# This code is part of Qiskit.
#
# (C) Copyright IBM 2021.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.
"""Half angle characterization."""
from typing import List, Optional, Sequence
import numpy as np
from qiskit import QuantumCircuit
from qiskit.providers import Backend
from qiskit_experiments.framework import BaseExperiment, Options
from qiskit_experiments.curve_analysis.standard_analysis import ErrorAmplificationAnalysis
from qiskit_experiments.curve_analysis import ParameterRepr
[docs]
class HalfAngle(BaseExperiment):
r"""An experiment class to measure the amount by which sx and x are not parallel.
# section: overview
This experiment runs circuits that repeat blocks of :code:`sx - sx - y` gates
inserted in a Ramsey type experiment, i.e. the full gate sequence is thus
:code:`Ry(π/2) - [sx - sx - y] ^ n - sx` where :code:`n` is varied.
.. parsed-literal::
┌─────────┐┌────┐┌────┐┌───┐ ┌────┐┌────┐┌───┐┌────┐ ░ ┌─┐
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 :code:`sx` and :code:`x`
rotation are not parallel. A similar experiment is described in Ref.~[1] where the
gate sequence :code:`x - y` is repeated to amplify errors caused by non-orthogonal
:code:`x` and :code:`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 :math:`+X` state, with a deviation :math:`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
:math:`y` axis in the :math:`xy` plane of the Bloch sphere, so the
:math:`δθ` deviation from :math:`+X` becomes a :math:`-δθ` from
:math:`-X`. The next ``sx - sx`` sequence rotates about the axis that
is :math:`+δθ` rotated in the :math:`xy` plane from :math:`+X`, which
takes the deviation from :math:`-X` from :math:`-δθ` to :math:`+3 δθ`.
Then the next ``y`` mirrors this across the :math:`y` axis, taking the
state to :math:`-3 δθ` from :math:`+X`. This pattern continues with
each iteration, with the angular deviation in units of :math:`δθ`
following the sequence 1, 3, 5, 7, 9, etc. from :math:`+X` and
:math:`-X`. The final ``sx`` rotation serves mainly to rotate these
deviations from :math:`+X` and :math:`-X` in the :math:`xy` plane into
deviations out of the :math:`xy` plane, so that they appear as a signal
in the :math:`Z` basis. Because ``sx`` has a :math:`δθ` deviation from
``x``, the final ``sx`` adds an extra :math:`δθ` to the deviations, so
the pattern ends up as 2, 4, 6, 8, etc., meaning that each iteration
adds :math:`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 :math:`π/2`.
# section: analysis_ref
:class:`.ErrorAmplificationAnalysis`
# section: reference
.. ref_arxiv:: 1 1504.06597
"""
@classmethod
def _default_experiment_options(cls) -> Options:
r"""Default values for the half angle experiment.
Experiment Options:
repetitions (List[int]): A list of the number of times that the gate
sequence :code:`[sx sx y]` is repeated.
"""
options = super()._default_experiment_options()
options.repetitions = list(range(15))
return options
def __init__(self, physical_qubits: Sequence[int], backend: Optional[Backend] = None):
"""Setup a half angle experiment on the given qubit.
Args:
physical_qubits: List containing the qubits on which to run the
fine amplitude calibration experiment.
backend: Optional, the backend to run the experiment on.
"""
analysis = ErrorAmplificationAnalysis()
default_bounds = analysis.options.bounds
default_bounds.update({"d_theta": (-np.pi / 2, np.pi / 2)})
analysis.set_options(
fixed_parameters={
"angle_per_gate": np.pi,
"phase_offset": -np.pi / 2,
"amp": 1.0,
},
result_parameters=[ParameterRepr("d_theta", "d_hac", "rad")],
normalization=True,
bounds=default_bounds,
)
super().__init__(physical_qubits, analysis=analysis, backend=backend)
@staticmethod
def _pre_circuit() -> QuantumCircuit:
"""Return the preparation circuit for the experiment."""
return QuantumCircuit(1)
[docs]
def circuits(self) -> List[QuantumCircuit]:
"""Create the circuits for the half angle calibration experiment."""
circuits = []
for repetition in self.experiment_options.repetitions:
circuit = self._pre_circuit()
# First ry gate
circuit.rz(np.pi / 2, 0)
circuit.sx(0)
circuit.rz(-np.pi / 2, 0)
# Error amplifying sequence
for _ in range(repetition):
circuit.sx(0)
circuit.sx(0)
circuit.rz(np.pi / 2, 0)
circuit.x(0)
circuit.rz(-np.pi / 2, 0)
circuit.sx(0)
circuit.measure_all()
circuit.metadata = {"xval": repetition}
circuits.append(circuit)
return circuits
def _metadata(self):
metadata = super()._metadata()
# Store measurement level and meas return if they have been
# set for the experiment
for run_opt in ["meas_level", "meas_return"]:
if hasattr(self.run_options, run_opt):
metadata[run_opt] = getattr(self.run_options, run_opt)
return metadata