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Circuit Simulator including Josephson Junctions in Python

Project description


Circuit Simulator including Josephson Junctions in Python


PyJJASim requires numpy, scipy and matplotlib

pip install pyjjasim


PyJJASim is a circuit simulator including Josephson Junctions as components,

intended to be used on large Josephson Junction Arrays (JJAs).

PyJJASim is specialized in keeping track of Josephson vortices in the circuit.

It can also compute static configurations that have vortices at desired

locations in the circuit.

This requires that the circuit is a planar embedding (in 2D), such that

one can unambiguously refer to faces of the circuit, and vortices reside

at faces. This imposes that nodes in the circuit must be placed

at 2D coordinates, and that no junctions can cross. This also means no

hierarchical structure is supported.


  • supports basic components (inductors, resistors, capacitors and current- and voltage sources)

  • keep track of (and place) Josephson vortices in the circuit

  • compute static configurations

  • determine dynamic stability of static configurations

  • maximize parameters that have stable static configurations

  • compute time evolutions

  • define external magnetic flux through each face

  • thermal fluctuations modeling nonzero temperature

  • visualization and animation of simulation results


tutorial \


whitepaper (in progress)

Example Usage

from pyjjasim import *

sq_array = SquareArray(10, 10)

problem = StaticProblem(sq_array, frustration=0.1)

config, status, info = problem.compute()


Program output:

alt text

n = np.zeros(sq_array.face_count())

n[sq_array.locate_faces(x=[2.5,6.5], y=[2.5,6.5])] = 1

config, status, info = problem.new_problem(vortex_configuration=n).compute()


Program output:

alt text

More examples:

alt text

figure 1: Example of a frustrated honeycomb array with horizontal current bias.

Snapshot of a time evolution; the vortices are drifting downward. The electric potential

gradually increases in the direction of the external current

(see examples/images/

alt text

figure 2: Example of giant Shapiro steps in a square array. The external

current has a DC and AC component causing resonance in the form of

voltage plateaus (see examples/images/

alt text

figure 3: Example of a disordered array with different types of Josephson vortices

(see examples/images/

If you have any questions, comments, complaints,

bug reports, feature requests, etc.

please contact me at!

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