Fluxonium with multi-path coupling(Simultaneous X gate)#
This example is based on Nguyen, L. B. et al. Blueprint for a High-Performance Fluxonium Quantum Processor. PRX Quantum 3, 037001 (2022). We simulate a 6 fluxonium qubit system from an underlying periodic lattice. Idling hamiltonian of the system is
\[H(0) = \sum_i H_{\mathrm{f},i} + \sum_{\langle i,j \rangle } H_{ij}.\]
Hamiltonian of single fluxonium is
\[H_{\mathrm{f},i} = 4E_{\mathrm{C},i} n_i^2 + \frac{1}{2} E_{\mathrm{L},i} (\varphi_i +\varphi_{\mathrm{ext},i})^2
-E_{\mathrm{J},i}\cos \left( \varphi_i \right).\]
The coupling terms have the form
\[H_{ij} = J_{\mathrm{C}} n_i n_j - J_{\mathrm{L}} \varphi_i \varphi_j.\]
The couplings are chosen in a way such that the idling \(ZZ\)-crosstalk is almost zero.
[1]:
import jax
import jax.numpy as jnp
import haiku as hk
import supergrad
from supergrad.helper import Evolve
from supergrad.utils import compute_fidelity_with_1q_rotation_axis
from supergrad.utils.gates import sigmax
from supergrad.utils.optimize import scipy_minimize, adam_opt
from supergrad.utils.utility import tree_print
from supergrad.utils.fidelity import pauli_diagnose_partition
from supergrad.scgraph.graph_mpc_fluxonium_5x5_periodic import XGatePeriodicGraphOpt
truncated_dim = 3 # how many levels we keep after diagonalization
add_random = True # whether to add deviations to fluxonium parameters ec,ej,el
share_params = True # whether we treat marked parameters as shared when computing gradients
unify_coupling = True # set all couplings to be equal
compensation_option = 'only_vz' # Use virtual-z compensation in fidelity computation
# instance the quantum processor graph, and choose a subset for time evolution
gate_graph = XGatePeriodicGraphOpt(1)
qubit_subset = gate_graph.subgraph(['q02', 'q03', 'q12', 'q13', 'q22', 'q23'])
evo = Evolve(qubit_subset, truncated_dim, add_random, share_params, unify_coupling, compensation_option)
target_unitary = supergrad.tensor(*([sigmax()] * len(qubit_subset.nodes)))
Let us print the parameters stored in the evo instance. These parameters are parsed from gate_graph. For how we construct this graph, please check examples/fluxonium_multipath_coupling/graph_5x5_periodic.py and the instructions inside.
[2]:
params = evo.all_params
tree_print(params)
{ 'capacitive_coupling_all_unify': {'strength': 0.07225663},
'inductive_coupling_all_unify': {'strength': -0.01256637},
'q02': {'ec': 6.3532393823, 'ej': 25.1103087675, 'el': 6.344787656},
'q02_pulse_cos': { 'amp': 0.07467672,
'length': 39.82459069,
'omega_d': 3.70771137,
'phase': 0.7558433},
'q03': {'ec': 6.2550610547000005, 'ej': 25.1411401038, 'el': 5.000964059},
'q03_pulse_cos': { 'amp': 0.06839676,
'length': 39.81302627,
'omega_d': 2.56897537,
'phase': 0.85390569},
'q12': {'ec': 6.2233456874, 'ej': 25.1512697752, 'el': 5.6012793457},
'q12_pulse_cos': { 'amp': 0.07142831,
'length': 39.85070846,
'omega_d': 3.07586917,
'phase': 1.58941357},
'q13': {'ec': 6.2867872105, 'ej': 25.1316550509, 'el': 6.9144529962},
'q13_pulse_cos': { 'amp': 0.07763859,
'length': 39.85217838,
'omega_d': 4.20299531,
'phase': 1.43135504},
'q22': { 'ec': 6.282846661600001,
'ej': 25.1329965509,
'el': 7.539286440900001},
'q22_pulse_cos': { 'amp': 0.08054434,
'length': 39.80346128,
'omega_d': 5.00262381,
'phase': 1.39100452},
'q23_pulse_cos': { 'amp': 0.07422721,
'length': 39.85217838,
'omega_d': 3.63596315,
'phase': 0.26554983},
'single_q_compensation': { 'post_comp_q02': -0.41941967,
'post_comp_q03': -0.11531302,
'post_comp_q12': 0.74593951,
'post_comp_q13': 0.58729911,
'post_comp_q22': 0.49022838,
'post_comp_q23': -1.02909962,
'pre_comp_q02': 0.42591073,
'pre_comp_q03': 0.11757419,
'pre_comp_q12': -0.74646573,
'pre_comp_q13': -0.58423741,
'pre_comp_q22': -0.48806854,
'pre_comp_q23': 1.03746918}}
[3]:
def comp_u(params, target_unitary):
params = hk.data_structures.merge(evo.all_params, params)
