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

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


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/════════════════════════════...═══════════════════════════╩═

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 \(π/2\).


[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


Experiment options

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

  • 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.


Setup a half angle experiment on the given qubit.

  • 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.



Return the analysis instance for the experiment


Return the backend for the experiment


Return the options for the experiment.


Return experiment type.


Return the number of qubits for the experiment.


Return the device qubits for the experiment.


Return options values for the experiment run() method.


Return the transpiler options for the run() method.



Create the circuits for the half angle calibration experiment.

Return type:



Return the config dataclass for this experiment

Return type:



Return a copy of the experiment

Return type:


classmethod from_config(config)#

Initialize an experiment from experiment config

Return type:



Get information about job distribution for the experiment on a specific backend.


backend (Backend) – Optional, the backend for which to get job distribution information. If not specified, the experiment must already have a set backend.


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:



QiskitError – if backend is not specified.

run(backend=None, analysis='default', timeout=None, **run_options)#

Run an experiment and perform analysis.

  • backend (Backend | None) – Optional, the backend to run the experiment on. This will override any currently set backends for the single execution.

  • 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.

  • run_options – backend runtime options used for circuit execution.


The experiment data object.


QiskitError – If experiment is run with an incompatible existing ExperimentData container.

Return type:



Set the experiment options.


fields – The fields to update the options


AttributeError – If the field passed in is not a supported options


Set options values for the experiment run() method.


fields – The fields to update the options

See also

The Setting options for your experiment guide for code example.


Set the transpiler options for run() method.


fields – The fields to update the options


QiskitError – If initial_layout is one of the fields.

See also

The Setting options for your experiment guide for code example.