Note
Click here to download the full example code
Cycle Benchmarking (CB)¶
This example explores implementing Cycle Benchmarking (CB), including the selection of useful parameters. While the example uses a simulator, the circuits generated by this protocol can also be used to characterize the process infidelity of a dressed cycle (a target cycle preceded by a cycle of random elements of the twirling group) in hardware.
Choosing Parameters¶
The make_cb()
method generates a circuit collection to perform cycle
benchmarking. The first argument required by make_cb()
is the cycle
to be benchmarked. The second parameter n_random_cycles
is also a required
parameter, it tells make_cb()
how many times to apply the dressed
cycle in each random circuitl.
The number of circuits for each circuit length, n_circuits
, is 30
by default
and should be chosen to optimize the tradeoff between desired speed and accuracy of
the estimation.
The number of randomly chosen Pauli decay strings used to measure the process
fidelity, n_decays
, should be chosen to exceed
\(min(20, 4 * n_{qubits} - 1)\). The default value for n_decays
is 20
to
satisfy this bound. Choosing a value lower than \(min(20, 4 * n_{qubits} - 1)\)
may result in a biased estimate of the fidelity of the dressed cycle.
The twirl
parameter specifies which twirling group the random gates which
form the pre-compiled dressed cycles are pulled from. By default,
make_cb()
uses the Pauli group, "P"
.
The choice of circuit lengths in n_random_cycles
depends on the cycle being
characterized as well as the selection of twirling group. If the cycle is a Clifford
and the twirling group is "P"
, lengths should be chosen such that applying the
cycle to be benchmarked n_random_cycles
times will result in an identity
operation. In the example below, we benchmark a cycle containing an \(X\) gate and
a controlled-\(Z\) gate, both of which apply an identity operation when raised to
even powers. We therefore choose cycle lengths 4, 12, 64
. While the values of
n_random_cycles
can be any multiple of 2
for this example, users should be
careful to choose a range of values such that the exponential decay is evident in the
plot; this will ensure that the fit function gets enough information to accurately
estimate the fidelity of the dressed cycle. To validate that this condition has been
satisfied, users can plot the data from the CB circuits after running the circuits on
a simulator or on hardware to see where the chosen data points fall.
The final parameter is a bool, propagate_correction
, which tells
make_cb()
whether to compile correction gates for the
twirling group into neighbouring cycles (propagate_correction = False
) or
propagate them to the end of the circuit (propagate_correction = True
). By
default, propagate_correction = False
. Warning: propagating correction to the
end of the circuit can result in arbitrary two-qubit gates at the end of the circuit!
The final circuit can be converted to a user-specified gateset using the
Configuration tools.
Benchmarking a Cycle¶
Initialize a cycle to benchmark:
import trueq as tq
cycle = {(0,): tq.Gate.x, (1, 2): tq.Gate.cz}
Generate a circuit collection to run CB on the above cycle with n_circuits = 30
random circuits for each circuit length in n_random_cycles = [4, 12, 64]
and
n_decays = 24
randomly chosen Pauli decay strings. For the purpose of demonstrating
how to recognize a poor choice of n_random_cycles
, we generate a second CB circuit
collection with the same parameters, except n_random_cycles = [2, 4, 6]
. A good
choice of n_random_cycles
will result in a lower uncertainty in the fit parameters
and therefore a more accurate estimate of the average gate fidelity.
circuits = tq.make_cb(cycle, [4, 12, 64], 30, 24)
bad_circuits = tq.make_cb(cycle, [2, 4, 6], 30, 6)
Initialize a simulator with stochastic Pauli noise and run the cycle benchmarking circuits on the simulator to populate their results. Given this error model, we expect the individual Pauli infidelities corresponding to strings with more than two \(Z\) or \(Y\) to be \(0.01 \times 2 \times\) # of \(Z/X\) terms, where the factor of two comes from simulating errors in both the random and interleaved cycles.
