Merge pull request #983 from qiboteam/protocol_docs

Protocol docs

doc/source/protocols/avoided_crossing.rst

@@ -0,0 +1,55 @@
+Avoided crossing
+================
+
+In the avoided crossing experiment the goal is to study the qubit-flux dependency
+of a couple of qubits to precisely tune the interaction between them at specific
+frequencies in order to calibrate the CZ and the iSWAP gates.
+
+In the avoided crossing experiment for CZ qubit gates, the interaction between
+two qubits is controlled by tuning their energy levels such that the :math:`\ket{11}`
+(both qubits in the excited state) and :math:`\ket{02}` (one qubit in the ground state and
+the other in the second excited state) states come into resonance.
+At this resonance point, the energy levels of these states experience an avoided
+crossing, a key phenomenon that enables the controlled-Z (CZ) gate operation.
+By observing the avoided crossing, one can confirm that the coupling between the
+qubits is strong enough to facilitate the necessary interaction for the CZ gate.
+Hence, precise tuning of these states is essential for achieving the correct gate
+operation.
+
+In the avoided crossing experiment for iSWAP qubit gates, the key focus is on
+the interaction between the :math:`\ket{10}` and :math:`\ket{01}` states.
+When tuning the qubits' energy levels, these two states come into resonance,
+creating an avoided crossing, which is the fundamental operation of
+the iSWAP gate.
+
+In this protocol, for each qubit pair we execute a qubit flux dependency of the
+01 and 02 transitions on the qubit with higher frequency and we fit the data to
+find the flux-frequency relationship that we use to estimate the bias needed to
+reach the CZ and iSWAP interaction points.
+
+Parameters
+^^^^^^^^^^
+
+.. autoclass::
+	qibocal.protocols.flux_dependence.avoided_crossing.AvoidedCrossingParameters
+	:noindex:
+
+Example
+^^^^^^^
+
+It follows a runcard example of this experiment.
+
+.. code-block:: yaml
+
+    - id: avoided crossing
+      operation: avoided_crossing
+      parameters:
+        bias_step: 0.01
+        bias_width: 0.2
+        drive_amplitude: 0.5
+        freq_step: 500000
+        freq_width: 100000000
+
+The expected output is the following:
+
+.. image:: avoided_crossing.png

doc/source/protocols/index.rst

@@ -27,4 +27,8 @@ In this section we introduce the basics of all protocols supported by ``qibocal`
     dispersive_shift
     allxy
     flipping
+    readout_mitigation_matrix
+    avoided_crossing
+    readout_optimization
+    standard_rb
     references

doc/source/protocols/readout_mitigation_matrix.rst

@@ -0,0 +1,36 @@
+Readout mitigation matrix
+=========================
+
+The idea behind this protocol is that we can correct the qubit readout errors
+by applying a corrective linear transformation to the readout results, in formula
+
+.. math::
+	O_{noisy} = M O_{ideal},
+
+where :math:`O_{noisy}` is the readout probabilities on the noisy device,
+:math:`O_{ideal}` is the expected one and :math:`M` is the readout mitigation matrix.
+The matrix :math:`M^{-1}` can be used to correct the noisy readouts.
+
+This protocol evaluates the readout matrix by preparing the qubit(s) in the
+computational base and measuring their states.
+
+Pramateters
+^^^^^^^^^^^
+
+.. autoclass:: qibocal.protocols.readout_mitigation_matrix.ReadoutMitigationMatrixParameters
+	:noindex:
+
+Example
+^^^^^^^
+
+.. code-block:: yaml
+
+	- id: readout_mitigation_matrix
+	  operation: readout_mitigation_matrix
+	  parameters:
+	    nshots: 1000
+	    pulses: true
+
+After the protocol execution, the result is the following
+
+.. image:: readout_mitigation_matrix.png

doc/source/protocols/readout_optimization.rst

@@ -0,0 +1,32 @@
+Readout optimization
+====================
+
+Qibocal provides a protocol to improve the readout pulse amplitude by optimize
+the assignment fidelity.
+
+Parameters
+^^^^^^^^^^
+
+.. autoclass:: qibocal.protocols.readout_optimization.resonator_amplitude.ResonatorAmplitudeParameters
+	:noindex:
+
+
+Example
+^^^^^^^
+
+It follows an example runcard of the resonator amplitude routine with the plot
+generated in the report.
+
+.. code-block:: yaml
+
+    - id: resonator_amplitude
+      operation: resonator_amplitude
+      parameters:
+          amplitude_step: 0.0005
+          amplitude_start: 0.001
+          amplitude_stop: 0.005
+
+As shown in the picture below, the protocol sweeps the readout amplitude and evaluates
+the probability errors
+
+.. image:: readout_amplitude.png

