Note
This is the documentation for the current state of the development branch of Qiskit Experiments. The documentation or APIs here can change prior to being released.
FineDrag¶
- class FineDrag(physical_qubits, gate, backend=None)[source]¶
An experiment that performs fine characterizations of DRAG pulse coefficients.
Overview
FineDrag
runs fine DRAG characterization experiments (seeRoughDrag
for the definition of DRAG pulses). Fine DRAG proceeds by iterating the gate sequence Rp - Rm where Rp is a rotation around an axis and Rm is the same rotation but in the opposite direction and is implemented by the gates Rz - Rp - Rz where the Rz gates are virtual Z-rotations, see Ref. [1]. The executed circuits are of the form┌─────┐┌────┐┌───────┐┌────┐┌───────┐ ┌──────┐ ░ ┌─┐ q_0: ┤ Pre ├┤ Rp ├┤ Rz(π) ├┤ Rp ├┤ Rz(π) ├ ... ┤ Post ├─░─┤M├ └─────┘└────┘└───────┘└────┘└───────┘ └──────┘ ░ └╥┘ meas: 1/══════════════════════════════════════════════════════╩═ 0
Here, “Pre” and “Post” designate gates that may be pre-appended and and post-appended, respectively, to the repeated sequence of Rp - Rz - Rp - Rz gates. When calibrating a pulse with a target rotation angle of π the Pre and Post gates are Id and RYGate(π/2), respectively. When calibrating a pulse with a target rotation angle of π/2 the Pre and Post gates are RXGate(π/2) and RYGate(π/2), respectively.
We now describe what this experiment corrects by following Ref. [2]. We follow equations 4.30 and onwards of Ref. [2] which state that the first-order corrections to the control fields are
\[\begin{split}\begin{align} \bar{\Omega}_x^{(1)}(t) = &\, 2\dot{s}^{(1)}_{x,0,1}(t) \\ \bar{\Omega}_y^{(1)}(t) = &\, 2\dot{s}^{(1)}_{y,0,1}(t) - s_{z,1}^{(1)}(t)t_g\Omega_x(t) \\ \bar{\delta}^{(1)}(t) = &\, \dot{s}_{z,1}^{(1)}(t) + 2s^{(1)}_{y,0,1}(t)t_g\Omega_x(t) + \frac{\lambda_1^2 t_g^2 \Omega_x^2(t)}{4} \end{align}\end{split}\]Here, the \(s\) terms are coefficients of the expansion of an operator \(S(t)\) that generates a transformation that keeps the qubit sub-space isolated from the higher-order states. \(t_g\) is the gate time, \(\Omega_x(t)\) is the pulse envelope on the in-phase component of the drive and \(\lambda_1\) is a parameter of the Hamiltonian. For additional details please see Ref. [2]. As in Ref. [2] we now set \(s^{(1)}_{x,0,1}\) and \(s^{(1)}_{z,1}\) to zero and set \(s^{(1)}_{y,0,1}\) to \(-\lambda_1^2 t_g\Omega_x(t)/8\). This results in a Z angle rotation rate of \(\bar{\delta}^{(1)}(t)=0\) in the equations above and defines the value for the ideal \(\beta\) parameter. In Qiskit pulse, the definition of the DRAG pulse is
\[\Omega(t) = \Omega_x(t) + i\beta\,\dot{\Omega}_x(t)\quad\Longrightarrow\quad \Omega_y(t)= \beta\,\dot{\Omega}_x(t)\]which implies that \(-\lambda_1^2 t_g/4\) is the ideal \(\beta\) value. We now assume that there is a small error \({\rm d}\beta\) in \(\beta\) such that the instantaneous Z-angle error induced by a single pulse is
\[\bar\delta(t) = {\rm d}\beta\, \Omega^2_x(t)\]We can integrate \(\bar{\delta}(t)\), i.e. the instantaneous \(Z\)-angle rotation error, to obtain the total rotation angle error per pulse, \({\rm d}\theta\):
