Trotterisation test update

[otbrown]

Resolves #715

[otbrown]

Bloody quad precision. I suspect calculating exponents is the underlying culprit here. We're probably checking against an overly optimistic absolute error in these. Will tweak it up for these tests.

[otbrown]

Ah, I see REQUIRE_AGREE uses tolerances hard-coded in tests/utils/compare.cpp, not validation epsilon... Also it's only the serial and quad precision tests that fail. What a confounding edge case 😑

[otbrown]

Okay, when tested locally all quad precision configurations failed, so I've applied the epsilon increase for all deployments, not just single-threaded.

[otbrown]

Hi @TysonRayJones, hopefully this version of the Trotter tests sparks joy!

We're now using a bit more of the general QuEST testing machinery, and testing across deployments. The unitary time evo tests are a bit trickier, as I really can't think of a way to do that that doesn't involve fixed numbers of qubits, but again I've updated them to work across deployments and test on density matrices as well as statevectors.

[TysonRayJones]

Wew amazing! 🎉 🎉 I'll do a micro change to the var-names in cache and compare for src consistency (no need for coauth ofc).

Note in quad-precision and with multithreading on my machine, I get a failure:

compare.cpp:177: FAILED:
explicitly with messages:
  scalar := (5.36958,0)
  reference := (5.36958,0)
  absolute_difference := 5.43153e-10
  absolute_epsilon := 1e-10
  relative_difference := 1.01154e-10
  relative_epsilon := 1e-10

Happy to just bump both epsilons by *10 ¯\(ツ)/¯

Finally, these tests are (relatively) slow, and we may wish to avoid them in paid CI runners (if they hypothetically return) since the trotter functions just call separately tested backend functions; they are ergo "backend agnostic". So we don't actually have to run these tests cross-platform to know they'll pass (although I'd so for rigour if time was free, of course). I'll add a flag to the github workflows to skip trotter tests in the paid CI

[otbrown]

All sounds good to me, thanks Tyson!

[TysonRayJones]

@otbrown this is ready to merge if you're happy with my changes above