Add fluxonium modelling and transmon–fluxonium comparison to scqubits notebook

[Copilot]

Extends the scqubits notebook with fluxonium qubit analysis and a side-by-side comparison to the transmon, leveraging the existing fluxonium layout cell and scq.Fluxonium.

Notebook restructure

Renamed to "Transmon and Fluxonium Parameter Analysis with scQubits" and organized into four parts:

• Part I — Transmon: Existing content preserved
• Part II — Fluxonium: Spectrum at half-flux-quantum sweet spot, flux-dependent spectrum, fluxonium–resonator dispersive shift via numerical diagonalization
• Part III — Comparison: Parameter table (frequency, anharmonicity, $|\alpha/\omega_{01}|$, dispersive shift, detuning) and anharmonicity landscape plots ($E_J/E_C$ sweep vs $E_L$ sweep)
• Part IV — Design Workflow: Transmon flow unchanged; added fluxonium circuit parameter extraction ($C_\Sigma$, $L_J$, $L_s$ from $E_C$, $E_J$, $E_L$) with separate summary table

Bibliography

• Somoroff et al. 2023 — millisecond fluxonium coherence (PRL 130, 267001)
• Zhu et al. 2013 — circuit QED with fluxonium (PRB 87, 024510)

docs/notebooks.rst

Updated notebook description and Hamiltonian analysis use cases to reflect fluxonium coverage.

Summary by Sourcery

Extend the scQubits parameter-analysis notebook to cover both transmon and fluxonium qubits, including comparative analysis and design workflows for each modality.

New Features:

• Add fluxonium qubit modelling with scqubits, including spectrum at the half-flux-quantum sweet spot, flux dependence, and resonator dispersive shift extraction.
• Introduce a side-by-side transmon–fluxonium comparison covering key parameters such as frequency, anharmonicity, anharmonicity ratio, dispersive shift, detuning, and noise sweet spots.
• Provide fluxonium-specific design workflow content, including extraction of circuit parameters and superinductance from Hamiltonian energies and summarizing them in a dedicated design table.

Enhancements:

• Restructure the notebook into clearly delineated parts for transmon analysis, fluxonium analysis, cross-comparison, and design workflow to improve readability and pedagogy.
• Expand the transmon design section to explicitly frame it alongside the new fluxonium design flow while preserving existing functionality.

Documentation:

• Update notebook documentation and bibliography to reference fluxonium physics, long-coherence implementations, and dispersive readout theory, adding relevant literature citations.

[sourcery-ai]

Reviewer's Guide

Extends the scqubits parameter calculation notebook from a transmon-only dispersive-shift analysis into a four-part transmon–fluxonium modelling and design workflow, adding fluxonium spectrum/flux dependence, numerical dispersive shift extraction, side-by-side transmon–fluxonium comparisons, and fluxonium circuit parameter extraction, while updating the executable .py export, bibliography, and notebook docs accordingly.

Sequence diagram for fluxonium–resonator dispersive-shift computation with scqubits

sequenceDiagram
    actor User
    participant Notebook
    participant Fluxonium as scq_Fluxonium
    participant Oscillator as scq_Oscillator
    participant Hilbert as scq_HilbertSpace
    participant Interaction as scq_InteractionTerm

    User->>Notebook: Set_fluxonium_energies_EJ_flx_EC_flx_EL_flx_and_flux
    Notebook->>Fluxonium: create(EJ_flx,EC_flx,EL_flx,flux,cutoff,truncated_dim)
    Fluxonium-->>Notebook: fluxonium_instance

    User->>Notebook: Choose_resonator_frequency_omega_r_flx_and_coupling_g_flx
    Notebook->>Oscillator: create(E_osc=omega_r_flx,truncated_dim)
    Oscillator-->>Notebook: resonator_flx_instance

    Notebook->>Hilbert: create([fluxonium_instance,resonator_flx_instance])
    Hilbert-->>Notebook: hilbert_space_flx

    Notebook->>Oscillator: annihilation_operator()
    Oscillator-->>Notebook: a_operator
    Notebook->>Oscillator: creation_operator()
    Oscillator-->>Notebook: adag_operator
    Notebook->>Notebook: build_a_plus_adag_operator

    Notebook->>Fluxonium: n_operator()
    Fluxonium-->>Notebook: n_op

    Notebook->>Interaction: create(g_strength=g_flx, operator_list=[(0,n_op),(1,a_plus_adag)])
    Interaction-->>Notebook: interaction_flx
    Notebook->>Hilbert: set_interaction_list([interaction_flx])

    Notebook->>Hilbert: eigensys(evals_count=20)
    Hilbert-->>Notebook: evals_flx_evecs_flx

    Notebook->>Notebook: construct_bare_basis_vectors_and_find_dressed_indices
    Notebook->>Notebook: compute_E00_E01_E10_E11
    Notebook->>Notebook: chi_flx=(E11-E10)-(E01-E00)

    Notebook-->>User: Display_fluxonium_resonator_dispersive_shift_chi_flx

Loading

File-Level Changes

Change	Details	Files
Extend the scqubits parameter analysis notebook to cover fluxonium qubits alongside transmons, including spectrum, flux dependence, dispersive shift, comparison plots, and design tables for both modalities.	Rename the notebook and reorganize its structure into four parts, keeping the existing transmon content as Part I and adding new Parts II–IV for fluxonium, comparison, and design workflow. Introduce fluxonium modelling using scq.Fluxonium with representative parameters, computing eigenvalues, qubit frequency, and anharmonicity, and visualizing flux-dependent spectra. Set up a fluxonium–resonator coupled system using scqubits HilbertSpace and InteractionTerm, then numerically extract the dispersive shift by mapping bare product states to dressed eigenstates. Add a transmon–fluxonium comparison section that constructs a Polars DataFrame summarizing key parameters (frequency, anharmonicity,	α/ω01

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