Basic Eigenmode Simulation of Transmon Coupled to a Resonator

Qiskit Metal Design

%reload_ext autoreload
%autoreload 2

import qiskit_metal as metal
from qiskit_metal import designs, draw
from qiskit_metal import MetalGUI, Dict, Headings
import pyEPR as epr
from qiskit_metal.qlibrary.terminations.open_to_ground import OpenToGround
from qiskit_metal.qlibrary.tlines.meandered import RouteMeander
from qiskit_metal.qlibrary.qubits.transmon_pocket import TransmonPocket

design = designs.DesignPlanar({}, True)
design.chips.main.size.center_x = '0.5mm'
design.chips.main.size.center_y = '0.1mm'
design.chips.main.size['size_x'] = '2.8mm'
design.chips.main.size['size_y'] = '2mm'

q1 = TransmonPocket(design, 'Q1', options = dict(
    pad_width = '425 um',
    pocket_height = '650um',
    connection_pads=dict(
        readout = dict(loc_W=+1,loc_H=+1, pad_width='200um')
    )))

otg = OpenToGround(design, 'open_to_ground', options=dict(pos_x='1.75mm',  pos_y='0um', orientation='0'))
RouteMeander(design, 'readout',  Dict(
        total_length='6 mm',
        hfss_wire_bonds = True,
        fillet='90 um',
        lead = dict(start_straight='100um'),
        pin_inputs=Dict(
        start_pin=Dict(component='Q1', pin='readout'),
        end_pin=Dict(component='open_to_ground', pin='open')), ))

gui = MetalGUI(design)
gui.rebuild()
gui.autoscale()

Eigenmode Simulation

Now to run the Palace simulation (make sure to update the path to the Palace binary first)

from SQDMetal.PALACE.Eigenmode_Simulation import PALACE_Eigenmode_Simulation
from SQDMetal.Utilities.Materials import MaterialInterface

#Eigenmode Simulation Options
user_defined_options = {
                "mesh_refinement":  0,                             #refines mesh in PALACE - essetially divides every mesh element in half
                "dielectric_material": "silicon",                  #choose dielectric material - 'silicon' or 'sapphire'
                "starting_freq": 5.5e9,                              #starting frequency in Hz
                "number_of_freqs": 3,                              #number of eigenmodes to find
                "solns_to_save": 3,                                #number of electromagnetic field visualizations to save
                "solver_order": 2,                                 #increasing solver order increases accuracy of simulation, but significantly increases sim time
                "solver_tol": 1.0e-8,                              #error residual tolerance for iterative solver
                "solver_maxits": 200,                              #number of solver iterations
                "fillet_resolution":12,                            #number of vertices per quarter turn on a filleted path
                "palace_dir":"~/spack/opt/spack/linux-ubuntu24.04-zen2/gcc-13.3.0/palace-develop-36rxmgzatchgymg5tcbfz3qrmkf4jnmj/bin/palace",#"PATH/TO/PALACE/BINARY",
                "num_cpus": 16
                }

#Create the Palace Eigenmode simulation
eigen_sim = PALACE_Eigenmode_Simulation(name ='Test1',                                              #name of simulation
                                        metal_design = design,                                      #feed in qiskit metal design
                                        sim_parent_directory = "",                                  #choose directory where mesh file, config file and HPC batch file will be saved
                                        mode = 'simPC',                                             #choose simulation mode 'HPC' or 'simPC'
                                        meshing = 'GMSH',                                           #choose meshing 'GMSH' or 'COMSOL'
                                        user_options = user_defined_options,                        #provide options chosen above
                                        create_files = True)                                        #create mesh and config files

#add in metals from the first layer
eigen_sim.add_metallic(1)

#add ground plane into simulation
eigen_sim.add_ground_plane()

#Create a lumped element port for the Josephson junction and assign Jospehson inductance and junction capacitance
eigen_sim.create_port_JosephsonJunction('Q1', L_J = 11e-9, C_J = 0e-15)

#Fine mesh the qubit and resonator - min_size/max_size is the min/max mesh element size
eigen_sim.fine_mesh_components(['Q1'], min_size=12e-6, max_size=100e-6, taper_dist_min=10e-6, metals_only=True)
eigen_sim.fine_mesh_along_path(qObjName='readout', dist_resolution=10e-6, min_size=12e-6, max_size=150e-6, taper_dist_min=10e-6)

#Lossy participatoin ratios calculated for MA, SA and MS
eigen_sim.setup_EPR_interfaces(metal_air=MaterialInterface('Aluminium-Vacuum'), substrate_air=MaterialInterface('Silicon-Vacuum'), substrate_metal=MaterialInterface('Silicon-Aluminium'))

#Prepare the simulation files - mesh file (.msh) and config file (.json)
eigen_sim.prepare_simulation()

Inspect the mesh before running the simulation

eigen_sim.open_mesh_gmsh()

Run the Simulation

eigen_sim.run()

Store the Hamiltonian parameters into a variable and print it as well for modes 1 and 2

hamil_params = eigen_sim.calculate_hamiltonian_parameters_EPR([1,2], print_output=True)