What did I do this week?

🛠️ Fixing Dimension Mismatch in Open-System TRACEDIFF (Issue #47)

This week, I continued work on Issue #47, where the JOPT algorithm failed in open-system state transfer problems using the TRACEDIFF fidelity type.

To resolve this, I proposed a solution by modifying the _infid() function to handle density matrices and state vectors uniformly, using JAX-compatible logic to compute the infidelity depending on whether the final state is a vector or a square matrix.

I submitted a pull request with the initial fix. After receiving feedback from @BoxiLi, I realized the root cause was an incorrect dimension specification when constructing the adjoint of a Qobj. Specifically, I had reused diff.dims while taking diff.data.adjoint(), which led to mismatches like [[4], [1]] instead of the expected [[1], [4]].

Boxi pointed out that updating the dimensions after taking the adjoint — as done in QuTiP’s dag() — would be more robust.

✅ The fix was revised to:

```python Qobj(diff.data.adjoint(), dims=Dimensions(diff.dims[1], diff.dims[0]), copy=False)

Investigating GRAPE Infidelity Mismatch (Issue #46)

I also began investigating Issue #46, where the GRAPE algorithm reports a significantly lower infidelity than what is observed via manual simulation in an open-system qubit control problem.

What I Did: Reproduced the issue locally using the script provided in the GitHub issue.

Confirmed that GRAPE reports an infidelity of 0.0008, while manual evolution with the optimized control yields 0.0038 — clearly violating the fidelity target.

Implemented a custom TRACEDIFF fidelity function using Liouville space formalism, and verified that this discrepancy is consistent and reproducible.

Findings: The mismatch isn’t just numerical noise — it suggests that GRAPE is using a fidelity formula suited for closed systems or pure states.

This formulation likely originates from qutip-qtrl and seems to have been carried over to qutip-qoc incorrectly for open systems.

Suspicions (To Be Confirmed): The root cause may lie in the fidelity logic within grape.py or FidelityComputer, which doesn’t correctly account for density matrices under dissipation.

This discrepancy undermines the validity of GRAPE’s convergence metrics in open-system problems.

Plan for next week

Try out BL’s suggested improvements on Issue #47 to further refine the TRACEDIFF fidelity fix.
Investigate the relationship between fidelity measures used in qutip-qtrl and those currently implemented in qutip-qoc, as discussed in Issue #46.
Begin exploring how qtrl’s fidelity logic could be adapted into qutip-qoc by:

Identifying key dependency points between the two,

Experimentally copying over relevant fidelity-related files from Qtrl into QOC and attempting to make them work as a proof-of-concept.

I’m excited to keep digging into these deeper architectural connections between Qtrl and QOC, as they could lay the groundwork for a unified and more reliable optimization framework in QuTiP.