[fix] Repair Dynamiqs backend resolve and add QuTiP parity tests

[Ronit-Raj9]

● Fixes the Dynamiqs backend so it actually runs and matches QuTiP. The old code called dq.sesolve with solver=dq.solver.Tsit5(), but that kwarg and the dq.solver namespace don't exist in dynamiqs 0.3.2, so it just crashed. Switched to method=dq.method.Tsit5 with explicit dq.Options.

Changes:

• New DynamiqsSolverOptions (Tsit5, rtol=atol=1e-8), progress meter off by default which also fixes the Jupyter ZMQError in DynamiqsBackend failing with ZMQError #26.
• Save times are built host-side from duration/timestep, so nothing traced gets branched on and the solve is jit-able.
• Added TaskArgsAtomicEmulator + run_task so solver options can go through a Task, like the analog emulator's QutipBackend.
• Dropped a duplicate Hilbert-space pass, raise a real ValueError instead of a bare string, and fixed the empty-gate timeline + initial_state check in both the Dynamiqs and QuTiP VMs.
• Documented the rad/s + seconds units in code and docs.

Fixes #43

• Please check if the PR fulfills these requirements

• The commit message follows our guidelines
• Tests for the changes have been added (for bug fixes / features)
• Docs have been added / updated (for bug fixes / features)

• What kind of change does this PR introduce? (Bug fix, feature, docs update, ...)

Mostly a bug fix, plus a small Task-based entry point and a docs update.

• What is the current behavior? (You can also link to an open issue here)

The backend crashes on any real run (#43) because of the bad sesolve call, and throws a ZMQError in Jupyter from the progress meter (#26). The existing tests only build the VMs, they never run a solve, so nothing was actually verified.

• What is the new behavior (if this is a feature change)?

It runs end to end and matches QuTiP to ~1e-8 on the Rabi carrier and red-sideband cases. Solver and tolerances are explicit and overridable (on the backend or via a Task), the progress meter is off by default, and the units are documented. Added parity, Hamiltonian-at-gate-time, jit and gradient tests.

• Does this PR introduce a breaking change? (What changes might users need to make in their application due to this PR?)

No. The only change is the solver_options default going from {} to None (None just falls back to the defaults). The old {} couldn't run anyway, and passing a dict still works.

• Other information:

run_task and TaskArgsAtomicEmulator are additive, so compile/run are untouched and still mirror QutipBackend. TaskArgsAtomicEmulator subclasses oqd-core's TaskArgsAtomic so a normal Task validates it (no model_construct). map_OperatorMul is left as-is, the 1e-8 parity confirms it's already correct. ruff, copyright, pytest (13 passed, 2 xfailed) and mkdocs all pass locally.

[benjimaclellan]

Going to accept this for the unitaryHACK bounty. The QuTiP parity at ~1e-8 is good, and I appreciate the explicit tests for end-to-end jax.jit and jax.grad compatibility, and the cleanups you made on the QuTiP side while you were in there. Thanks for the work!

[Ronit-Raj9]

Thanks for accepting this @benjimaclellan.. Do let me know if i could do any changes or something... I liked working with this... Probably want to contribute after unitaryHack too..

[benjimaclellan]

Thanks @Ronit-Raj9, that sounds great. We have a few changes/PRs to merge from the unitaryHACK and other work, so I'm going to leave this PR open as-is, and we'll keep in touch if there's some tweaks that would be useful here or other contributions to the repo.

[Ronit-Raj9]

Sure @benjimaclellan