Qubit Coupled to a resonator
The first structure we want to analyze is the transmon qubit coupled to a \(\lambda /2\) resonator, we’ll consider the structure presented here and we’ll compare the result obtained with QuLTRA and ANSYS
Note: \(\lambda/2\) resonators have an open end. To model this aspect on QuLTRA we can both leave the node opne or terminated it on a very small capacitance
[1]:
%load_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
[2]:
design = designs.DesignPlanar({}, True)
design.chips.main.size['size_x'] = '2mm'
design.chips.main.size['size_y'] = '2mm'
gui = MetalGUI(design)
[3]:
from qiskit_metal.qlibrary.qubits.transmon_pocket import TransmonPocket
from qiskit_metal.qlibrary.terminations.open_to_ground import OpenToGround
from qiskit_metal.qlibrary.tlines.meandered import RouteMeander
design.delete_all_components()
q1 = TransmonPocket(design, 'Q1', options = dict(
pad_width = '425 um',
pocket_height = '650um',
hfss_inductance='12.31nH',
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'))
readout = 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.rebuild()
gui.autoscale()
[14]:
from qiskit_metal.analyses.quantization import LOManalysis
c1=LOManalysis(design, "q3d")
c1.sim.run(components=['Q1'], open_terminations=[('Q1','readout')])
c1.sim.capacitance_matrix
INFO 07:42PM [connect_project]: Connecting to Ansys Desktop API...
INFO 07:42PM [load_ansys_project]: Opened Ansys App
INFO 07:42PM [load_ansys_project]: Opened Ansys Desktop v2022.2.0
INFO 07:42PM [load_ansys_project]: Opened Ansys Project
Folder: C:/Users/simona.zaccaria4/Documents/Ansoft/
Project: Project38
INFO 07:42PM [connect_design]: Opened active design
Design: Design_hfss [Solution type: Eigenmode]
INFO 07:42PM [get_setup]: Opened setup `Setup` (<class 'pyEPR.ansys.HfssEMSetup'>)
INFO 07:42PM [connect]: Connected to project "Project38" and design "Design_hfss" 😀
INFO 07:42PM [connect_design]: Opened active design
Design: Design_q3d [Solution type: Q3D]
INFO 07:42PM [get_setup]: Opened setup `Setup` (<class 'pyEPR.ansys.AnsysQ3DSetup'>)
INFO 07:42PM [analyze]: Analyzing setup Setup
INFO 07:43PM [get_matrix]: Exporting matrix data to (C:\Users\SIMONA~1.ZAC\AppData\Local\Temp\tmp1lq3b2uq.txt, C, , Setup:LastAdaptive, "Original", "ohm", "nH", "fF", "mSie", 5000000000, Maxwell, 1, False
INFO 07:43PM [get_matrix]: Exporting matrix data to (C:\Users\SIMONA~1.ZAC\AppData\Local\Temp\tmp7re0czcr.txt, C, , Setup:AdaptivePass, "Original", "ohm", "nH", "fF", "mSie", 5000000000, Maxwell, 1, False
INFO 07:43PM [get_matrix]: Exporting matrix data to (C:\Users\SIMONA~1.ZAC\AppData\Local\Temp\tmpixi_h1w5.txt, C, , Setup:AdaptivePass, "Original", "ohm", "nH", "fF", "mSie", 5000000000, Maxwell, 2, False
INFO 07:43PM [get_matrix]: Exporting matrix data to (C:\Users\SIMONA~1.ZAC\AppData\Local\Temp\tmpjgt8d6lq.txt, C, , Setup:AdaptivePass, "Original", "ohm", "nH", "fF", "mSie", 5000000000, Maxwell, 3, False
INFO 07:43PM [get_matrix]: Exporting matrix data to (C:\Users\SIMONA~1.ZAC\AppData\Local\Temp\tmply4eecdr.txt, C, , Setup:AdaptivePass, "Original", "ohm", "nH", "fF", "mSie", 5000000000, Maxwell, 4, False
INFO 07:43PM [get_matrix]: Exporting matrix data to (C:\Users\SIMONA~1.ZAC\AppData\Local\Temp\tmpzoeu7eb3.txt, C, , Setup:AdaptivePass, "Original", "ohm", "nH", "fF", "mSie", 5000000000, Maxwell, 5, False
INFO 07:43PM [get_matrix]: Exporting matrix data to (C:\Users\SIMONA~1.ZAC\AppData\Local\Temp\tmpldvmpus8.txt, C, , Setup:AdaptivePass, "Original", "ohm", "nH", "fF", "mSie", 5000000000, Maxwell, 6, False