# evolve system on the eigen basis.
sim_u = evo.eigen_basis(params)
fidelity_vz, compensated_u = compute_fidelity_with_1q_rotation_axis(target_unitary,
sim_u,
opt_method=None)
return compensated_u
compensated_u = comp_u(params, target_unitary)
In the comp_u function in the above cell, we begin by computing the result of the time evolution unitary, sim_u, for the given parameters in params. The computation involves determining the time-evolution unitary matrix in the eigenbasis of the idling Hamiltonian. Subsequently, we calculate a suitable virtual-Z compensation, to ensure that the resulting compensated_u closely resembles the matrix of simultaneous X gates.
We want to assess the level of correlation in the error. Let us define \(U_\mathrm{error} = U_{\mathrm{compensated}}^{\dagger} U_{\mathrm{target}}\). By expanding \(U_\mathrm{error}\) in the Pauli basis, we obtain \(U_\mathrm{error} = \sum_{\vec{j}} a(\vec{j})P_{\vec{j}}\). In the following list, we will provide pairs of \((P_{\vec{j}}, |a(\vec{j})|^2)\). The values \(|a(\vec{j})|^2\) can be interpreted as the probabilities of stochastic errors after performing Pauli twirling. The colors of the text help visualize the weights of errors.
[4]:
partition = [[0],[1],[2],[3],[4],[5]]
res = pauli_diagnose_partition(target_unitary, compensated_u, 20, partition, 'black')
IIIIII 9.9944e-01
IIIZIZ 1.2491e-04
IIIXIY 7.9677e-05
IIIYIY 3.5984e-05
ZIXIII 1.6914e-05
XIZIII 1.6327e-05
ZIZIII 1.4852e-05
XIXIII 1.3981e-05
XYZIII 1.3079e-05
ZZZIII 1.2957e-05
XZXIII 1.2299e-05
ZYXIII 1.1375e-05
ZIZZII 6.4212e-06
XIXZII 6.1497e-06
ZIXYII 4.9756e-06
YIXXIZ 4.8337e-06
XZYIII 4.6177e-06
IZZZII 4.6046e-06
XIZYII 4.2224e-06
IYXZII 4.2033e-06
For optimization, let us use an object function based on the average gate fidelity with leakage. The formula is from Physical Review A 87, 022309 (2013).
\[C = 1 - \frac{1}{D(D + 1)}[Tr(PU^{\dagger}_{\text{sim}}P U_{\text{sim}}P)+|Tr(PU^{\dagger}_{\text{sim}} P U_{\text{target}})|^2],\]
where \(P\) is the projector into the computational subspace \(S\), and \(D=2^n\) is the dimension of \(S\).
[5]:
def infidelity(params, target_unitary):
params = hk.data_structures.merge(evo.all_params, params)
# evolve system on the eigen basis.
sim_u = evo.eigen_basis(params)
# calculate fidelity
fidelity_vz, _ = compute_fidelity_with_1q_rotation_axis(target_unitary,
sim_u,
opt_method=None)
return jnp.log10(1 - fidelity_vz)
[6]:
vg = jax.value_and_grad(infidelity)(params, target_unitary)
print('The infidelity of simultaneous X gates is ', 10**vg[0])
The infidelity of simultaneous X gates is 0.0005508053113444381
[7]:
print('The gradient of log10(infidelity):')
tree_print(vg[1])
The gradient of log10(infidelity):
{ 'capacitive_coupling_all_unify': {'strength': -0.5309703964015999},
'inductive_coupling_all_unify': {'strength': -95.33299084989262},
'q02': { 'ec': 4.510991108929419,
'ej': -1.4335877413870044,
'el': 3.897402459816575},
'q02_pulse_cos': { 'amp': -0.17616989416433634,
'length': -0.011767924126371818,
'omega_d': 0.2070796027309285,
'phase': 0.03886113034190464},
'q03': { 'ec': 1.035356860352813,
'ej': -0.3032938510555648,
'el': 0.923941929183315},
'q03_pulse_cos': { 'amp': -0.1594577926023879,
'length': -0.0035851303999968245,
'omega_d': 0.386760960760304,
'phase': 0.024276396660514205},
'q12': { 'ec': 0.858607626495589,
'ej': -0.2519334257783299,
'el': 0.7343185925646882},
'q12_pulse_cos': { 'amp': -1.0882532478198161,
'length': -0.014192456677496124,
'omega_d': 0.27373879846830107,
'phase': 0.019033004362276618},
'q13': { 'ec': -4.661671509091108,
'ej': 1.5449095480944766,
'el': -4.080660782131437},
'q13_pulse_cos': { 'amp': -1.2224262140670905,
'length': 0.19313453846235853,
'omega_d': -0.15899129273125823,
'phase': 0.00459555419787705},
'q22': { 'ec': 0.09209865451529571,
'ej': -0.02751788836968752,
'el': 0.074544529850944},
'q22_pulse_cos': { 'amp': -1.299310958230257,
'length': -0.002716994492545508,
'omega_d': 0.9313182639936493,
'phase': 0.051166669889598726},
'q23_pulse_cos': { 'amp': 0.20005495732966772,
'length': 0.1980654666753813,
'omega_d': 0.25733070460747953,
'phase': 0.0033182381306149367},
'single_q_compensation': { 'post_comp_q02': 0.002914560484782669,
'post_comp_q03': 0.025256846771640085,
'post_comp_q12': 0.03393082007426074,
'post_comp_q13': 0.029890328615124417,
'post_comp_q22': 0.05376604669856988,
'post_comp_q23': 0.08912374261944933,
'pre_comp_q02': -0.0029145604848963558,
'pre_comp_q03': -0.025256846771640085,
'pre_comp_q12': -0.03393082007426074,
'pre_comp_q13': -0.029890328615124417,
'pre_comp_q22': -0.05376604669891094,
'pre_comp_q23': -0.08912374261956302}}
Show the optimization procedure of control parameters
[8]:
adam_opt(infidelity,
params,
args=(target_unitary,),
options={
'adam_lr': 1e-6,
'steps': 3
})
{'adam_lr': 1e-06, 'adam_lr_decay_rate': 1000, 'steps': 3, 'adam_b1': 0.9, 'adam_b2': 0.999}
step: 0
parameters:
{ 'capacitive_coupling_all_unify': {'strength': 0.07225663},
'inductive_coupling_all_unify': {'strength': -0.01256637},
'q02': {'ec': 6.3532393823, 'ej': 25.1103087675, 'el': 6.344787656},
'q02_pulse_cos': { 'amp': 0.07467672,
'length': 39.82459069,
'omega_d': 3.70771137,
'phase': 0.7558433},
'q03': {'ec': 6.2550610547000005, 'ej': 25.1411401038, 'el': 5.000964059},
'q03_pulse_cos': { 'amp': 0.06839676,
'length': 39.81302627,
'omega_d': 2.56897537,
'phase': 0.85390569},
'q12': {'ec': 6.2233456874, 'ej': 25.1512697752, 'el': 5.6012793457},
'q12_pulse_cos': { 'amp': 0.07142831,
'length': 39.85070846,
'omega_d': 3.07586917,
'phase': 1.58941357},
'q13': {'ec': 6.2867872105, 'ej': 25.1316550509, 'el': 6.9144529962},
'q13_pulse_cos': { 'amp': 0.07763859,
'length': 39.85217838,
'omega_d': 4.20299531,
'phase': 1.43135504},
'q22': { 'ec': 6.282846661600001,
'ej': 25.1329965509,
'el': 7.539286440900001},
'q22_pulse_cos': { 'amp': 0.08054434,
'length': 39.80346128,
'omega_d': 5.00262381,
'phase': 1.39100452},
'q23_pulse_cos': { 'amp': 0.07422721,
'length': 39.85217838,
'omega_d': 3.63596315,
'phase': 0.26554983},
'single_q_compensation': { 'post_comp_q02': -0.41941967,
'post_comp_q03': -0.11531302,
'post_comp_q12': 0.74593951,
'post_comp_q13': 0.58729911,
'post_comp_q22': 0.49022838,
'post_comp_q23': -1.02909962,
'pre_comp_q02': 0.42591073,
'pre_comp_q03': 0.11757419,
'pre_comp_q12': -0.74646573,
'pre_comp_q13': -0.58423741,
'pre_comp_q22': -0.48806854,
'pre_comp_q23': 1.03746918}}
gradient:
{ 'capacitive_coupling_all_unify': {'strength': -0.5309703962971142},
'inductive_coupling_all_unify': {'strength': -12.566370000000001},
'q02': { 'ec': 4.5109916454355625,
'ej': -1.43358791427732,
'el': 3.89740293011098},
'q02_pulse_cos': { 'amp': -0.1761698848549405,
'length': -0.011767924091515855,
'omega_d': 0.2070796098721317,
'phase': 0.03886113029913507},
'q03': { 'ec': 1.0353563751907067,
'ej': -0.30329370608877765,
'el': 0.9239414878825936},
'q03_pulse_cos': { 'amp': -0.15945791464940484,
'length': -0.0035851305565649727,
'omega_d': 0.38676157300785974,
'phase': 0.024276396213001566},
'q12': { 'ec': 0.8586069383446885,
'ej': -0.2519332150768232,
'el': 0.734317978665821},
'q12_pulse_cos': { 'amp': -1.0882534093545768,
'length': -0.014192456894282439,
'omega_d': 0.27373958895040573,
'phase': 0.019033004225246675},
'q13': { 'ec': -4.66167184061817,
'ej': 1.5449096565274032,
'el': -4.080661068342186},
'q13_pulse_cos': { 'amp': -1.2224263082277544,
'length': 0.19313453741225772,
'omega_d': -0.15899095732966373,
'phase': 0.0045955541659363774},
'q22': { 'ec': 0.09209822039514216,
'ej': -0.027517745670091506,
'el': 0.07454416410299658},
'q22_pulse_cos': { 'amp': -1.2993110576468987,
'length': -0.002716994681462594,
'omega_d': 0.9313186385949308,
'phase': 0.05116666956881577},
'q23_pulse_cos': { 'amp': 0.20005508076881806,
'length': 0.19806546598835154,
'omega_d': 0.25733010692021097,
'phase': 0.0033182382134091526},
'single_q_compensation': { 'post_comp_q02': 0.002914560502636886,
'post_comp_q03': 0.02525684631687016,
'post_comp_q12': 0.03393081991372355,
'post_comp_q13': 0.029890328536382075,
'post_comp_q22': 0.05376604637268697,
'post_comp_q23': 0.08912374255095235,
'pre_comp_q02': -0.0029145605028022465,
'pre_comp_q03': -0.025256846316783668,
'pre_comp_q12': -0.03393081991393448,
'pre_comp_q13': -0.029890328536420534,
'pre_comp_q22': -0.05376604637258394,
'pre_comp_q23': -0.08912374255079346}}
loss: -3.259001879689383
step: 1
parameters:
{ 'capacitive_coupling_all_unify': {'strength': 0.07225762999998117},
'inductive_coupling_all_unify': {'strength': -0.012565370000000796},
'q02': { 'ec': 6.3532383823000025,
'ej': 25.110309767499995,
'el': 6.344786656000003},
'q02_pulse_cos': { 'amp': 0.07467771999994324,
'length': 39.82459168999915,
'omega_d': 3.7077103700000484,
'phase': 0.7558423000002573},
'q03': { 'ec': 6.25506005470001,