\[{\rm d}\theta = \int\bar\delta(t){\rm d}t = {\rm d}\beta \int\Omega^2_x(t){\rm d}t\]If we assume a Gaussian pulse, i.e. \(\Omega_x(t)=A\exp[-t^2/(2\sigma^2)]\) then the integral of \(\Omega_x^2(t)\) in the equation above results in \(A^2\sigma\sqrt{\pi}\). Furthermore, the integral of \(\Omega_x(t)\) is \(A\sigma\sqrt{\pi/2}=\theta_\text{target}\), where \(\theta_\text{target}\) is the target rotation angle, i.e. the area under the pulse. This last point allows us to rewrite \(A^2\sigma\sqrt{\pi}\) as \(\theta^2_\text{target}/(2\sigma\sqrt{\pi})\). The total \(Z\) angle error per pulse is therefore
\[{\rm d}\theta= \int\bar\delta(t){\rm d}t={\rm d}\beta\,\frac{\theta^2_\text{target}}{2\sigma\sqrt{\pi}}\]Here, \({\rm d}\theta\) is the \(Z\) angle error per pulse. The qubit population produced by the gate sequence shown above is used to measure \({\rm d}\theta\). Indeed, each gate pair Rp - Rm will produce a small unwanted \(Z\)-rotation out of the \(ZX\) plane with a magnitude \(2\,{\rm d}\theta\). The total rotation out of the \(ZX\) plane is then mapped to a qubit population by the final Post gate. Inverting the relation above after cancelling out the factor of two due to the Rp - Rm pulse pair yields the error in \(\beta\) that produced the rotation error \({\rm d}\theta\) as
\[{\rm d}\beta=\frac{\sqrt{\pi}\,{\rm d}\theta\sigma}{ \theta_\text{target}^2}.\]This is the correction formula in the FineDRAG Updater.
References
[1] David C. McKay, Christopher J. Wood, Sarah Sheldon, Jerry M. Chow, Jay M. Gambetta, Efficient Z-Gates for Quantum Computing, Phys. Rev. A 96, 022330 (2017), doi: 10.1103/PhysRevA.96.022330 (open)
[2] J. M. Gambetta, F. Motzoi, S. T. Merkel, F. K. Wilhelm, Analytic control methods for high fidelity unitary operations in a weakly nonlinear oscillator, Phys. Rev. A 83, 012308 (2011), doi: 10.1103/PhysRevA.83.012308 (open)
Analysis class reference
Experiment options
These options can be set by the
set_experiment_options()
method.- Options
Defined in the class
FineDrag
:repetitions (List[int])
Default value: [0
,1
,2
,3
,4
, …]A list of the number of times that Rp - Rm gate sequence is repeated.schedule (ScheduleBlock)
Default value:None
The schedule for the plus rotation.gate (Gate)
Default value:None
This is the gate such as XGate() that will be in the circuits.
Defined in the class
BaseExperiment
:max_circuits (Optional[int])
Default value:None
The maximum number of circuits per job when running an experiment on a backend.
Example
from qiskit.circuit.library import XGate from qiskit_experiments.library.characterization import FineDrag exp = FineDrag(physical_qubits=(0,), gate=XGate(), backend=backend) exp_data = exp.run().block_for_results() display(exp_data.figure(0)) exp_data.analysis_results(dataframe=True)
name experiment components value quality backend run_time chisq d873f7ae @Parameters_ErrorAmplificationAnalysis FineDrag [Q0] CurveFitResult:\n - fitting method: least_squa... good PulseBackendV2 None None dbc52e1b d_theta FineDrag [Q0] -0.5555+/-0.0007 good PulseBackendV2 None 1.19708 Initialization
Setup a fine amplitude experiment on the given qubit.
- Parameters:
Attributes
- analysis: BaseAnalysis¶
Return the analysis instance for the experiment
- backend¶
Return the backend for the experiment
- experiment_options¶
Return the options for the experiment.
- experiment_type¶
Return experiment type.
- num_qubits¶
Return the number of qubits for the experiment.
- physical_qubits¶
Return the device qubits for the experiment.
Methods
- circuits()[source]¶
Create the circuits for the fine DRAG calibration experiment.
- Returns:
A list of circuits with a variable number of gates. Each gate has the same pulse schedule.
- Return type:
List[QuantumCircuit]
- config()¶
Return the config dataclass for this experiment
- Return type:
- copy()¶
Return a copy of the experiment
- Return type:
- enable_restless(rep_delay=None, override_processor_by_restless=True, suppress_t1_error=False)¶
Enables a restless experiment by setting the restless run options and the restless data processor.
Deprecated since version 0.8: The method
qiskit_experiments.framework.restless_mixin.RestlessMixin.enable_restless()
is deprecated as of qiskit-experiments 0.8. It will be removed no earlier than 3 months after the release date. Support for restless experiments has been deprecated.- Parameters:
rep_delay (float | None) – The repetition delay. This is the delay between a measurement and the subsequent quantum circuit. Since the backends have dynamic repetition rates, the repetition delay can be set to a small value which is required for restless experiments. Typical values are 1 us or less.
override_processor_by_restless (bool) – If False, a data processor that is specified in the analysis options of the experiment is not overridden by the restless data processor. The default is True.
suppress_t1_error (bool) – If True, the default is False, then no error will be raised when
rep_delay
is larger than the T1 times of the qubits. Instead, a warning will be logged as restless measurements may have a large amount of noise.
- Raises:
DataProcessorError – If the attribute rep_delay_range is not defined for the backend.
DataProcessorError – If a data processor has already been set but override_processor_by_restless is True.
DataProcessorError – If the experiment analysis does not have the data_processor option.
DataProcessorError – If the rep_delay is equal to or greater than the T1 time of one of the physical qubits in the experiment and the flag
ignore_t1_check
is False.
- classmethod from_config(config)¶
Initialize an experiment from experiment config
- Return type:
- job_info(backend=None)¶
Get information about job distribution for the experiment on a specific backend.
- Parameters:
backend (Backend) – Optional, the backend for which to get job distribution information. If not specified, the experiment must already have a set backend.
- Returns:
A dictionary containing information about job distribution.
”Total number of circuits in the experiment”: Total number of circuits in the experiment.
”Maximum number of circuits per job”: Maximum number of circuits in one job based on backend and experiment settings.
”Total number of jobs”: Number of jobs needed to run this experiment on the currently set backend.
- Return type:
dict
- Raises:
QiskitError – if backend is not specified.
- run(backend=None, sampler=None, analysis='default', timeout=None, backend_run=None, **run_options)¶
Run an experiment and perform analysis.
- Parameters:
backend (Backend | None) – Optional, the backend to run on. Will override existing backend settings.
sampler (BaseSamplerV2 | None) – Optional, the sampler to run the experiment on. If None then a sampler will be invoked from previously set backend
analysis (BaseAnalysis | None) – Optional, a custom analysis instance to use for performing analysis. If None analysis will not be run. If
"default"
the experimentsanalysis()
instance will be used if it contains one.timeout (float | None) – Time to wait for experiment jobs to finish running before cancelling.
backend_run (bool | None) – Use backend run (temp option for testing)
run_options – backend runtime options used for circuit execution.
- Returns:
The experiment data object.
- Raises:
QiskitError – If experiment is run with an incompatible existing ExperimentData container.
- Return type:
- set_experiment_options(**fields)¶
Set the experiment options.
- Parameters:
fields – The fields to update the options
- Raises:
AttributeError – If the field passed in is not a supported options
- set_run_options(**fields)¶
Set options values for the experiment
run()
method.- Parameters:
fields – The fields to update the options
See also
The Setting options for your experiment guide for code example.
- set_transpile_options(**fields)¶
Set the transpiler options for
run()
method.- Parameters:
fields – The fields to update the options
- Raises:
QiskitError – If initial_layout is one of the fields.
See also
The Setting options for your experiment guide for code example.