INFO 07:43PM [get_matrix]: Exporting matrix data to (C:\Users\SIMONA~1.ZAC\AppData\Local\Temp\tmpg9mvmnc1.txt, C, , Setup:AdaptivePass, "Original", "ohm", "nH", "fF", "mSie", 5000000000, Maxwell, 7, False
INFO 07:43PM [get_matrix]: Exporting matrix data to (C:\Users\SIMONA~1.ZAC\AppData\Local\Temp\tmpymvsb8b5.txt, C, , Setup:AdaptivePass, "Original", "ohm", "nH", "fF", "mSie", 5000000000, Maxwell, 8, False
INFO 07:43PM [get_matrix]: Exporting matrix data to (C:\Users\SIMONA~1.ZAC\AppData\Local\Temp\tmpkh447lai.txt, C, , Setup:AdaptivePass, "Original", "ohm", "nH", "fF", "mSie", 5000000000, Maxwell, 9, False
INFO 07:43PM [get_matrix]: Exporting matrix data to (C:\Users\SIMONA~1.ZAC\AppData\Local\Temp\tmpftdn3uin.txt, C, , Setup:AdaptivePass, "Original", "ohm", "nH", "fF", "mSie", 5000000000, Maxwell, 10, False
[14]:
| ground_main_plane | pad_bot_Q1 | pad_top_Q1 | readout_connector_pad_Q1 | |
|---|---|---|---|---|
| ground_main_plane | 177.78538 | -44.74611 | -38.34722 | -37.03041 |
| pad_bot_Q1 | -44.74611 | 82.84141 | -32.48515 | -2.30760 |
| pad_top_Q1 | -38.34722 | -32.48515 | 93.38943 | -19.67329 |
| readout_connector_pad_Q1 | -37.03041 | -2.30760 | -19.67329 | 60.14998 |
[8]:
c1.sim.close()
Warning! 6 COM references still alive
Ansys will likely refuse to shut down
[3]:
import qultra as qu
C_pad_bot=(82.84141-32.48515-2.30760)*1e-15 #capacitance of the bottom pad respect to ground
C_pad_top=(93.38943-32.48515-19.67329)*1e-15 #capacitance of the top pad respect to ground
C_pads=32.48515e-15 #capacitance between the two pads
Cg_bot=2.30760e-15 #capacitance between the bottom pad and the coupling pad
Cg_top=19.67329e-15 #capacitance between the top pad and the coupling pad
Cg0=(60.14998-2.30760-19.67329)*1e-15 #capacitance between the coupling pad and ground
Lj=12.31e-9 #inductance of the Josephson junction
l=6e-3 #length of the CPW resonator
net=[qu.C(0,1,C_pad_bot),qu.C(2,0,C_pad_top),qu.C(1,2,C_pads),qu.C(1,3,Cg_bot),qu.C(2,3,Cg_top),qu.C(3,0,Cg0),qu.J(1,2,Lj),qu.CPW(4,3,l)]#,qu.C(4,0,1e-25)]
qubit_resonator=qu.QCircuit(net,5,10)
qubit_resonator.show_all()
+------+------------+----------+
| Mode | Freq [GHz] | k [MHz] |
+------+------------+----------+
| 1 | 5.85e+00 | 0.00e+00 |
| 2 | 9.34e+00 | 0.00e+00 |
+------+------------+----------+
Chi matrix [MHz]:
+------+----------+----------+
| Mode | 1 | 2 |
+------+----------+----------+
| 1 | 3.21e+02 | 1.93e+00 |
| 2 | 1.93e+00 | 2.91e-03 |
+------+----------+----------+
[9]:
from qiskit_metal.analyses.quantization import EPRanalysis
eig_qb = EPRanalysis(design, "hfss")
[12]:
eig_qb.sim.setup.max_passes = 12
eig_qb.sim.setup.max_delta_f = 0.1
eig_qb.sim.setup.min_freq_ghz=1
eig_qb.sim.setup.n_modes = 2
eig_qb.sim.setup.vars = Dict(Lj= '12.31 nH', Cj= '0 fF')
eig_qb.sim.setup
[12]:
{'name': 'Setup',
'reuse_selected_design': True,
'reuse_setup': True,
'min_freq_ghz': 1,
'n_modes': 2,
'max_delta_f': 0.1,
'max_passes': 12,
'min_passes': 1,
'min_converged': 1,
'pct_refinement': 30,
'basis_order': 1,
'vars': {'Lj': '12.31 nH', 'Cj': '0 fF'},
'run': {'name': None,
'components': ['Q1', 'readout'],
'open_terminations': [('readout', 'end')],
'port_list': [],
'jj_to_port': None,
'ignored_jjs': None,
'box_plus_buffer': True}}
[13]:
eig_qb.sim.run(components=['Q1','readout'], open_terminations=[('readout','end')],port_list=[])
INFO 05:53PM [connect_design]: Opened active design
Design: Design_hfss [Solution type: Eigenmode]
INFO 05:53PM [get_setup]: Opened setup `Setup` (<class 'pyEPR.ansys.HfssEMSetup'>)
INFO 05:53PM [analyze]: Analyzing setup Setup
05:56PM 54s INFO [get_f_convergence]: Saved convergences to c:\Users\simona.zaccaria4\Desktop\GitHub\QuLTRA\tutorial\hfss_eig_f_convergence.csv
