Sweeping over a paramter range in HFSS 🧹

Analyzing the cavity is nice and all, but it very likely that you'll want to modify and optimize the cavity and it's properties for your needs. For this you can simulate many different possibilities and choose the best paramters for you.

Let's say, for example, you want the coupling between the readout resonator and transmon would be around $1$ MHz, what should be the distance between them? Let's check!

In [1]:
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
import pyEPR as epr

plt.style.use('ggplot')
plt.style.use('seaborn-darkgrid')

🔹 Connecting to HFSS

In [2]:
pinfo = epr.Project_Info(project_path = '.', 
                         project_name = 'transmon-cavity-ro',  # File name
                         design_name  = 'design')

INFO 10:58PM [connect]: Connecting to Ansys Desktop API...
INFO 10:58PM [load_ansys_project]: 	File path to HFSS project found.
INFO 10:58PM [load_ansys_project]: 	Opened Ansys App
INFO 10:58PM [load_ansys_project]: 	Opened Ansys Desktop v2020.1.0
INFO 10:58PM [load_ansys_project]: 	Opened Ansys Project
	Folder:    C:/Users/rosengrp/Downloads/sweep-ro/
	Project:   transmon-cavity-ro
INFO 10:58PM [connect]: 	Opened active design
	Design:    design [Solution type: Eigenmode]
INFO 10:58PM [get_setup]: 	Opened setup `Setup1`  (<class 'pyEPR.ansys.HfssEMSetup'>)
INFO 10:58PM [connect]: 	Connection to Ansys established successfully. 😀

🧹 Sweep over the parameter

The parameter defining the distance between the transmon and readout is ro_gap, let's see what's it's value in the design

In [3]:
ro_gap = pinfo.design.get_variable_value('ro_gap')
ro_gap
Out[3]:
'2mm'

Let's sweep then between $0.5$mm and $3$mm and see which is the best value

In [4]:
swp_var = 'ro_gap'  # Sweep ove 'ro_gap'
def to_swp_val(x): return f'{x}mm' 

for swp_param in np.linspace(0.5, 3, 6):
    swp_val = to_swp_val(swp_param)
    epr.logger.info(f'Setting sweep variable {swp_var}={swp_val}')
    pinfo.design.set_variable(swp_var, swp_val)
    pinfo.setup.analyze()

INFO 10:58PM [<module>]: Setting sweep variable ro_gap=0.5mm
INFO 10:58PM [analyze]: Analyzing setup Setup1
INFO 11:00PM [<module>]: Setting sweep variable ro_gap=1.0mm
INFO 11:00PM [analyze]: Analyzing setup Setup1
INFO 11:01PM [<module>]: Setting sweep variable ro_gap=1.5mm
INFO 11:01PM [analyze]: Analyzing setup Setup1
INFO 11:02PM [<module>]: Setting sweep variable ro_gap=2.0mm
INFO 11:02PM [analyze]: Analyzing setup Setup1
INFO 11:02PM [<module>]: Setting sweep variable ro_gap=2.5mm
INFO 11:02PM [analyze]: Analyzing setup Setup1
INFO 11:04PM [<module>]: Setting sweep variable ro_gap=3.0mm
INFO 11:04PM [analyze]: Analyzing setup Setup1

🔹 Define the junction (and any other non-linear component)

In [5]:
pinfo.junctions['j1'] = {'Lj_variable' : 'Lj_1',
                         'rect'        : 'rect_jj1', 
                         'line'        : 'line_jj1', 
                         'length'      : epr.parse_units('100um')}

# Check that valid names of variables and objects have been supplied.
# An error is raised with a message if something is wrong.
pinfo.validate_junction_info()

🔹 Distributed Analysis (not quantum)

Note that 3 modes is the maximum we can analyze fully❗ See this issue

Also, now when we do the EPR analysis we can see that there are 6 variations, one for each value of the parameter we check

In [6]:
eprh = epr.DistributedAnalysis(pinfo)

eprh.do_EPR_analysis(modes=[0,1,4]);

Design "design" info:
	# eigenmodes    5
	# variations    6

Variation 0  [1/6]

  Mode 0 at 4.57 GHz   [1/5]
    Calculating ℰ_magnetic,ℰ_electric
       (ℰ_E-ℰ_H)/ℰ_E       ℰ_E       ℰ_H
               97.4%  1.776e-24  4.61e-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)= 98.70%
	j1              0.972288  (+)        0.0128067
		(U_tot_cap-U_tot_ind)/mean=0.72%

