des-scq

Designing Superconducting Quantum Circuits — a PyTorch-powered simulation and optimization library for lumped-element superconducting circuit models.

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Overview

des-scq provides a differentiable Hamiltonian simulation stack for superconducting qubit circuits. Circuits are described as a network of lumped elements (Josephson junctions, capacitors, inductors), the circuit Hamiltonian is assembled automatically via nodal analysis, and eigenenergies are obtained by exact diagonalization. Because the entire pipeline is built on PyTorch, gradients flow back through the spectrum to the circuit parameters — enabling gradient-based optimization of qubit properties such as transition frequencies, anharmonicity, and flux sensitivity.

Key capabilities:

• Automated Hamiltonian assembly from a graph of lumped elements
• Two fully supported basis representations: Charge and Kerman (mixed oscillator / charge / Josephson modes)
• Exact diagonalization over a configurable Hilbert space truncation
• External flux and charge-offset control with differentiable loop-flux threading
• Gradient-descent optimization of circuit parameters against arbitrary spectral targets
• Stochastic search over circuit parameter spaces for global exploration
• Built-in library of standard qubit models: transmon, fluxonium, zero-pi, c-shunted qubit, prismon, and more

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Architecture

des_scq/
├── components.py   Element classes (J, C, L, Control) and unit conversions
├── dense.py        Operator algebra — basis operators, tensor products, Fourier transforms
├── circuit.py      Circuit graph, Hamiltonian assembly, diagonalization
│   ├── Circuit     Base class: nodal analysis, loop-flux threading
│   ├── Charge      Subclass: pure charge-basis representation
│   └── Kerman      Subclass: mixed O/I/J basis (Kerman decomposition)
├── models.py       Pre-built circuit constructors (transmon, fluxonium, zeroPi, …)
├── optimization.py Gradient-descent optimizer wrapping circuit + loss function
├── discovery.py    Loss functions and parameter-space sampling utilities
└── utils.py        Plotting helpers (Plotly-based)

Data flows as follows:

models.py  ──►  circuit.py  ──►  dense.py
   │               │
   │         spectrumManifold()
   │               │
   ▼               ▼
components.py   eigenenergies
                    │
              discovery.py (loss)
                    │
              optimization.py (∂loss/∂params → Adam / RMSprop / LBFGS)

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Installation

pip install des-scq

Dependencies: torch, numpy, scipy, networkx, pandas

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Energy Units Convention

All energies inside the library are expressed in GHz (i.e., divided by Planck's constant h). Physical SI values must be converted before being passed to element constructors. Helper functions for this are provided in components.py:

Quantity	SI unit	Natural unit	Energy unit (GHz)	Converter (SI → GHz)
Capacitance	F	e²/h · 10⁹	Ec = e²/2Ch	capE(C_SI)
Inductance	H	Φ₀²/h · 10⁹	El = Φ₀²/4π²Lh	indE(L_SI)
Junction	—	—	Ej (given)	direct (GHz)

from des_scq.components import capE, indE

Ec = capE(45e-15)   # 45 fF  →  GHz
El = indE(10e-9)    # 10 nH  →  GHz

Flux values are expressed as reduced flux Φ/Φ₀ ∈ [0, 1], where Φ₀ = h/2e is the flux quantum.

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Quickstart

1 — Transmon spectrum in Charge basis

from des_scq import models
from des_scq.circuit import Charge, hamiltonianEnergy
from torch import tensor

# Build circuit: Ej = 30 GHz, Ec = 0.3 GHz, 256 charge states
circuit = models.transmon(Charge, basis=[256], Ej=30.0, Ec=0.3)

# Assemble and diagonalize
H = circuit.hamiltonianLC() + circuit.hamiltonianJosephson()
energies = hamiltonianEnergy(H)
E10 = energies[1] - energies[0]
print(f"E₁₀ = {E10:.4f} GHz")

2 — Flux profile over a manifold of external flux values

from numpy import linspace
from torch import tensor

flux_range  = tensor(linspace(0, 1, 51))
flux_profile = [[phi] for phi in flux_range]   # list of control points

Spectrum = circuit.spectrumManifold(flux_profile)

for phi, (energies, _) in zip(flux_range, Spectrum):
    E10 = (energies[1] - energies[0]).item()
    print(f"Φ/Φ₀ = {phi:.2f}   E₁₀ = {E10:.4f} GHz")

3 — Charge offset sensitivity (Charge basis)

from torch import tensor

offset = {1: tensor(0.5)}   # 0.5 Cooper pairs on node 1
H = (circuit.hamiltonianLC()
     + circuit.hamiltonianJosephson()
     + circuit.hamiltonianChargeOffset(offset))
energies = hamiltonianEnergy(H)

4 — Zero-pi qubit in Kerman basis

from des_scq import models
from des_scq.circuit import Kerman

basis   = {'O': [32], 'I': [], 'J': [8, 8]}
circuit = models.zeroPi(Kerman, basis, Ej=10., Ec=50., El=0.5)

No, Ni, Nj = circuit.kermanDistribution()
print(f"Oscillator modes: {No}, Island modes: {Ni}, Josephson modes: {Nj}")

flux_profile = [[tensor(phi)] for phi in linspace(0, 1, 21)]
Spectrum     = circuit.spectrumManifold(flux_profile)

5 — Gradient-descent optimization

from des_scq.optimization import Optimization
from des_scq.discovery import lossTransition
from torch import tensor, float64 as double

# Target transition energies across the flux profile (in GHz)
E10_target = tensor([5.0] * 21, dtype=double)
E21_target = tensor([4.8] * 21, dtype=double)

loss_fn = lossTransition(E10_target, E21_target)
optim   = Optimization(circuit, flux_profile, loss_fn)
optim.initAlgo(lr=0.05)

dLogs, dParams, dCircuit = optim.optimization(iterations=200)
print(dLogs[['loss']].tail())
print(dCircuit.iloc[-1])   # final circuit parameters (GHz)

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Example Notebooks

Notebook	Circuit	Demonstrates
C-shunted_qubit.ipynb	C-shunted qubit	Kerman basis, pre/post-optimization spectrum, loss landscape
Flux_profile.ipynb	Fluxonium	Target-guided flux-profile optimization
Insensitive_Flux_profile.ipynb	Fluxonium	Anharmonicity-flatness optimization
Charge_Sensitivity_-_Transmon.ipynb	Transmon	Charge dispersion vs. Ej/Ec ratio
CPR_-_Modeling.ipynb	Transmon	Parameter estimation from experimental CPR data

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Module Reference

Module	Key symbols
components	J, C, L, Control, capE, indE, capSINat, indSINat
dense	basisQq, basisFq, basisQo, basisFo, chargeDisplacePlus/Minus, modeTensorProduct, transformationMatrix
circuit	Circuit, Charge, Kerman, hamiltonianEnergy
models	transmon, zeroPi, fluxonium, shuntedQubit, prismon, fluxoniumArray, oscillatorLC
optimization	Optimization
discovery	lossTransition, lossAnharmonicity, lossTransitionFlatness, lossDegeneracyWeighted, uniformParameters, truncNormalParameters, domainParameters

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Design Notes

Sigmoid reparametrization. Every circuit element parameter is stored as an unconstrained real number that maps to a bounded physical range through a sigmoid transform. This keeps optimization stable and prevents parameters from wandering outside physically meaningful bounds without requiring projected-gradient methods.

Symmetry constraints. The pairs dictionary passed to circuit constructors enforces hard equality between named components (e.g., pairs={'Jy': 'Jx'} ties the two junctions in a zero-pi qubit together). Symmetric components share the same base tensor, so gradients accumulate correctly.

Basis truncation. Hilbert-space dimension grows as the product of per-mode sizes. Typical stable values: n = 32–512 for single-mode charge/oscillator circuits; n = 8–16 per mode in multi-mode circuits. Verify convergence by checking that eigenenergies are stable as n increases.

GPU support. Pass device='cuda' to any circuit constructor. All PyTorch tensors are placed on that device; numpy calls in graph analysis run on CPU automatically.