Plot expectation value benchmarks

[natestemen]

Description

This PR refactors the expectation value benchmarking script to ensure it works with the run_benchmarks.sh script. It also introduces new circuits to broaden the test of the expectation value testing. Scripts to visualize relative and absolute errors across different compilers over time are added, with one plot added to the README.

@jordandsullivan we have the option to plot relative or absolute error, but relative is much higher for ucc, which I don't understand the reason for.

[jordandsullivan]

Thanks for your work in this! Great getting to hack in person together.

I'm wondering why are the relative errors in the hundreds in the first place? What are the actual expectation values? I'd say we want to report errors in terms of a percent.

[natestemen]

why are the relative errors in the hundreds

I think it's because the ideal values are coming out so close to 0 that the relative errors are blowing up. You can find all the most recent results in benchmarks/results/expval_2025-01-14_20.csv. E.g. for QFT the ideal expectation value (last column) is $\mathcal{O}(10^{-21})$ so it's easy to be $>100\%$ off.

ucc/benchmarks/results/expval_2025-01-14_20.csv

Lines 11 to 14 in 8471ab3

	ucc,qft,ZZZZZZZZZZ,4.7704895589362195e-18,4.771491994589455e-18,4759.8985323285315,-1.002435653235501e-21
	qiskit,qft,ZZZZZZZZZZ,8.673617379884035e-19,8.68364173641639e-19,866.2542786051877,-1.002435653235501e-21
	pytket,qft,ZZZZZZZZZZ,-3.2526065174565133e-18,3.2516040818032778e-18,3243.703544769454,-1.002435653235501e-21
	cirq,qft,ZZZZZZZZZZ,2.168404344971009e-19,2.178428701503364e-19,217.31356965129692,-1.002435653235501e-21

Not sure what the best course of action here is.

[jordandsullivan]

Okay just as a sanity check can you plot the simulated and ideal expectation values and standard deviation, similar to what I did here for #58 (where I was running on real hardware)?

This reminds me, we can also simply measure an array of observables in addition to ZZZZZZ like I did there. Maybe just adding in some that measure like XIIIIIII or XXXXXZZZZZ, etc.

[jordandsullivan]

Looking good, a few suggestions.

[jordandsullivan]

Trying to understand why the relative errors are in the hundreds? What are the actual expectation values we're getting? Are they what we'd expect?

[jordandsullivan]

Perhaps we shouldn't use the same observable on all circuits if it is giving answers that don't seem meaningful.

[jordandsullivan]

Per @willzeng , we want to split off the customization of specific observables with the different benchmarks into a separate issue. Can complete this issue with the current all Z observable.

[natestemen]

It's a little suspicious how the QAOA, QV, and QCNN circuit results are all basically identical. We should make sure this is real and not an artifact of how we perform simulation (or something else)!

[jordandsullivan]

Did you plot the expectation values themselves and standard deviations as suggested above?

[jordandsullivan]

Let's compare the compiled gate counts between the different compilers in case they are returning approximately the same circuits.