sim = tq.Simulator().add_stochastic_pauli(px=0.01)
sim.run(circuits)
sim.run(bad_circuits)
Plot the results of the circuits with badly chosen n_random_cycles
:
bad_circuits.plot.raw()
![CB on [0, 1, 2]](../../_images/sphx_glr_cb_001.png)
We can see in the plots above that our choices of n_random_cycles
are sampling
from the nearly linear portion of the exponential decay. While this is valid, it is
not efficient (in terms of the amount of required data) at precisely learning the
decay rates. Below, we show the same plots for the better choice n_random_cycles =
[4, 12, 64]
(ideally, the best place to sample is \(1/e\approx 0.37\)).
circuits.plot.raw()
![CB on [0, 1, 2]](../../_images/sphx_glr_cb_002.png)
The output parameters of this protocol are displayed below using the
fit()
function. When the circuits were generated,
n_decays = 24
random three-qubit Paulis were chosen as representatives, and the
rate of decay of each was measured; these decay rates are reported. However, the
parameter of interest is the composite parameter e_F
, which is an estimate of the
process infidelity of the entire cycle.
circuits.fit()
CB
Cycle Benchmarking
|
Paulis
(0,) : Gate.x (1, 2) : Gate.cz
|
${e}_{F}$
The probability of an error acting on the specified labels during a dressed cycle of interest.
|
5.7e-02 (4.7e-03)
0.05660654923833819, 0.004651099795834904
|
${e}_{III}$
The probability of the subscripted error acting on the specified labels.
|
9.4e-01 (4.7e-03)
0.9433934507616618, 0.004651099795834904
|
${p}_{ZZY}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.1e-01 (1.3e-02)
0.9053051804643937, 0.012590916312234522
|
${p}_{ZYI}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.2e-01 (9.2e-03)
0.9245533103635547, 0.00923579427069386
|
${p}_{ZIY}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.0e-01 (9.0e-03)
0.8955364483345173, 0.008998635824359556
|
${p}_{YZY}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.2e-01 (7.3e-03)
0.9203356774466217, 0.00726224758407149
|
${p}_{YZX}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.3e-01 (6.8e-03)
0.9344528258401963, 0.006755455492898369
|
${p}_{YYX}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.2e-01 (7.0e-03)
0.9155208717334846, 0.006950959684362106
|
${p}_{YYI}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.0e-01 (8.8e-03)
0.8999426438882577, 0.008797457453960444
|
${p}_{YXZ}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.4e-01 (6.5e-03)
0.9438001906500402, 0.006529825040108822
|
${p}_{YIY}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.1e-01 (9.9e-03)
0.9070257470528932, 0.009896315149491982
|
${p}_{YIX}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.4e-01 (4.1e-03)
0.9377341250255873, 0.0040872246620158315
|
${p}_{YII}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.6e-01 (1.7e-03)
0.9607484098869462, 0.001670067901087908
|
${p}_{XZY}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.4e-01 (7.2e-03)
0.9358553723753719, 0.007163354493942693
|
${p}_{XYZ}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.3e-01 (7.7e-03)
0.9339053498716433, 0.007705723460885306
|
${p}_{XYY}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.5e-01 (5.1e-03)
0.9496257198617648, 0.0051032119185471896
|
${p}_{XYX}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.6e-01 (3.8e-03)
0.9569602141611232, 0.003846174396255157
|
${p}_{XXX}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.6e-01 (4.0e-03)
0.9575797369789444, 0.003969634320915266
|
${p}_{XXI}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.8e-01 (1.7e-03)
0.979054256306648, 0.001688094647198883
|
${p}_{XIY}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.4e-01 (3.7e-03)
0.9419064972036065, 0.003747889634726731
|
${p}_{IZY}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.4e-01 (3.5e-03)
0.9412321957059028, 0.00346449717011279
|
${p}_{IZX}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.8e-01 (1.1e-03)
0.9828991166489309, 0.0010609037345137044
|
${p}_{IXZ}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.8e-01 (1.4e-03)
