answer to my question in #6312 (comment), maybe here or in the linked issue quantumlib/Qualtran#389

What's the expected behavior of the ancilla register? Do we need to expose it as a LEFT / RIGHT register at all ?

From a quick glance, it looks like the answer is yes and that the gate is essentially using leaving dirty ancillas in the output, which get cleaned up by its adjoint, in order to reduce the T-counts. If that is the case, it'd be nice to clarify this as part of the docstring.

[fdmalone]

I'll defer to @NoureldinYosri

[codecov]

Codecov Report

All modified lines are covered by tests ✅

Comparison is base (fefe350) 97.89% compared to head (b222feb) 97.89%.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #6313      +/-   ##
==========================================
- Coverage   97.89%   97.89%   -0.01%     
==========================================
  Files        1106     1106              
  Lines       96156    96157       +1     
==========================================
- Hits        94134    94132       -2     
- Misses       2022     2025       +3     

Files	Coverage Δ
cirq-ft/cirq_ft/algos/arithmetic_gates.py	99.09% <100.00%> (+<0.01%)	⬆️

... and 2 files with indirect coverage changes

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[NoureldinYosri]

"ancilla" here is a misnomer that follows from the original paper. it should be more like target registers that are assumed to be clean.

@tanujkhattar the gate is simillar to cirq_ft.And in the sense that it assumes its target to be clean before it acts ont it and that its adjoint is the way to clean it.

so yea they should be sided (and probably renamed)

[NoureldinYosri]

lets rename it target. this will result in some changes to the decomposition and docstring

[tanujkhattar]

Let's also improve the docstring to more clearly specify what each of the 3 target bits contain. It's not clear to me right now by just reading the docstring.

[NoureldinYosri]

the short answer is .. enough information to do the adjoint. coming to think of it, this is why I kept the register name from the paper as ancilla. because they have no use otherthan as information holders for that will be used by the adjoint.

the actually useful information is stored inplace.

so maybe skip renaming it for now and I will come back for it later.

[tanujkhattar]

hmm, we've renamed such registers to junk in Qualtran.

@fdmalone As part of this PR, I think we should at least capture this discussion in the docstring and let the reader know that the ancilla is used to reduce the T-counts and assumes that it should be cleaned up later by the adjoint.

[fdmalone]

Ok. I'll try distill something later today. We should open an issue to track either here or in qualtran.

[fdmalone]

Done.