  Mode 1 at 4.85 GHz   [2/5]
    Calculating ℰ_magnetic,ℰ_electric
       (ℰ_E-ℰ_H)/ℰ_E       ℰ_E       ℰ_H
                0.1%   9.56e-21 9.554e-21

    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)= 98.54%
	j1              0.000159513  (+)        2.36977e-06
		(U_tot_cap-U_tot_ind)/mean=0.02%

  Mode 4 at 7.62 GHz   [5/5]
    Calculating ℰ_magnetic,ℰ_electric
       (ℰ_E-ℰ_H)/ℰ_E       ℰ_E       ℰ_H
                2.0%  3.223e-22 3.159e-22

    Calculating junction energy participation ration (EPR)
	method=`line_voltage`. First estimates:
	junction        EPR p_4j   sign s_4j    (p_capacitive)
		Energy fraction (Lj over Lj&Cj)= 96.46%
	j1              0.00097423  (+)        3.57338e-05
		(U_tot_cap-U_tot_ind)/mean=0.95%

Variation 1  [2/6]

  Mode 0 at 4.51 GHz   [1/5]
    Calculating ℰ_magnetic,ℰ_electric
       (ℰ_E-ℰ_H)/ℰ_E       ℰ_E       ℰ_H
               96.6%  1.298e-24 4.413e-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)= 98.73%
	j1              0.963758  (+)        0.0123721
		(U_tot_cap-U_tot_ind)/mean=0.73%

  Mode 1 at 4.85 GHz   [2/5]
    Calculating ℰ_magnetic,ℰ_electric
       (ℰ_E-ℰ_H)/ℰ_E       ℰ_E       ℰ_H
                0.1%  5.605e-21 5.602e-21

    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)= 98.54%
	j1              0.000192748  (+)        2.8636e-06
		(U_tot_cap-U_tot_ind)/mean=0.02%

  Mode 4 at 7.61 GHz   [5/5]
    Calculating ℰ_magnetic,ℰ_electric
       (ℰ_E-ℰ_H)/ℰ_E       ℰ_E       ℰ_H
                2.9%  5.051e-23 4.907e-23

    Calculating junction energy participation ration (EPR)
	method=`line_voltage`. First estimates:
	junction        EPR p_4j   sign s_4j    (p_capacitive)
		Energy fraction (Lj over Lj&Cj)= 96.47%
	j1              0.00849854  (+)        0.000311068
		(U_tot_cap-U_tot_ind)/mean=1.03%

Variation 2  [3/6]

  Mode 0 at 4.58 GHz   [1/5]
    Calculating ℰ_magnetic,ℰ_electric
       (ℰ_E-ℰ_H)/ℰ_E       ℰ_E       ℰ_H
               97.1%  4.169e-24  1.21e-25

    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)= 98.69%
	j1              0.968802  (+)        0.0128262
		(U_tot_cap-U_tot_ind)/mean=0.75%

  Mode 1 at 4.85 GHz   [2/5]
    Calculating ℰ_magnetic,ℰ_electric
       (ℰ_E-ℰ_H)/ℰ_E       ℰ_E       ℰ_H
                0.1%  2.031e-20  2.03e-20

    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)= 98.54%
	j1              0.000177361  (+)        2.63501e-06
		(U_tot_cap-U_tot_ind)/mean=0.02%

  Mode 4 at 7.62 GHz   [5/5]
    Calculating ℰ_magnetic,ℰ_electric
       (ℰ_E-ℰ_H)/ℰ_E       ℰ_E       ℰ_H
                2.5%  2.581e-22 2.517e-22

    Calculating junction energy participation ration (EPR)
	method=`line_voltage`. First estimates:
	junction        EPR p_4j   sign s_4j    (p_capacitive)
		Energy fraction (Lj over Lj&Cj)= 96.47%
	j1              0.00397624  (+)        0.000145655
		(U_tot_cap-U_tot_ind)/mean=1.07%

Variation 3  [4/6]

  Mode 0 at 4.57 GHz   [1/5]
    Calculating ℰ_magnetic,ℰ_electric
       (ℰ_E-ℰ_H)/ℰ_E       ℰ_E       ℰ_H
               97.3%  3.277e-24 8.999e-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)= 98.70%
	j1              0.969842  (+)        0.0127802
		(U_tot_cap-U_tot_ind)/mean=0.77%

  Mode 1 at 4.85 GHz   [2/5]
    Calculating ℰ_magnetic,ℰ_electric
       (ℰ_E-ℰ_H)/ℰ_E       ℰ_E       ℰ_H
                0.1%  1.808e-20 1.807e-20

    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)= 98.54%
	j1              0.000155679  (+)        2.31278e-06
		(U_tot_cap-U_tot_ind)/mean=0.02%

  Mode 4 at 7.62 GHz   [5/5]
    Calculating ℰ_magnetic,ℰ_electric
       (ℰ_E-ℰ_H)/ℰ_E       ℰ_E       ℰ_H
                2.0%  3.358e-22 3.291e-22

    Calculating junction energy participation ration (EPR)
	method=`line_voltage`. First estimates:
	junction        EPR p_4j   sign s_4j    (p_capacitive)
		Energy fraction (Lj over Lj&Cj)= 96.46%
	j1              0.00201137  (+)        7.37939e-05
		(U_tot_cap-U_tot_ind)/mean=0.91%

Variation 4  [5/6]

  Mode 0 at 4.52 GHz   [1/5]
    Calculating ℰ_magnetic,ℰ_electric
       (ℰ_E-ℰ_H)/ℰ_E       ℰ_E       ℰ_H
               97.6%  3.637e-24 8.818e-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)= 98.72%
	j1              0.973094  (+)        0.0125819
		(U_tot_cap-U_tot_ind)/mean=0.76%

  Mode 1 at 4.85 GHz   [2/5]
    Calculating ℰ_magnetic,ℰ_electric
       (ℰ_E-ℰ_H)/ℰ_E       ℰ_E       ℰ_H
                0.0%  1.664e-20 1.663e-20

    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)= 98.54%
	j1              0.000184762  (+)        2.74508e-06
		(U_tot_cap-U_tot_ind)/mean=0.01%

  Mode 4 at 7.64 GHz   [5/5]
    Calculating ℰ_magnetic,ℰ_electric
       (ℰ_E-ℰ_H)/ℰ_E       ℰ_E       ℰ_H
                1.9%   2.04e-22 2.002e-22

    Calculating junction energy participation ration (EPR)
	method=`line_voltage`. First estimates:
	junction        EPR p_4j   sign s_4j    (p_capacitive)
		Energy fraction (Lj over Lj&Cj)= 96.44%
	j1              0.000473822  (+)        1.74688e-05
		(U_tot_cap-U_tot_ind)/mean=0.93%

Variation 5  [6/6]

  Mode 0 at 4.54 GHz   [1/5]
    Calculating ℰ_magnetic,ℰ_electric
       (ℰ_E-ℰ_H)/ℰ_E       ℰ_E       ℰ_H
               97.6%  2.615e-24 6.398e-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)= 98.72%
	j1              0.973765  (+)        0.0126657
		(U_tot_cap-U_tot_ind)/mean=0.72%

  Mode 1 at 4.85 GHz   [2/5]
    Calculating ℰ_magnetic,ℰ_electric
       (ℰ_E-ℰ_H)/ℰ_E       ℰ_E       ℰ_H
                0.1%  1.432e-20 1.431e-20

    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)= 98.54%
	j1              0.000156612  (+)        2.32669e-06
		(U_tot_cap-U_tot_ind)/mean=0.02%

  Mode 4 at 7.64 GHz   [5/5]
    Calculating ℰ_magnetic,ℰ_electric
       (ℰ_E-ℰ_H)/ℰ_E       ℰ_E       ℰ_H
                2.1%  3.809e-22 3.731e-22

    Calculating junction energy participation ration (EPR)
	method=`line_voltage`. First estimates:
	junction        EPR p_4j   sign s_4j    (p_capacitive)
		Energy fraction (Lj over Lj&Cj)= 96.45%
	j1              0.000255005  (+)        9.39298e-06
		(U_tot_cap-U_tot_ind)/mean=1.03%

ANALYSIS DONE. Data saved to:

D:\data-pyEPR\transmon-cavity-ro\design\2020-09-22 23-05-39.npz

🔹 Quantum Analysis (yes quantum)

In [7]:
epra = epr.QuantumAnalysis(eprh.data_filename)
epra.analyze_all_variations(cos_trunc = 8, fock_trunc = 15);

	 Differences in variations:
variation 0 1 2 3 4 5
_ro_gap 2mm 0.5mm 1mm 1.5mm 2.5mm 3mm 


 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
Variation 0

Starting the diagonalization
Finished the diagonalization
Pm_norm=
modes
0     1.014784
1     2.373458
4    10.808200
dtype: float64

Pm_norm idx =
      j1
0   True
1  False
4  False

*** Different parameters

_ro_gap    2mm
Name: 0, dtype: object

*** P (participation matrix, not normlz.)
         j1
0  0.959994
1  0.000160
4  0.000974

*** S (sign-bit matrix)
   s_j1
0     1
1     1
4     1
*** P (participation matrix, normalized.)
      0.97
   0.00016
   0.00097

*** Chi matrix O1 PT (MHz)
    Diag is anharmonicity, off diag is full cross-Kerr.
       121   0.0421    0.404
    0.0421 3.66e-06 7.03e-05
     0.404 7.03e-05 0.000337

*** Chi matrix ND (MHz) 
       129   0.0164    0.381
    0.0164 7.82e-07  3.2e-05
     0.381  3.2e-05 0.000297

*** Frequencies O1 PT (MHz)
0    4445.186438
1    4849.678816
2    7620.046235
dtype: float64

*** Frequencies ND (MHz)
0    4441.791707
1    4849.684856
2    7620.048491
dtype: float64

*** Q_coupling
Empty DataFrame
Columns: []
Index: [0, 1, 4]

 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
Variation 1

Starting the diagonalization
Finished the diagonalization
Pm_norm=
modes
0    1.014906
1    2.168980
4    2.217915
dtype: float64

Pm_norm idx =
      j1
0   True
1  False
4  False

*** Different parameters

_ro_gap    0.5mm
Name: 1, dtype: object

*** P (participation matrix, not normlz.)
         j1
0  0.951980
1  0.000193
4  0.008496

*** S (sign-bit matrix)
   s_j1
0     1
1     1
4     1
*** P (participation matrix, normalized.)
      0.97
   0.00019
    0.0085

*** Chi matrix O1 PT (MHz)
    Diag is anharmonicity, off diag is full cross-Kerr.
       116   0.0498     3.45
    0.0498 5.35e-06  0.00074
      3.45  0.00074   0.0256

*** Chi matrix ND (MHz) 
       124   0.0229     3.27
    0.0229 1.49e-06 0.000381
      3.27 0.000381   0.0226

*** Frequencies O1 PT (MHz)
0    4390.336639
1    4849.752351
2    7610.547454
dtype: float64

*** Frequencies ND (MHz)
0    4387.018415
1    4849.758446
2    7610.564399
dtype: float64

*** Q_coupling
Empty DataFrame
Columns: []
Index: [0, 1, 4]

 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
Variation 2

Starting the diagonalization
Finished the diagonalization
Pm_norm=
modes
0    1.015272
1    2.038642
4    3.691355
dtype: float64

Pm_norm idx =
      j1
0   True
1  False
4  False

*** Different parameters

_ro_gap    1mm
Name: 2, dtype: object

*** P (participation matrix, not normlz.)
         j1
0  0.956533
1  0.000177
4  0.003976

*** S (sign-bit matrix)
   s_j1
0     1
1     1
4     1
*** P (participation matrix, normalized.)
      0.97
   0.00018
     0.004

*** Chi matrix O1 PT (MHz)
    Diag is anharmonicity, off diag is full cross-Kerr.
       121   0.0468     1.65
    0.0468 4.53e-06 0.000319
      1.65 0.000319  0.00561

*** Chi matrix ND (MHz) 
       129   0.0177     1.55
    0.0177 9.11e-07 0.000141
      1.55 0.000141  0.00492

*** Frequencies O1 PT (MHz)
0    4456.383436
1    4849.755344
2    7614.458066
dtype: float64

*** Frequencies ND (MHz)
0    4452.934948
1    4849.762324
2    7614.467588
dtype: float64

*** Q_coupling
Empty DataFrame
Columns: []
Index: [0, 1, 4]

 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
Variation 3

Starting the diagonalization
Finished the diagonalization
Pm_norm=
modes
0    1.015738
1    2.455907
4    5.536927
dtype: float64

Pm_norm idx =
      j1
0   True
1  False
4  False

*** Different parameters

_ro_gap    1.5mm
Name: 3, dtype: object

*** P (participation matrix, not normlz.)
         j1
0  0.957604
1  0.000156
4  0.002011

*** S (sign-bit matrix)
   s_j1
0     1
1     1
4     1
*** P (participation matrix, normalized.)
      0.97
   0.00016
     0.002

*** Chi matrix O1 PT (MHz)
    Diag is anharmonicity, off diag is full cross-Kerr.
       121    0.041    0.833
     0.041 3.49e-06 0.000142
     0.833 0.000142  0.00144