doc/source/protocols/standard_rb.rst

@@ -0,0 +1,85 @@
+Standard Randomize Benchmarking
+===============================
+
+An approach to obtain the average gate fidelity is to perform randomized
+benchmarking :cite:p:`Emerson_2005`.
+The key idea is that if we average the error process over the uniform space of
+unitaries the result is a depolarizing channel that maps any pure state to the
+maximally mixed state.
+Such uniform space of unitaries is known as *Haar measure*.
+It can be shown :cite:p:`Emerson_2005` that the average induced error is proportional
+to the depolarization probability.
+However, this approach is inefficient because we sample randomly from the Haar measure.
+A simplification was proposed in :cite:p:`Knill2008` by restricting the unitaries
+to the Clifford group, which consists of unitary rotations mapping the group
+of Pauli operators in itself.
+Among the advantages of such group are the fact of the number of Clifford
+gates is finite given the Hilbert space and being a group we can easily found
+the inverse within the group.
+The generic procedure to perform a randomized benchmarking is the following:
+
+1. initialize the system in ground state
+2. for each sequence length :math:`m` draw sequence of Clifford group elements
+3. calculate inverse gate
+4. measure sequence and inverse gate
+5. repeat the process for multiple sequence of same length and varying the length
+
+The previous approach works because it has been shown :cite:p:`Nielsen_2002` that
+randomization with Clifford gates provides again a depolarized noise channel
+
+.. math::
+    :name: eq:1
+
+    \rho \rightarrow \frac{d}{2} I + ( 1 - d) \rho
+
+with depolarization probability :math:`d`.
+If we follow the previous procedure and we measure the survival probability, i.e.
+the probability of measuring the qubit in :math:`\ket{0}`, for
+different sequence length :math:`m` we expect the following behavior
+
+.. math::
+    :name: eq:2
+
+    F(m) = A p^m + B
+
+where :math:`1-p` is the rate of depolarization while :math:`A` and :math:`B`
+capture state preparation and measurement errors.
+Finally, we can extract the average error per Clifford as
+
+.. math::
+    :name: eq:3
+
+    \epsilon_\text{Clifford} = \frac{1 - p}{1 - 2^{-n}}
+
+where :math:`n` is the number of qubits. The error per gate can be derived by dividing
+the Clifford error by the physical gates per Clifford which usually is 1.875.
+One of the main feature of RB is the possibility to estimate the gate fidelity
+alone without taking into account both state preparation and measurement errors
+which can be computed using the :math:`A` and :math:`B` terms in :ref:`Eq. 2 <eq:2>`.
+
+Parameters
+^^^^^^^^^^
+
+
+.. autoclass::
+	qibocal.protocols.randomized_benchmarking.standard_rb.StandardRBParameters
+	:noindex:
+
+
+Example
+^^^^^^^
+
+It follows a runcard where we execute a standard RB.
+
+.. code-block:: yaml
+
+    - id: standard rb
+      operation: standard_rb
+      parameters:
+        depths: [1,5,10,20,50,100]
+        niter: 20
+        nshots: 100
+
+The expected output is the following:
+
+.. image:: standard_rb.png

doc/source/refs.bib

@@ -150,3 +150,43 @@ @misc{pedicillo2023
       archivePrefix={arXiv},
       primaryClass={id='quant-ph' full_name='Quantum Physics' is_active=True alt_name=None in_archive='quant-ph' is_general=False description=None}
 }
+
+@article{Knill2008,
+   title={Randomized benchmarking of quantum gates},
+   volume={77},
+   ISSN={1094-1622},
+   url={http://dx.doi.org/10.1103/PhysRevA.77.012307},
+   DOI={10.1103/physreva.77.012307},
+   number={1},
+   journal={Physical Review A},
+   publisher={American Physical Society (APS)},
+   author={Knill, E. and Leibfried, D. and Reichle, R. and Britton, J. and Blakestad, R. B. and Jost, J. D. and Langer, C. and Ozeri, R. and Seidelin, S. and Wineland, D. J.},
+   year={2008},
+   month={jan},
+}
+
+@article{Emerson_2005,
+   title={Scalable noise estimation with random unitary operators},
+   volume={7},
+   ISSN={1741-3575},
+   url={http://dx.doi.org/10.1088/1464-4266/7/10/021},
+   DOI={10.1088/1464-4266/7/10/021},
+   number={10},
+   journal={Journal of Optics B: Quantum and Semiclassical Optics},
+   publisher={IOP Publishing},
+   author={Emerson, Joseph and Alicki, Robert and Życzkowski, Karol},
+   year={2005},
+   month=sep, pages={S347–S352} }
+
+@article{Nielsen_2002,
+   title={A simple formula for the average gate fidelity of a quantum dynamical operation},
+   volume={303},
+   ISSN={0375-9601},
+   url={http://dx.doi.org/10.1016/S0375-9601(02)01272-0},
+   DOI={10.1016/s0375-9601(02)01272-0},
+   number={4},
+   journal={Physics Letters A},
+   publisher={Elsevier BV},
+   author={Nielsen, Michael A},
+   year={2002},
+   month=oct, pages={249–252} }