fix(docs): resolve Taylor expansion flakiness in Fermi-Hubbard FQE tutorial (#870)

[akushnarov]

Summary

Fixes sporadic numerical divergence and flakiness during time evolution in the Fermi-Hubbard tutorial notebook (docs/fqe/tutorials/fermi_hubbard.ipynb).

Fixes #870

Problem & Root Cause

In docs/fqe/tutorials/fermi_hubbard.ipynb, the time evolution demo calls:

true_evolved_fqe = init_wfn.time_evolve(e_time, hubbard)

1. The initial wavefunction was generated using init_wfn.set_wfn(strategy="random") without an explicit random seed, creating arbitrary initial spectral weights.
2. An evolution time of e_time = 0.9 resulted in a large Taylor expansion parameter ($t |H| \approx 5.4$), causing the single-step Taylor series to occasionally fail to converge within the required tolerance and triggering CI failures on notebook execution.

Solution & Approach

• Set a fixed random seed (np.random.seed(0)) before generating the random initial state for deterministic reproducibility.
• Reduced the single-step evolution parameter to e_time = 0.1 ($t |H| \approx 0.6 \ll 1$), ensuring rapid, monotonic, and unconditional convergence of the Taylor series while preserving the physical demonstration of wavepacket dynamics and the exact fidelity assertion (fidelity == 1.0) against matrix exponentiation.

Validation

• check/nbformat passed cleanly.
• Verified deterministic notebook execution.

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[gemini-code-assist]

Code Review

This pull request updates the Fermi-Hubbard tutorial notebook by setting a random seed to ensure reproducibility when initializing the wavefunction randomly, and reducing the time evolution parameter e_time from 0.9 to 0.1. There are no review comments, so no additional feedback is provided.