[Discussion] Adding quantum math features

Sometimes, it is useful to be able to analyze circuits in ways that aren’t valid on a quantum computer, but might still be interesting for theory reasons. I came across this issue a little while ago when wanting to compute the overlap <psi_1 | psi_2> of a state and had a hard time keeping memory limits under control with larger batch and state sizes using tfq.layers.State. I ultimately ended up simulating the circuits one by one, and doing the inner products in tf manually. It worked, but it wasn’t pretty.

Would people be interested in implementing things like:

Examples that can be done right now, but are tricky to get right without blowing up memory:

tfq.math.overlap # => analytically compute state overlap between the two circuits
tfq.math.amplitudes # => analytically compute requested state amplitudes (could use qsimh ?).
tfq.math.fideltiy # => analytically compute fidelity between two circuits.

Other interesting math functions might be worth having

tfq.math.operator_matrix # => ingest a cirq.PauliSum and compute the matrix
tfq.math.operator_commutators # => compute commutators on operator matrices

Does anyone else have any suggestions for useful math function ? @dabacon @zaqqwerty @jaeyoo @we-taper

Final thought: If we do end up making this .math module , maybe we should move calculate_unitary and calculate_state inside of it.

[MichaelBroughton]

I’d say a good approach would be this:

1. Open an issue titled “[Math] Implement tfq.math.whatever op you pick” with the basic steps you envision for implementing it.
2. Assign it to yourself and put a reference back to this issue in the description.
3. Add any needed support code in small PRs before the main op contribution PR.
4. Create the op PR with similar structure to something like #508 or #387 .
5. Once merged we can cross the op off the list on here.

Since op contributions aren’t coming in very quickly and are a fairly sizable undertaking, I think anyone looking to contribute a new op should definitely take this “one at a time issue creation followed by PR chain” approach.

[MichaelBroughton]

Looks like we had an implementation of fidelity go in here #554 from @jaeyoo so we can cross it off the list here.