*** Chi matrix ND (MHz) 
       129    0.016    0.787
     0.016 7.42e-07 6.44e-05
     0.787 6.44e-05  0.00126

*** Frequencies O1 PT (MHz)
0    4446.307215
1    4849.653175
2    7620.797354
dtype: float64

*** Frequencies ND (MHz)
0    4442.910030
1    4849.659084
2    7620.802016
dtype: float64

*** Q_coupling
Empty DataFrame
Columns: []
Index: [0, 1, 4]

 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
Variation 4

Starting the diagonalization
Finished the diagonalization
Pm_norm=
modes
0     1.015473
1     1.798462
4    20.613832
dtype: float64

Pm_norm idx =
      j1
0   True
1  False
4  False

*** Different parameters

_ro_gap    2.5mm
Name: 4, dtype: object

*** P (participation matrix, not normlz.)
         j1
0  0.961003
1  0.000185
4  0.000474

*** S (sign-bit matrix)
   s_j1
0     1
1     1
4     1
*** P (participation matrix, normalized.)
      0.98
   0.00018
   0.00047

*** Chi matrix O1 PT (MHz)
    Diag is anharmonicity, off diag is full cross-Kerr.
       119   0.0484    0.196
    0.0484 4.91e-06 3.97e-05
     0.196 3.97e-05 8.02e-05

*** Chi matrix ND (MHz) 
       127   0.0212    0.185
    0.0212 1.27e-06 1.99e-05
     0.185 1.99e-05 7.09e-05

*** Frequencies O1 PT (MHz)
0    4404.970690
1    4849.858772
2    7639.745937
dtype: float64

*** Frequencies ND (MHz)
0    4401.653775
1    4849.864919
2    7639.746894
dtype: float64

*** Q_coupling
Empty DataFrame
Columns: []
Index: [0, 1, 4]

 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
Variation 5

Starting the diagonalization
Finished the diagonalization
Pm_norm=
modes
0     1.014646
1     2.203604
4    41.495446
dtype: float64

Pm_norm idx =
      j1
0   True
1  False
4  False

*** Different parameters

_ro_gap    3mm
Name: 5, dtype: object

*** P (participation matrix, not normlz.)
         j1
0  0.961586
1  0.000157
4  0.000255

*** S (sign-bit matrix)
   s_j1
0     1
1     1
4     1
*** P (participation matrix, normalized.)
      0.98
   0.00016
   0.00026

*** Chi matrix O1 PT (MHz)
    Diag is anharmonicity, off diag is full cross-Kerr.
       120   0.0411    0.105
    0.0411 3.53e-06 1.81e-05
     0.105 1.81e-05 2.32e-05

*** Chi matrix ND (MHz) 
       128   0.0174   0.0999
    0.0174 8.63e-07 8.81e-06
    0.0999 8.81e-06 2.05e-05

*** Frequencies O1 PT (MHz)
0    4417.824694
1    4849.694794
2    7636.332029
dtype: float64

*** Frequencies ND (MHz)
0    4414.488101
1    4849.700220
2    7636.332566
dtype: float64

*** Q_coupling
Empty DataFrame
Columns: []
Index: [0, 1, 4]

Does this make sense?🤔

We can plot the results and see weather or not they make sense. We expect two things:

  • The anharmonicities should not change, since we don't change the structure of the devices
  • The cross-kerr frequencies should drop exponentialy, since electromagnetic waves decay exponentialy in a waveguide and the cross-kerr (aka the coupling) between the components is how much can they interact through the electric field, which is closely related to how much of the electric field 'survives' when going from one component to the other
In [8]:
epra.plot_hamiltonian_results();

C:\Users\rosengrp\anaconda3\lib\site-packages\pandas\plotting\_matplotlib\core.py:1235: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_xticklabels(xticklabels)
C:\Users\rosengrp\anaconda3\lib\site-packages\pandas\plotting\_matplotlib\core.py:1235: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_xticklabels(xticklabels)
C:\Users\rosengrp\anaconda3\lib\site-packages\pandas\plotting\_matplotlib\core.py:1235: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_xticklabels(xticklabels)
C:\Users\rosengrp\anaconda3\lib\site-packages\pandas\plotting\_matplotlib\core.py:1235: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_xticklabels(xticklabels)

Success 🎉🎈🎊🥳💃

OK, maybe $0.5$ mm is too close but as you can see, if we want the coupling between the readout and transmon to be around $1$ MHz we need the distance between them to be roughly $1.8$ mm

In [ ]: