Restless Measurements
=====================

.. caution::

   Support for restless measurements is deprecated as of Qiskit Experiments 0.8
   and will be removed in a future version.

When running circuits, the qubits are typically reset to the ground state after
each measurement to ensure that the next circuit has a well-defined initial state.
This can be done passively by waiting several :math:`T_1`-times so that qubits in
the excited state decay to :math:`\left\vert0\right\rangle`. Since :math:`T_1`-times
are continuously improving (they already increased beyond :math:`100\,\mu s`), this
initialization procedure is now inefficient. This makes active reset necessary.
Active qubit reset, as employed by IBM Quantum systems is more efficient and saves
time but also lasts a few microseconds (between :math:`3` and :math:`5\,\mu s`).
Furthermore, a delay, typically lasting :math:`250\,\mu s`, after the reset
operation is often necessary to ensure a high initialization quality.
However, for several types of characterization and calibration experiments we can
avoid qubit reset by post-processing the measurement outcomes and continue directly
with the next circuit after an optional short delay, even if the qubit was measured
in the excited state. Foregoing qubit reset is the main idea behind restless measurements.

The IBM Quantum systems have dynamical repetition delays enabled. We can thus choose
the delay between the execution of two quantum circuits. This delay
typically ranges from :math:`0` to :math:`500\,\mu s` depending on the system.
The default value for most devices is :math:`250\,\mu s`. Restless measurements
set this delay to small values such as :math:`1\,\mu s` or lower. Note that sometimes
the measurement instructions already contain a delay after the measurement pulse to
allow the readout resonator to depopulate.

When the qubit is not reset it will either be in the :math:`\left\vert0\right\rangle`
or in the :math:`\left\vert1\right\rangle` state when the next circuit starts.
Therefore, the measured outcomes of the restless experiments require post-processing.
The following example, taken from Ref. [1]_, illustrates what happens to the single
measurement outcomes represented as complex numbers in the IQ plane in a restless
setting. Here, we run three circuits with an identity gate and three circuits with
an :math:`X` gate, each followed by a measurement. The numbers in the IQ shots indicate the
order in which the shots were acquired. The IQ plane on the left shows the single
measurement shots gathered when the qubits are reset. Here, the blue and red points,
corresponding to measurements following the :math:`Id` and :math:`X` gates, are associated with the
:math:`\left\vert0\right\rangle` and :math:`\left\vert1\right\rangle` states,
respectively.
By contrast, with restless measurements the qubit is not reset after a
measurement. As one can see in the IQ plane on the right the single measurement
outcomes of the :math:`Id`` and :math:`X` circuits no longer match with the
:math:`\left\vert0\right\rangle` and :math:`\left\vert1\right\rangle` states,
respectively. This is why restless measurements need special post-processing.

.. image:: restless_shots.png
   :width: 600

Enabling restless measurements
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

In Qiskit Experiments, the experiments that support restless measurements
have a special method :meth:`~.RestlessMixin.enable_restless` to set the restless run options
and define the data processor that will process the measured data.
If you are an experiment developer, you can add the :class:`.RestlessMixin`
to your experiment class to add support for restless measurements.
Here, we will show how to activate restless measurements using
a fake backend and a rough DRAG experiment. Note however, that you will not
observe any meaningful outcomes with fake backends since the circuit simulator
they use always starts with the qubits in the ground state.

.. note::
    This tutorial requires the :external+qiskit_ibm_runtime:doc:`qiskit-ibm-runtime <index>` package to model a
    backend.  You can install it with ``python -m pip install qiskit-ibm-runtime``.

.. jupyter-execute::
    :hide-code:

    import warnings

    warnings.filterwarnings(
        "ignore",
        message=".*Support for restless.*",
        category=DeprecationWarning,
    )
    warnings.filterwarnings(
        "ignore",
        message=".*The entire Qiskit Pulse package is being deprecated.*",
        category=DeprecationWarning,
    )
    warnings.filterwarnings(
        "ignore",
        message=".*QuantumCircuit.duration.*",
        category=DeprecationWarning,
    )

.. jupyter-execute::

    from qiskit_ibm_runtime.fake_provider import FakePerth

    from qiskit_experiments.library import RoughDragCal
    from qiskit_experiments.calibration_management import (
        Calibrations,
        FixedFrequencyTransmon,
    )
    from qiskit_experiments.data_processing.data_processor import DataProcessor

    # replace this lines with an IBM Quantum backend to run the experiment.
    backend = FakePerth()
    cals = Calibrations.from_backend(backend, libraries=[FixedFrequencyTransmon()])

    # Define the experiment
    qubit = 2
    cal_drag = RoughDragCal((qubit,), cals, schedule_name='sx', backend=backend)

    # Enable restless measurements by setting the run options and data processor
    cal_drag.enable_restless(rep_delay=1e-6)

    print(cal_drag.analysis.options.data_processor)
    print(cal_drag.run_options)

As you can see, a restless data processor is automatically chosen for the experiment. This
data processor post-processes the restless measured shots according to the order in which
they were acquired. Furthermore, the appropriate run options are also set. Note that
these run options might be unique to IBM Quantum providers. Therefore, execute may fail
on non-IBM Quantum providers if the required options are not supported.

