Quantum RF

Mirrored from the notebooks page of QPDK v0.4.1; the QPDK documentation has the latest version. The examples linked below include outputs from validated notebook snapshots executed with the QPDK kernel; their source cells are checked against the downloadable templates during every documentation build. Notebooks without a template here link to the QPDK documentation.

Worked, executable examples that take a qpdk component from requirements to a simulated result. Each notebook covers one stage of the design flow with one simulation method, so pick the one that fits your question and tooling.

• S-parameter models: Fast JAX/SAX circuit models for resonators, capacitors, and couplers.

• FEM electromagnetics: Full-wave and quasi-static solvers: HFSS, Q2D, COMSOL, Elmer, Palace.

• Hamiltonian analysis: Qubit frequency, anharmonicity, and dispersive shift from the circuit Hamiltonian.

• Pulse-level simulation: Gate fidelity, leakage, and decoherence under realistic control pulses.

• Differentiable circuits: Harmonic-balance and transient solvers with gradients through jax.grad.

• External integration: Drive qpdk from MATLAB and its RF Toolbox.

Where each method fits in the design flow

No single tool covers every physical scale of a superconducting chip, so a practical flow combines complementary methods. Each stage may loop back as the design is refined, and any of them can sit inside an optimization loop (e.g. with Optuna).

flowchart TB
    A["Physical requirements<br>(qubit frequency, coupling, T₁, …)"]
    B["Hamiltonian / perturbation analysis<br>(map requirements → circuit parameters)"]
    C["Circuit / S-parameter models<br>(design passive components)"]
    D["Layout with gdsfactory<br>(draw the chip in qpdk)"]
    E["FEM verification<br>(validate geometry with a full-wave solver)"]
    F["Pulse-level simulation<br>(predict gate performance)"]
    G["Fabrication & measurement"]
    A --> B --> C --> D --> E --> F --> G
    F -.-> A
    E -.-> C

S-parameter circuit models

Microwave components as linear, frequency-dependent scattering matrices, implemented in JAX and composed into circuits with SAX.

• Model library tour: Every S-parameter model in qpdk.models: capacitors, inductors, waveguides, couplers, resonators.

  Tools: qpdk, JAX · Install: models

• Circuit simulation with SAX: From single components to an assembled quarter-wave resonator.

  Tools: SAX, JAX · Install: models

• Resonator frequency model: Analytical resonance-frequency estimates against SAX circuit simulation.

  Tools: SAX · Install: models

• Monte Carlo fabrication tolerance: Vary CPW width and gap on a YAML-netlist test chip and measure the spread in S₂₁ resonances.

  Tools: SAX, gdsfactory · Install: models, ray

• Validation against Qucs-S: qpdk models checked against Qucs-S reference data for passive components.

  Tools: SAX, Qucs-S · Install: models

• JAX backend benchmark: SAX circuit evaluation on CPU, CUDA, and Apple Silicon (MPS), with matching precision baselines and accuracy checks. Recorded runs from both machines share a scaling plot rendered from Parquet records in CI. Recording requires the corresponding hardware.

  Tools: JAX, CUDA, MPS · Install: models

FEM-based electromagnetic simulations

Finite-element and full-wave solvers discretize Maxwell's equations over the real geometry, capturing radiation, surface currents, and substrate modes that analytical models miss.

• Q2D CPW impedance: CPW impedance from the cross-section, against conformal-mapping estimates.

  Tools: Ansys Q2D · Install: models, hfss · licensed solver

• HFSS eigenmode resonator: Resonant frequencies and Q-factors of a meandering CPW resonator.

  Tools: Ansys HFSS · Install: models, hfss · licensed solver

• HFSS driven capacitor: Driven-modal S-parameters of an interdigital capacitor.

  Tools: Ansys HFSS · Install: models, hfss · licensed solver

• Elmer capacitance extraction: Quasi-static capacitance of an interdigital capacitor with the open-source Elmer solver.

  Tools: Elmer, meshwell · Install: models, gplugins[elmer] from Git · open source

• COMSOL CPW resonator: Ported resonator layout, adaptive S-parameter sweep, and field map.

  Tools: COMSOL, MPh · Install: comsol · licensed solver

• COMSOL qubit capacitance: Electrostatic extraction of transmon pad capacitance, with field map.

  Tools: COMSOL, MPh · Install: comsol · licensed solver

• Capacitor optimization with Optuna: Optuna drives the Palace FEM solver towards a target capacitance.

  Tools: Optuna, Palace · Install: models · open source

• FEM dataset lookups: Palace plate-capacitor and CPW datasets, lazy queries, multidimensional interpolation and SAX models.

  Tools: JAX, Polars · Install: models

• More FEM and FDTD in gsim: The gsim notebooks take a GDSFactory layout to a 3-D simulation with open-source solvers: Palace eigenmode and driven-port runs, Meep FDTD with S-parameter extraction, meshing, and field post-processing.

  Tools: Palace, Meep · open source

Hamiltonian analysis

Diagonalizing the circuit Hamiltonian yields qubit frequencies, anharmonicities, and coupling strengths that feed back into the layout.

• scQubits parameters: Full numerical diagonalization of the transmon–resonator Hamiltonian, against perturbation theory.

  Tools: scQubits · Install: models, scqubits

• Dispersive shift with Pymablock: Symbolic block-diagonalization mapped to layout parameters.

  Tools: Pymablock, SymPy · Install: models, pymablock

• Transmon design with NetKet: Exact diagonalization and variational methods, converted to layout dimensions.

  Tools: NetKet, JAX · Install: models, netket

Pulse-level simulations

With qubit parameters in hand, time-domain simulation under microwave control pulses predicts gate fidelity, leakage to non-computational states, and the impact of decoherence.

• Transmon gates with QuTiP-QIP: Single-qubit (X, Y) and two-qubit (Bell-state) gates with realistic pulse shapes: population dynamics, leakage to higher levels, and \(T_1\)/\(T_2\) effects on fidelity.

  Tools: QuTiP-QIP, JAX · Install: models, qutip

Differentiable circuit simulation

The circuit as a system of differential-algebraic equations, solved with automatic differentiation: gradients of any simulated output with respect to physical parameters, without finite differences.

• Transmon optimization with Circulax: Harmonic-balance and transient solvers on a transmon: optimize junction parameters with jax.grad and trace crosstalk sensitivity to the coupling capacitance.

  Tools: Circulax, Optax · Install: models, circulax

External integration

Driving qpdk from outside Python, for teams whose primary tooling lives elsewhere.

• qpdk from MATLAB: GDS generation, parameter sweeps, inverse design with fzero, and Touchstone round-trips through the RF Toolbox, via MATLAB's built-in Python interface.

  Tools: MATLAB, RF Toolbox · Install: models

Installing optional extras

pip install qpdk gives you the layout PDK and nothing else: the analytical models, FEM drivers, and Hamiltonian/pulse solvers all live in extras, declared under [project.optional-dependencies] in pyproject.toml. Extras compose, so install them together in one command, and always quote the brackets — zsh and fish treat them as globs.

uv

# add qpdk with extras to the current project (writes pyproject.toml)
uv add "qpdk[models,netket]"

# install into the active environment without touching pyproject.toml
uv pip install "qpdk[models,netket]"

# run a notebook in a throwaway environment, no install step
uvx --with "qpdk[models,netket]" --from jupyterlab jupyter lab

pip

pip install "qpdk[models]"
pip install "qpdk[models,netket]"
pip install "qpdk[circulax,comsol,graphics,hfss,models,netket,pymablock,qutip,ray,scqubits]"

From a checkout

# sync the locked environment with the extras you need
uv sync --extra models --extra netket
uv sync --all-extras

# or reproduce the rendered documentation, every backend included
uv sync --group docs

Summary table

Every notebook at a glance; the Extras column links back to Installing optional extras.