HalfAngle¶

class HalfAngle(physical_qubits, backend=None)[source]¶

An experiment class to measure the amount by which sx and x are not parallel.

Overview

This experiment runs circuits that repeat blocks of sx - sx - y gates inserted in a Ramsey type experiment, i.e. the full gate sequence is thus Ry(π/2) - [sx - sx - y] ^ n - sx where n is varied.

        ┌─────────┐┌────┐┌────┐┌───┐   ┌────┐┌────┐┌───┐┌────┐ ░ ┌─┐
   q_0: ┤ Ry(π/2) ├┤ sx ├┤ sx ├┤ y ├...┤ sx ├┤ sx ├┤ y ├┤ sx ├─░─┤M├
        └─────────┘└────┘└────┘└───┘   └────┘└────┘└───┘└────┘ ░ └╥┘
meas: 1/════════════════════════════...═══════════════════════════╩═
                                                                  0

This sequence measures angle errors where the axis of the sx and x rotation are not parallel. A similar experiment is described in Ref.~[1] where the gate sequence x - y is repeated to amplify errors caused by non-orthogonal x and y rotation axes.

One cause of such errors is non-linearity in the microwave mixer used to produce the pulses for the x and sx gates. Typically, these gates are calibrated to have the same duration and so have different pulse amplitudes. Non-linearities in the mixer’s skew can cause the angle to differ for these different pulse amplitudes.

The way the experiment works is that the initial Ry(π/2) puts the qubit close to the \(+X\) state, with a deviation \(δθ\), due to the misalignment between sx and x (Ry(π/2) is implemented with sx as described below). The first sx - sx do nothing as they should be rotations about the axis the qubit is pointing along. The first y then mirrors the qubit about the \(y\) axis in the \(xy\) plane of the Bloch sphere, so the \(δθ\) deviation from \(+X\) becomes a \(-δθ\) from \(-X\). The next sx - sx sequence rotates about the axis that is \(+δθ\) rotated in the \(xy\) plane from \(+X\), which takes the deviation from \(-X\) from \(-δθ\) to \(+3 δθ\). Then the next y mirrors this across the \(y\) axis, taking the state to \(-3 δθ\) from \(+X\). This pattern continues with each iteration, with the angular deviation in units of \(δθ\) following the sequence 1, 3, 5, 7, 9, etc. from \(+X\) and \(-X\). The final sx rotation serves mainly to rotate these deviations from \(+X\) and \(-X\) in the \(xy\) plane into deviations out of the \(xy\) plane, so that they appear as a signal in the \(Z\) basis. Because sx has a \(δθ\) deviation from x, the final sx adds an extra \(δθ\) to the deviations, so the pattern ends up as 2, 4, 6, 8, etc., meaning that each iteration adds \(2 δθ\) to the deviation from the equator of the Bloch sphere (with the sign alternating due to the y gates, so the deviations are really -2, 4, -6, 8, etc.).

For the implementation of the circuits, the experiment uses Rz(π/2) - sx - Rz(-π/2) to implement the Ry(π/2) and Rz(π/2) - x - Rz(-π/2) to implement the y. So the experiment makes use of only sx, x, Rz(π/2), and Rz(-π/2) gates. For the experiment’s analysis to be valid, it is important that the sx and x gates are not replaced (such as by a transpiler pass that replaces x with sx - sx), as it is the angle between them which is being inferred. It is assumed that the angle between x and Rz is exactly \(π/2\).

References

[1] Sarah Sheldon, Lev S. Bishop, Easwar Magesan, Stefan Filipp, Jerry M. Chow, Jay M. Gambetta, Characterizing errors on qubit operations via iterative randomized benchmarking, Phys. Rev. A 93, 012301 (2016), doi: 10.1103/PhysRevA.93.012301 (open)

Analysis class reference

ErrorAmplificationAnalysis

Experiment options

These options can be set by the set_experiment_options() method.

Options

Defined in the class HalfAngle:
- repetitions (List[int])
  
  Default value: [0, 1, 2, 3, 4, …]
  
  A list of the number of times that the gate sequence [sx sx y] is repeated.
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_experiments.library.characterization import HalfAngle

exp = HalfAngle((0,), backend=backend)

exp_data = exp.run().block_for_results()
display(exp_data.figure(0))
exp_data.analysis_results(dataframe=True)

../_images/qiskit_experiments.library.characterization.HalfAngle_1_0.png

	name	experiment	components	value	quality	backend	run_time	chisq	unit
409e03e0	@Parameters_ErrorAmplificationAnalysis	HalfAngle	[Q0]	CurveFitResult:\n - fitting method: least_squa...	bad	PulseBackendV2	None	None	None
27478807	d_hac	HalfAngle	[Q0]	-0.0022+/-0.0010	bad	PulseBackendV2	None	7.295721	rad

Initialization

Setup a half angle experiment on the given qubit.

Parameters:

physical_qubits (Sequence[int]) – List containing the qubits on which to run the fine amplitude calibration experiment.
backend (Backend | None) – Optional, the backend to run the experiment on.

Attributes

analysis¶: 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.

run_options¶: Return options values for the experiment run() method.

transpile_options¶: Return the transpiler options for the run() method.

Methods

circuits()[source]¶

Create the circuits for the half angle calibration experiment.

Return type:: List[QuantumCircuit]

config()¶

Return the config dataclass for this experiment

Return type:: ExperimentConfig

copy()¶

Return a copy of the experiment

Return type:: BaseExperiment

classmethod from_config(config)¶

Initialize an experiment from experiment config

Return type:: BaseExperiment

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 experiments analysis() 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:

ExperimentData

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