After calling :meth:`~.RestlessMixin.enable_restless` the experiment is ready to be run
in a restless mode. With a hardware backend, this would be done by calling the
:meth:`~.BaseExperiment.run` method:

.. jupyter-input::

    drag_data_restless = cal_drag.run()

As shown by the example, the code is identical to running a normal experiment aside
from a call to the method :meth:`~.RestlessMixin.enable_restless`. Note that you can also choose to keep
the standard data processor by providing it to the analysis options and telling
:meth:`~.RestlessMixin.enable_restless` not to override the data processor.

.. jupyter-execute::

    from qiskit_experiments.data_processing import (
        DataProcessor,
        Probability,
    )

    # define a standard data processor.
    standard_processor = DataProcessor("counts", [Probability("1")])

    cal_drag = RoughDragCal((qubit,), cals, schedule_name='sx', backend=backend)
    cal_drag.analysis.set_options(data_processor=standard_processor)

    # enable restless mode and set override_processor_by_restless to False.
    cal_drag.enable_restless(rep_delay=1e-6, override_processor_by_restless=False)

If you run the experiment in this setting you will see that the data is often
unusable which illustrates the importance of the data processing. As detailed
in Ref. [2]_, restless measurements can be done with a wide variety
of experiments such as fine amplitude and drag error amplifying gate sequences
as well as randomized benchmarking.

Calculating restless quantum processor speed-ups
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Following Ref. [2]_, we can compare the time spent by the quantum processor executing
restless and standard jobs. This allows us to compute the effective speed-up we gain
when performing restless experiments. Note that we do not consider any classical
run-time contributions such as runtime-compilation or data transfer times [3]_.
The time to run :math:`K` circuits and gather :math:`N` shots for each
circuit is

.. math::

    \tau^{(x)} = NK\left(\tau^{(x)}_\text{reset}+\tau^{(x)}_\text{delay}+
    \langle{\tau}_\text{circ}\rangle+\tau_\text{meas}\right),

where :math:`\tau^{(x)}_\text{reset}` and :math:`\tau^{(x)}_\text{delay}`
are the reset and post measurement delay times, respectively. The superscript
:math:`(x)` indicates restless :math:`(r)` or standard :math:`(s)` measurements.
The average duration of all :math:`K` circuits in an experiment is
:math:`\langle{\tau}_\text{circ}\rangle=K^{-1}\sum_{k=1}^{K} \tau_{\text{circ},k}`
where :math:`\tau_{\text{circ},k}` is the duration of only the gates in circuit
:math:`k`. We therefore compute the quantum processor speed-up of restless
measurements as :math:`\tau^{(\text{s})}/\tau^{(\text{r})}` which is independent
of the number of circuits and shots.

We approximate the standard reset time in IBM Quantum backends by
:math:`\tau^{(s)}_\text{reset} = 4\,\mu s` whereas :math:`\tau^{(r)}_\text{reset} = 0\,\mu s`
since we do not reset the qubit in a restless experiment. By default, the repetition delay is
:math:`\tau^{(s)}_\text{delay} = 250\,\mu s`. For our restless experiments we
set :math:`\tau^{(r)}_\text{delay} = 1\,\mu s`. These speed-ups can be evaluated
using the code below.

.. jupyter-execute::

    from qiskit import schedule, transpile
    from qiskit_experiments.framework import BackendData

    dt = BackendData(backend).dt
    inst_map = backend.instruction_schedule_map
    meas_length = inst_map.get("measure", (qubit,)).duration * dt

    # Compute the average duration of all circuits
    # Remove measurement instructions
    circuits = []
    for qc in cal_drag.circuits():
        qc.remove_final_measurements(inplace=True)
        circuits.append(qc)

    # Schedule the circuits to obtain the duration of all the gates
    executed_circs = transpile(
        circuits,
        backend,
        initial_layout=[qubit],
        scheduling_method="alap",
        **cal_drag.transpile_options.__dict__,
    )
    durations = [c.duration for c in executed_circs]

    tau = sum(durations) * dt / (len(durations))

    n_circs = len(cal_drag.circuits())
    # can be obtained from backend.default_rep_delay on a backend from qiskit-ibm-runtime

    delay_s = 0.0025
    delay_r = 1e-6  # restless delay
    reset = 4e-6  # Estimated reset duration
    speed_up = (meas_length + reset + delay_s + tau) / (meas_length + delay_r + tau)
    print(f"The QPU will spend {speed_up:.1f}x less time running restless Drag.")

The example above is applicable to other experiments and shows that restless
measurements can greatly speed-up characterization and calibration tasks.

References
----------

.. [1] Max Werninghaus, Daniel J. Egger, Stefan Filipp, High-speed calibration and
    characterization of superconducting quantum processors without qubit reset,
    PRX Quantum **2**, 020324 (2021). https://arxiv.org/abs/2010.06576.

.. [2] Caroline Tornow, Naoki Kanazawa, William E. Shanks, Daniel J. Egger,
    Minimum quantum run-time characterization and calibration via restless
    measurements with dynamic repetition rates, Physics Review Applied **17**,
    064061 (2022). https://arxiv.org/abs/2202.06981.

.. [3] Andrew Wack, Hanhee Paik, Ali Javadi-Abhari, Petar Jurcevic, Ismael Faro,
    Jay M. Gambetta, Blake R. Johnson, Quality, Speed, and Scale: three key
    attributes to measure the performance of near-term quantum computers,
    https://arxiv.org/abs/2110.14108.

See also
--------

* API documentation: :mod:`~qiskit_experiments.framework.RestlessMixin`