0.9810349128584269, 0.001409681908763225
|
${p}_{IXX}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.6e-01 (3.8e-03)
0.9568179794118687, 0.0037847069685601
|
${p}_{IIX}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.8e-01 (7.4e-04)
0.9796160362091574, 0.0007362251872071042
|
${p}_{III}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
1.0e+00 (2.2e-09)
1.0, 2.170496550269722e-09
|
${A}_{ZZY}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.0e-01 (6.6e-02)
0.8968733030704008, 0.06616223023647273
|
${A}_{ZYI}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
8.5e-01 (5.5e-02)
0.8504728835910567, 0.05494179933418948
|
${A}_{ZIY}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.8e-01 (6.1e-02)
0.9765195506057125, 0.060927743311153054
|
${A}_{YZY}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
8.5e-01 (4.6e-02)
0.8535023845325862, 0.046258734383362594
|
${A}_{YZX}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.9e-01 (4.1e-02)
0.9859362053097065, 0.04119725532130212
|
${A}_{YYX}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
1.0e+00 (5.2e-02)
0.999278255077473, 0.05153925001923236
|
${A}_{YYI}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
1.0e+00 (5.9e-02)
1.0245904088053226, 0.05909372578675903
|
${A}_{YXZ}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
8.9e-01 (4.0e-02)
0.8928809480074662, 0.04002755262265458
|
${A}_{YIY}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.1e-01 (5.3e-02)
0.9084506725282604, 0.052604244960084985
|
${A}_{YIX}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.9e-01 (2.4e-02)
0.9888171628784383, 0.023806642517675978
|
${A}_{YII}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.8e-01 (1.2e-02)
0.9759200166149938, 0.01224817328380758
|
${A}_{XZY}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.2e-01 (4.4e-02)
0.9241883785691308, 0.04439436960038296
|
${A}_{XYZ}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.8e-01 (4.8e-02)
0.9750176981068496, 0.0475308456632014
|
${A}_{XYY}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
1.0e+00 (3.4e-02)
0.9968581437876421, 0.034416333437979035
|
${A}_{XYX}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.7e-01 (2.5e-02)
0.9687064322335756, 0.025055777631174114
|
${A}_{XXX}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.1e-01 (3.0e-02)
0.9145267548003483, 0.029780405159035052
|
${A}_{XXI}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.6e-01 (1.5e-02)
0.955082154321567, 0.015301636958452259
|
${A}_{XIY}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.5e-01 (3.0e-02)
0.9545824689199089, 0.029505570966807566
|
${A}_{IZY}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.4e-01 (2.3e-02)
0.9397477012163681, 0.022571831119255967
|
${A}_{IZX}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.5e-01 (1.3e-02)
0.9493020221776663, 0.013399505865611288
|
${A}_{IXZ}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.4e-01 (1.5e-02)
0.9397676865925965, 0.015139725493968633
|
${A}_{IXX}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.4e-01 (2.8e-02)
0.9424339681016649, 0.028269364714816853
|
${A}_{IIX}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.8e-01 (6.9e-03)
0.9847151929043907, 0.006859559064510375
|
${A}_{III}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
1.0e+00 (8.2e-08)
1.0, 8.175216868571883e-08
|
The default fit is to the process infidelity of the entire dressed cycle. We can also manually specify qubit labels to query the process infidelity of subsets of qubits, whose errors will be with respect to the context of the entire cycle.
circuits.fit(labels=[0, [1, 2], [0, 1, 2]]).plot.compare_twirl("e_F")
![Comparison for Paulis on [0, 1, 2]](../../_images/sphx_glr_cb_003.png)
Finally, we can compare the individual Pauli infidelities (see CB for definitions), whose average value estimates the process infidelity. See also stochastic calibration SC to select these curves manually.
circuits.plot.compare_pauli_infidelities()

Targeting Specific Errors¶
We can also use cycle benchmarking to estimate the probabilities of specific errors.
These errors can be supplied using an optional parameter targeted_errors
at
generation (see make_cb()
for more details) or by updating the keys
of existing CB circuits. We demonstrate the latter approach below. Note that
if your circuits are already populated with results, the length of each error must
correspond to the number of measurements in your circuits.
targets = ("XII", "ZII", "IIX", "IIZ")
circuits.update_keys(targeted_errors=targets)
circuits.fit()
CB
Cycle Benchmarking
|
Paulis
(0,) : Gate.x (1, 2) : Gate.cz
|
${e}_{F}$
The probability of an error acting on the specified labels during a dressed cycle of interest.
|
5.7e-02 (4.7e-03)
0.05660654923833819, 0.004651099795834904
|
${e}_{ZII}$
The probability of the subscripted error acting on the specified labels.
|
6.8e-03 (5.7e-03)
0.006795922057048764, 0.005698112798605512
|
${e}_{XII}$
The probability of the subscripted error acting on the specified labels.
|
1.9e-02 (3.5e-03)
0.019499792533576532, 0.003456498109553345
|
${e}_{IIZ}$
The probability of the subscripted error acting on the specified labels.
|
7.1e-03 (5.6e-03)
0.007114825099896027, 0.005640662679771895
|
${e}_{IIX}$
The probability of the subscripted error acting on the specified labels.
|
1.0e-02 (4.4e-03)
0.010218013976483697, 0.004373369829085244
|
${e}_{III}$
The probability of the subscripted error acting on the specified labels.
|
9.4e-01 (4.7e-03)
0.9433934507616618, 0.004651099795834904
|
${p}_{ZZY}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.1e-01 (1.3e-02)
0.9053051804643937, 0.012590916312234522
|
${p}_{ZYI}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.2e-01 (9.2e-03)
0.9245533103635547, 0.00923579427069386
|
${p}_{ZIY}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.0e-01 (9.0e-03)
0.8955364483345173, 0.008998635824359556
|
${p}_{YZY}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.2e-01 (7.3e-03)
0.9203356774466217, 0.00726224758407149
|
${p}_{YZX}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.3e-01 (6.8e-03)
0.9344528258401963, 0.006755455492898369
|
${p}_{YYX}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.2e-01 (7.0e-03)
0.9155208717334846, 0.006950959684362106
|
${p}_{YYI}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.0e-01 (8.8e-03)
0.8999426438882577, 0.008797457453960444
|
${p}_{YXZ}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.4e-01 (6.5e-03)
0.9438001906500402, 0.006529825040108822
|
${p}_{YIY}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.1e-01 (9.9e-03)
0.9070257470528932, 0.009896315149491982
|
${p}_{YIX}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.4e-01 (4.1e-03)
0.9377341250255873, 0.0040872246620158315
|
${p}_{YII}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.6e-01 (1.7e-03)
0.9607484098869462, 0.001670067901087908
|
${p}_{XZY}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.4e-01 (7.2e-03)
0.9358553723753719, 0.007163354493942693
|
${p}_{XYZ}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.3e-01 (7.7e-03)
0.9339053498716433, 0.007705723460885306
|
${p}_{XYY}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.5e-01 (5.1e-03)
0.9496257198617648, 0.0051032119185471896
|
${p}_{XYX}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.6e-01 (3.8e-03)
0.9569602141611232, 0.003846174396255157
|
${p}_{XXX}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.6e-01 (4.0e-03)
0.9575797369789444, 0.003969634320915266
|
${p}_{XXI}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.8e-01 (1.7e-03)
0.979054256306648, 0.001688094647198883
|
${p}_{XIY}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.4e-01 (3.7e-03)
0.9419064972036065, 0.003747889634726731
|
${p}_{IZY}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.4e-01 (3.5e-03)
0.9412321957059028, 0.00346449717011279
|
${p}_{IZX}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.8e-01 (1.1e-03)
0.9828991166489309, 0.0010609037345137044
|
${p}_{IXZ}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.8e-01 (1.4e-03)
0.9810349128584269, 0.001409681908763225
|
${p}_{IXX}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.6e-01 (3.8e-03)
0.9568179794118687, 0.0037847069685601
|
${p}_{IIX}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.8e-01 (7.4e-04)
0.9796160362091574, 0.0007362251872071042
|
${p}_{III}$
Decay parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
1.0e+00 (2.2e-09)
1.0, 2.170496550269722e-09
|
${A}_{ZZY}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.0e-01 (6.6e-02)
0.8968733030704008, 0.06616223023647273
|
${A}_{ZYI}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
8.5e-01 (5.5e-02)
0.8504728835910567, 0.05494179933418948
|
${A}_{ZIY}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.8e-01 (6.1e-02)
0.9765195506057125, 0.060927743311153054
|
${A}_{YZY}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
8.5e-01 (4.6e-02)
0.8535023845325862, 0.046258734383362594
|
${A}_{YZX}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.9e-01 (4.1e-02)
0.9859362053097065, 0.04119725532130212
|
${A}_{YYX}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
1.0e+00 (5.2e-02)
0.999278255077473, 0.05153925001923236
|
${A}_{YYI}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
1.0e+00 (5.9e-02)
1.0245904088053226, 0.05909372578675903
|
${A}_{YXZ}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
8.9e-01 (4.0e-02)
0.8928809480074662, 0.04002755262265458
|
${A}_{YIY}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.1e-01 (5.3e-02)
0.9084506725282604, 0.052604244960084985
|
${A}_{YIX}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.9e-01 (2.4e-02)
0.9888171628784383, 0.023806642517675978
|
${A}_{YII}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.8e-01 (1.2e-02)
0.9759200166149938, 0.01224817328380758
|
${A}_{XZY}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.2e-01 (4.4e-02)
0.9241883785691308, 0.04439436960038296
|
${A}_{XYZ}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.8e-01 (4.8e-02)
0.9750176981068496, 0.0475308456632014
|
${A}_{XYY}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
1.0e+00 (3.4e-02)
0.9968581437876421, 0.034416333437979035
|
${A}_{XYX}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.7e-01 (2.5e-02)
0.9687064322335756, 0.025055777631174114
|
${A}_{XXX}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.1e-01 (3.0e-02)
0.9145267548003483, 0.029780405159035052
|
${A}_{XXI}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.6e-01 (1.5e-02)
0.955082154321567, 0.015301636958452259
|
${A}_{XIY}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.5e-01 (3.0e-02)
0.9545824689199089, 0.029505570966807566
|
${A}_{IZY}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.4e-01 (2.3e-02)
0.9397477012163681, 0.022571831119255967
|
${A}_{IZX}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.5e-01 (1.3e-02)
0.9493020221776663, 0.013399505865611288
|
${A}_{IXZ}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.4e-01 (1.5e-02)
0.9397676865925965, 0.015139725493968633
|
${A}_{IXX}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.4e-01 (2.8e-02)
0.9424339681016649, 0.028269364714816853
|
${A}_{IIX}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
9.8e-01 (6.9e-03)
0.9847151929043907, 0.006859559064510375
|
${A}_{III}$
SPAM parameter of the exponential decay $Ap^m$ for the given Pauli term.
|
1.0e+00 (8.2e-08)
1.0, 8.175216868571883e-08
|
We can plot the probability of specific errors acting on the qubits during the cycle of interest:
circuits.plot.compare_twirl([f"e_{targ}" for targ in targets])
![Comparison for Paulis on [0, 1, 2]](../../_images/sphx_glr_cb_005.png)
Total running time of the script: ( 0 minutes 8.572 seconds)