'ej': 25.141141103799967,
'el': 5.000963059000011},
'q03_pulse_cos': { 'amp': 0.06839775999993729,
'length': 39.813027269997214,
'omega_d': 2.568974370000026,
'phase': 0.853904690000412},
'q12': { 'ec': 6.223344687400012,
'ej': 25.15127077519996,
'el': 5.601278345700013},
'q12_pulse_cos': { 'amp': 0.07142930999999081,
'length': 39.850709459999294,
'omega_d': 3.0758681700000365,
'phase': 1.5894125700005255},
'q13': { 'ec': 6.2867882104999975,
'ej': 25.131654050900007,
'el': 6.914453996199997},
'q13_pulse_cos': { 'amp': 0.0776395899999918,
'length': 39.85217738000005,
'omega_d': 4.2029963099999375,
'phase': 1.431354040002176},
'q22': { 'ec': 6.282845661600109,
'ej': 25.132997550899635,
'el': 7.539285440900135},
'q22_pulse_cos': { 'amp': 0.0805453399999923,
'length': 39.80346227999632,
'omega_d': 5.002622810000011,
'phase': 1.3910035200001956},
'q23_pulse_cos': { 'amp': 0.07422621000004999,
'length': 39.85217738000005,
'omega_d': 3.6359621500000388,
'phase': 0.2655488300030136},
'single_q_compensation': { 'post_comp_q02': -0.41942066999656896,
'post_comp_q03': -0.11531401999960407,
'post_comp_q12': 0.7459385100002948,
'post_comp_q13': 0.5872981100003346,
'post_comp_q22': 0.490227380000186,
'post_comp_q23': -1.0291006199998878,
'pre_comp_q02': 0.42591172999656896,
'pre_comp_q03': 0.11757518999960406,
'pre_comp_q12': -0.7464647300002948,
'pre_comp_q13': -0.5842364100003345,
'pre_comp_q22': -0.488067540000186,
'pre_comp_q23': 1.0374701799998878}}
gradient:
{ 'capacitive_coupling_all_unify': {'strength': -0.5273966146927396},
'inductive_coupling_all_unify': {'strength': -12.565370000000796},
'q02': { 'ec': 4.273884077591268,
'ej': -1.3569788724799359,
'el': 3.6882175947639935},
'q02_pulse_cos': { 'amp': 0.5165145757945755,
'length': -0.010469588589201651,
'omega_d': -0.29625737264844787,
'phase': 0.0003284544607551343},
'q03': { 'ec': 1.025827286479245,
'ej': -0.2998099007972784,
'el': 0.912474989447552},
'q03_pulse_cos': { 'amp': 0.6780106441152334,
'length': -0.002176091834997098,
'omega_d': -0.3520369172444746,
'phase': -0.01333214221694587},
'q12': { 'ec': 0.8786513925179348,
'ej': -0.2574031666959221,
'el': 0.7495531501063301},
'q12_pulse_cos': { 'amp': -0.2816824450342992,
'length': -0.012773134305567837,
'omega_d': -0.511753616833019,
'phase': -0.018974920853638277},
'q13': { 'ec': -4.73875989124974,
'ej': 1.5709925019406492,
'el': -4.150067038684184},
'q13_pulse_cos': { 'amp': -0.5381872316067566,
'length': 0.045259892714813905,
'omega_d': 0.3758555722978514,
'phase': 0.0276743974121354},
'q22': { 'ec': -0.15808763018467983,
'ej': 0.05556322339779525,
'el': -0.1388338352090208},
'q22_pulse_cos': { 'amp': -0.7482316920868876,
'length': -0.0016074898629542286,
'omega_d': 0.3625288528298647,
'phase': 0.011602100803222104},
'q23_pulse_cos': { 'amp': -0.44643326896387214,
'length': 0.04761720007338306,
'omega_d': -0.5219385157412759,
'phase': -0.03512154557035796},
'single_q_compensation': { 'post_comp_q02': -0.03560532400637424,
'post_comp_q03': -0.012352406108427392,
'post_comp_q12': -0.004079659384774278,
'post_comp_q13': 0.05297038714020887,
'post_comp_q22': 0.014201209204872802,
'post_comp_q23': 0.05067526506193966,
'pre_comp_q02': 0.035605324006545605,
'pre_comp_q03': 0.012352406108332768,
'pre_comp_q12': 0.00407965938473423,
'pre_comp_q13': -0.052970387140359405,
'pre_comp_q22': -0.014201209204919296,
'pre_comp_q23': -0.05067526506182068}}
loss: -3.2591219857145908
step: 2
parameters:
{ 'capacitive_coupling_all_unify': {'strength': 0.07225862912544936},
'inductive_coupling_all_unify': {'strength': -0.012564370694982277},
'q02': { 'ec': 6.353237384762291,
'ej': 25.11031076500107,
'el': 6.344785658508757},
'q02_pulse_cos': { 'amp': 0.07467723221127619,
'length': 39.824592684569886,
'omega_d': 3.7077105961044103,
'phase': 0.7558416241424665},
'q03': { 'ec': 6.255059055644446,
'ej': 25.141142102789434,
'el': 5.000962060037683},
'q03_pulse_cos': { 'amp': 0.06839718933301207,
'length': 39.81302822830671,
'omega_d': 2.5689743756201064,
'phase': 0.8539044612497163},
'q12': { 'ec': 6.223343687558409,
'ej': 25.151271775008826,
'el': 5.60127734591076},
'q12_pulse_cos': { 'amp': 0.07143014463529188,
'length': 39.85071045518592,
'omega_d': 3.0758685100784677,
'phase': 1.589412621068456},
'q13': { 'ec': 6.286789210200679,
'ej': 25.131653051191865,
'el': 6.914454995910838},
'q13_pulse_cos': { 'amp': 0.07764050254016314,
'length': 39.852176558337966,
'omega_d': 4.20299588583625,
'phase': 1.4313531967810833},
'q22': { 'ec': 6.282845967280642,
'ej': 25.1329971815084,
'el': 7.539285779497451},
'q22_pulse_cos': { 'amp': 0.08054629141853735,
'length': 39.80346323499337,
'omega_d': 5.0026219161897885,
'phase': 1.3910027024790863},
'q23_pulse_cos': { 'amp': 0.07422661495055978,
'length': 39.852176555069526,
'omega_d': 3.6359625210522197,
'phase': 0.2655495073797313},
'single_q_compensation': { 'post_comp_q02': -0.4194199834534741,
'post_comp_q03': -0.1153142946143694,
'post_comp_q12': 0.7459379340128642,
'post_comp_q13': 0.5872971333535005,
'post_comp_q22': 0.4902265426405682,
'post_comp_q23': -1.0291015697047188,
'pre_comp_q02': 0.4259110434534741,
'pre_comp_q03': 0.1175754646143694,
'pre_comp_q12': -0.7464641540128643,
'pre_comp_q13': -0.5842354333535005,
'pre_comp_q22': -0.4880667026405682,
'pre_comp_q23': 1.0374711297047188}}
gradient:
{ 'capacitive_coupling_all_unify': {'strength': -0.5279331786496049},
'inductive_coupling_all_unify': {'strength': -12.564370694982278},
'q02': { 'ec': 3.8082055307494596,
'ej': -1.2066205010430673,
'el': 3.2781399827373052},
'q02_pulse_cos': { 'amp': 0.16672646739530567,
'length': -0.011105302593538608,
'omega_d': 0.1691722882725415,
'phase': 0.005938361422954452},
'q03': { 'ec': 0.9571225435643961,
'ej': -0.279661208916767,
'el': 0.8516502438825546},
'q03_pulse_cos': { 'amp': 0.2131641872005019,
'length': -0.0029697987794102044,
'omega_d': -0.3186574006716274,
'phase': -0.016075512595097458},
'q12': { 'ec': 0.7941697224091889,
'ej': -0.23094638574915566,
'el': 0.6718542587784281},
'q12_pulse_cos': { 'amp': 0.3767204464392062,
'length': -0.01158075235125628,
'omega_d': -0.28261094825207067,
'phase': -0.012174157169112743},
'q13': { 'ec': -4.678308896334449,
'ej': 1.5520279056032755,
'el': -4.100527664408728},
'q13_pulse_cos': { 'amp': 0.1226077247469517,
'length': 0.023639843205722724,
'omega_d': -0.08378522538959032,
'phase': 0.00760574806680836},
'q22': { 'ec': -0.07143070554939267,
'ej': 0.027883114096305176,
'el': -0.06829565677939539},
'q22_pulse_cos': { 'amp': -0.1514861542144743,
'length': -0.0004137275054945845,
'omega_d': -0.40397032222735874,
'phase': -0.023045497370974832},
'q23_pulse_cos': { 'amp': -0.14820643636574737,
'length': -0.027288075189174525,
'omega_d': -0.2424687090947586,
'phase': -0.027900841356400807},
'single_q_compensation': { 'post_comp_q02': -0.029982160501806087,
'post_comp_q03': -0.015094365741657845,
'post_comp_q12': 0.002716169366036633,
'post_comp_q13': 0.03290300780957872,
'post_comp_q22': -0.02044666650391172,
'post_comp_q23': 0.05788650777019478,
'pre_comp_q02': 0.029982160501621807,
'pre_comp_q03': 0.015094365741554403,
'pre_comp_q12': -0.00271616936622226,
'pre_comp_q13': -0.032903007809740245,
'pre_comp_q22': 0.020446666504006058,
'pre_comp_q23': -0.05788650777033777}}
loss: -3.2592407923863385
[8]:
{'capacitive_coupling_all_unify': {'strength': Array(0.07225963, dtype=float64)},
'inductive_coupling_all_unify': {'strength': Array(-0.01256337, dtype=float64)},
'q02': {'ec': Array(6.35323639, dtype=float64),
'ej': Array(25.11031176, dtype=float64),
'el': Array(6.34478467, dtype=float64)},
'q02_pulse_cos': {'amp': Array(0.07467669, dtype=float64),
'length': Array(39.82459368, dtype=float64),
'omega_d': Array(3.70771048, dtype=float64),
'phase': Array(0.75584101, dtype=float64)},
'q03': {'ec': Array(6.25505806, dtype=float64),
'ej': Array(25.1411431, dtype=float64),
'el': Array(5.00096106, dtype=float64)},
'q03_pulse_cos': {'amp': Array(0.06839658, dtype=float64),
'length': Array(39.8130292, dtype=float64),
'omega_d': Array(2.56897471, dtype=float64),
'phase': Array(0.85390463, dtype=float64)},
'q12': {'ec': Array(6.22334269, dtype=float64),
'ej': Array(25.15127277, dtype=float64),
'el': Array(5.60127635, dtype=float64)},
'q12_pulse_cos': {'amp': Array(0.07143055, dtype=float64),
'length': Array(39.85071144, dtype=float64),
'omega_d': Array(3.07586903, dtype=float64),
'phase': Array(1.58941292, dtype=float64)},
'q13': {'ec': Array(6.28679021, dtype=float64),
'ej': Array(25.13165205, dtype=float64),
'el': Array(6.91445599, dtype=float64)},
'q13_pulse_cos': {'amp': Array(0.07764115, dtype=float64),
'length': Array(39.85217585, dtype=float64),
'omega_d': Array(4.20299569, dtype=float64),
'phase': Array(1.4313524, dtype=float64)},
'q22': {'ec': Array(6.28284642, dtype=float64),
'ej': Array(25.13299666, dtype=float64),
'el': Array(7.53928627, dtype=float64)},
'q22_pulse_cos': {'amp': Array(0.08054709, dtype=float64),
'length': Array(39.80346405, dtype=float64),
'omega_d': Array(5.00262152, dtype=float64),
'phase': Array(1.39100238, dtype=float64)},
'q23_pulse_cos': {'amp': Array(0.0742271, dtype=float64),
'length': Array(39.85217601, dtype=float64),
'omega_d': Array(3.63596303, dtype=float64),
'phase': Array(0.26555031, dtype=float64)},
'single_q_compensation': {'post_comp_q02': Array(-0.41941917, dtype=float64),
'post_comp_q03': Array(-0.11531418, dtype=float64),
'post_comp_q12': Array(0.74593744, dtype=float64),
'post_comp_q13': Array(0.58729617, dtype=float64),
'post_comp_q22': Array(0.49022616, dtype=float64),
'post_comp_q23': Array(-1.02910252, dtype=float64),
'pre_comp_q02': Array(0.42591023, dtype=float64),
'pre_comp_q03': Array(0.11757535, dtype=float64),
'pre_comp_q12': Array(-0.74646366, dtype=float64),
'pre_comp_q13': Array(-0.58423447, dtype=float64),
'pre_comp_q22': Array(-0.48806632, dtype=float64),
'pre_comp_q23': Array(1.03747208, dtype=float64)}}