HybridSuperQubits 0.10.8

Package to simulate hybrid superconducting qubits

HybridSuperQubits

HybridSuperQubits is a Python framework for simulating hybrid semiconductor-superconductor quantum circuits. It provides numerical tools for diagonalizing circuit Hamiltonians, computing energy spectra, analyzing noise susceptibility, and visualizing wavefunctions across several qubit architectures.

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Overview

Superconducting quantum circuits based on semiconductor weak links are a growing family of devices where gate-tunable Andreev bound states replace or complement conventional Josephson tunnel junctions. HybridSuperQubits provides a unified numerical framework for studying these systems -- from simple gate-tunable junctions (gatemon) to circuits that hybridize fermionic and bosonic degrees of freedom (FerBo).

The package covers a range of hybrid qubit architectures:

• Charge-basis qubits -- Andreev pair qubit, gatemon -- where the junction potential depends on the transmission of a semiconductor weak link.
• Flux-basis qubits -- fluxonium, gatemonium -- where a large inductance shunts the junction, providing phase delocalization and anharmonicity.
• Hybrid-basis qubits -- FerBo -- where the Hilbert space is a tensor product of a bosonic (LC) mode and a fermionic (Andreev) degree of freedom.
• Metamaterial elements -- Josephson junction arrays, resonators -- for modeling coupling environments and readout cavities.

All qubit classes share a common interface for Hamiltonian diagonalization, parameter sweeps, matrix element computation, noise analysis (T1, T_phi), and wavefunction visualization.

This package was used in: FerBo: a noise resilient qubit hybridizing Andreev and fluxonium states J. J. Caceres, D. Sanz Marco, J. Ortuzar, E. Flurin, C. Urbina, H. Pothier, M. F. Goffman, F. J. Matute-Canadas, A. Levy Yeyati arXiv:2604.01145 (2026)

Supported qubit types

Qubit	Description	Basis
Ferbo	Fermionic-bosonic hybrid qubit (Andreev + LC oscillator)	Hybrid (Fock x Andreev)
Andreev	Andreev pair qubit in a superconducting weak link	Charge
Fluxonium	Inductive-dominated superconducting qubit	Fock
Gatemon	Gate-tunable Josephson junction qubit	Charge
Gatemonium	Gate-tunable junction shunted by an inductance	Fock
JJA	Josephson junction array (metamaterial modes)	Analytical
Resonator	Quantum LC resonator / cavity	Fock

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Installation

Quick install (all platforms)

pip install HybridSuperQubits[full]

Recommended for Apple Silicon (M1/M2/M3/M4)

For optimal performance with accelerated scientific libraries:

conda env create -f environment.yml
conda activate hybridsuperqubits

Or manually:

conda create -n hybridsuperqubits python>=3.10
conda activate hybridsuperqubits
conda install -c conda-forge numpy scipy matplotlib qutip scqubits
pip install -e . --no-deps

See INSTALL_APPLE_SILICON.md for a detailed guide.

Development install

git clone https://github.com/joanjcaceres/HybridSuperQubits.git
cd HybridSuperQubits
pip install -e .[full]

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Quick start

Fluxonium

import numpy as np
from HybridSuperQubits import Fluxonium

qubit = Fluxonium(
    Ec=1.0,            # Charging energy [GHz]
    El=0.5,            # Inductive energy [GHz]
    Ej=4.0,            # Josephson energy [GHz]
    phase=np.pi,       # External flux (2pi Phi/Phi_0)
    dimension=100      # Fock space dimension
)

# Eigenvalues and eigenstates
evals, evecs = qubit.eigensys(evals_count=6)

# Energy spectrum vs external flux
spectrum = qubit.get_spectrum_vs_paramvals(
    param_name="phase",
    param_vals=np.linspace(0, 2 * np.pi, 101),
    evals_count=6
)

Andreev pair qubit

from HybridSuperQubits import Andreev

qubit = Andreev(
    Ec=0.5,            # Charging energy [GHz]
    Gamma=15.0,        # Andreev coupling [GHz]
    delta_Gamma=0.1,   # Coupling asymmetry [GHz]
    er=0.0,            # Resonant level detuning [GHz]
    phase=0.0,         # External phase
    ng=0.0,            # Charge offset
    n_cut=25           # Charge basis cutoff
)

Gatemonium

from HybridSuperQubits import Gatemonium

qubit = Gatemonium(
    Ec=1.2,            # Charging energy [GHz]
    El=0.5,            # Inductive energy [GHz]
    Ej=8.0,            # Josephson energy [GHz]
    T=np.array([0.9]), # Transmission coefficient(s)
    phase=0.0,         # External flux
    dimension=100      # Hilbert space dimension
)

FerBo (Fermionic-Bosonic) qubit

from HybridSuperQubits import Ferbo

qubit = Ferbo(
    Ec=1.2,            # Charging energy [GHz]
    El=0.8,            # Inductive energy [GHz]
    Gamma=5.0,         # Andreev coupling strength [GHz]
    delta_Gamma=0.1,   # Coupling asymmetry [GHz]
    er=0.05,           # Resonant level detuning [GHz]
    phase=0.3,         # External flux (2pi Phi/Phi_0)
    dimension=100      # Hilbert space dimension
)

# Wavefunction visualization in the Andreev basis
qubit.plot_wavefunction(which=[0, 1], andreev_basis="Andreev")

Noise analysis

# T1 from capacitive losses
t1_cap = qubit.t1_capacitive(i=0, j=1, Q_cap=1e6, T=0.02)

# T1 from inductive losses
t1_ind = qubit.t1_inductive(i=0, j=1, Q_ind=500e6, T=0.02)

# Dephasing from 1/f flux noise
tphi = qubit.tphi_1_over_f_flux(A_noise=1e-6)

# Matrix elements for transition analysis
mel_table = qubit.matrixelement_table(
    operator=qubit.n_operator(),
    evecs=evecs,
    evals_count=4
)

Parameter sweeps and visualization

import numpy as np

# Spectrum vs flux
spectrum = qubit.get_spectrum_vs_paramvals(
    param_name="phase",
    param_vals=np.linspace(0, 2 * np.pi, 201),
    evals_count=6
)

# Matrix elements vs parameter
matelems = qubit.get_matelements_vs_paramvals(
    operator=qubit.n_operator(),
    param_name="phase",
    param_vals=np.linspace(0, 2 * np.pi, 101),
    evals_count=4
)

# Save / load results
spectrum.filewrite("spectrum_data.hdf5")

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Key features

• 7 qubit types with a shared interface: Ferbo, Andreev, Fluxonium, Gatemon, Gatemonium, JJA, Resonator
• Hamiltonian construction and diagonalization using scipy.linalg.eigh
• Parameter sweeps over any circuit parameter (flux, charge offset, energies, transmission) with get_spectrum_vs_paramvals
• Noise analysis: capacitive and inductive T1, 1/f flux dephasing, flux bias line losses
• Matrix element computation for arbitrary operators across energy levels
• Wavefunction visualization with support for hybrid (Andreev + Fock) bases
• Wigner function computation via QuTiP integration
• First and second Hamiltonian derivatives with respect to all circuit parameters
• HDF5 storage for spectrum data, matrix elements, and coherence times
• Unit conversions between circuit parameters (inductance/capacitance) and energy scales

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Documentation

Full API reference and theory background: hybridsuperqubits.readthedocs.io

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Citation

If you use HybridSuperQubits in your research, please cite the software:

Software:

@software{caceres2025hybridsuperqubits,
  author    = {Joan J. C{\'a}ceres},
  title     = {HybridSuperQubits},
  year      = {2025},
  publisher = {Zenodo},
  doi       = {10.5281/zenodo.15773124},
  url       = {https://github.com/joanjcaceres/HybridSuperQubits}
}

If you use the FerBo qubit specifically, please also cite the paper:

@article{caceres2026ferbo,
  title     = {FerBo: a noise resilient qubit hybridizing Andreev and fluxonium states},
  author    = {Caceres, J. J. and Sanz Marco, D. and Ortuzar, J. and Flurin, E.
               and Urbina, C. and Pothier, H. and Goffman, M. F.
               and Matute-Ca{\~n}adas, F. J. and Levy Yeyati, A.},
  year      = {2026},
  eprint    = {2604.01145},
  archivePrefix = {arXiv},
  primaryClass  = {cond-mat.mes-hall},
  url       = {https://arxiv.org/abs/2604.01145}
}

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Contributing

We welcome contributions! See CONTRIBUTING.md for guidelines.

License

MIT License. This project includes portions of code derived from scqubits (BSD 3-Clause License). See LICENSE for details.