[12]:
eig_qb.setup.junctions.jj = Dict(rect='JJ_rect_Lj_Q1_rect_jj', line='JJ_Lj_Q1_rect_jj_',
Lj_variable='Lj', Cj_variable='Cj')
eig_qb.setup
[12]:
{'junctions': {'jj': {'rect': 'JJ_rect_Lj_Q1_rect_jj',
'line': 'JJ_Lj_Q1_rect_jj_',
'Lj_variable': 'Lj',
'Cj_variable': 'Cj'}},
'dissipatives': {'dielectrics_bulk': ['main']},
'cos_trunc': 8,
'fock_trunc': 7,
'sweep_variable': 'Lj'}
[13]:
eig_qb.run_epr()
Design "Design_hfss" info:
# eigenmodes 2
# variations 1
Design "Design_hfss" info:
# eigenmodes 2
# variations 1
energy_elec_all = 1.85420701261036e-24
energy_elec_substrate = 1.69917553337127e-24
EPR of substrate = 91.6%
energy_mag = 1.85068391186877e-24
energy_mag % of energy_elec_all = 99.8%
Variation 0 [1/1]
Mode 0 at 5.64 GHz [1/2]
Calculating ℰ_magnetic,ℰ_electric
(ℰ_E-ℰ_H)/ℰ_E ℰ_E ℰ_H
99.4% 2.139e-24 1.379e-26
Calculating junction energy participation ration (EPR)
method=`line_voltage`. First estimates:
junction EPR p_0j sign s_0j (p_capacitive)
Energy fraction (Lj over Lj&Cj)= 97.00%
jj 0.992592 (+) 0.0307052
(U_tot_cap-U_tot_ind)/mean=1.56%
Calculating Qdielectric_main for mode 0 (0/1)
p_dielectric_main_0 = 0.9194945926377162
Mode 1 at 9.34 GHz [2/2]
Calculating ℰ_magnetic,ℰ_electric
(ℰ_E-ℰ_H)/ℰ_E ℰ_E ℰ_H
0.2% 9.271e-25 9.253e-25
Calculating junction energy participation ration (EPR)
method=`line_voltage`. First estimates:
junction EPR p_1j sign s_1j (p_capacitive)
Energy fraction (Lj over Lj&Cj)= 92.18%
jj 0.00190362 (+) 0.000161566
(U_tot_cap-U_tot_ind)/mean=0.01%
Calculating Qdielectric_main for mode 1 (1/1)
p_dielectric_main_1 = 0.9163893361503169
WARNING 04:41PM [__init__]: <p>Error: <class 'IndexError'></p>
ANALYSIS DONE. Data saved to:
C:\data-pyEPR\Project37\Design_hfss\2025-07-17 16-40-56.npz
Differences in variations:
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Variation 0
Starting the diagonalization
Finished the diagonalization
Pm_norm=
modes
0 1.031801
1 1.041584
dtype: float64
Pm_norm idx =
jj
0 True
1 False
WARNING:py.warnings:c:\Users\simona.zaccaria4\.conda\envs\qiskit-metal\Lib\site-packages\pyEPR\core_quantum_analysis.py:711: FutureWarning: Support for multi-dimensional indexing (e.g. `obj[:, None]`) is deprecated and will be removed in a future version. Convert to a numpy array before indexing instead.
result['Q_coupling'] = self.Qm_coupling[variation][self.Qm_coupling[variation].columns[junctions]][modes]#TODO change the columns to junctions
WARNING:py.warnings:c:\Users\simona.zaccaria4\.conda\envs\qiskit-metal\Lib\site-packages\pyEPR\core_quantum_analysis.py:716: FutureWarning: Support for multi-dimensional indexing (e.g. `obj[:, None]`) is deprecated and will be removed in a future version. Convert to a numpy array before indexing instead.
result['Qs'] = self.Qs[variation][self.PM[variation].columns[junctions]][modes] #TODO change the columns to junctions
*** P (participation matrix, not normlz.)
jj
0 0.963022
1 0.001903
*** S (sign-bit matrix)
s_jj
0 1
1 -1
*** P (participation matrix, normalized.)
0.99
0.0019
*** Chi matrix O1 PT (MHz)
Diag is anharmonicity, off diag is full cross-Kerr.
296 1.88
1.88 0.00298
*** Chi matrix ND (MHz)
333 1.69
1.69 0.00238
*** Frequencies O1 PT (MHz)
0 5344.782102
1 9343.662915
dtype: float64
*** Frequencies ND (MHz)
0 5326.965047
1 9343.679300
dtype: float64
*** Q_coupling
Empty DataFrame
Columns: []
Index: [0, 1]
Mode frequencies (MHz)
Numerical diagonalization
| Lj | 12.31 |
|---|---|
| 0 | 5326.97 |
| 1 | 9343.68 |
Kerr Non-linear coefficient table (MHz)
Numerical diagonalization
| 0 | 1 | ||
|---|---|---|---|
| Lj | |||
| 12.31 | 0 | 332.93 | 1.69e+00 |
| 1 | 1.69 | 2.38e-03 |
[ ]: