Merge pull request #1079 from qiboteam/chevron_doc

Chevron doc

doc/source/protocols/chevron.rst

@@ -1,6 +1,20 @@
 Chevron
 =======
 
+In order to implement a two-qubit gate in superconducting quantum computing, it is necessary to bring the two qubits near resonance using specific pulse sequences.
+The Chevron protocol implemented in Qibocal can be used to calibrate both CZ and iSWAP gates.
+
+The pulse sequence used to calibrate the iSWAP gate consists of a :math:`\pi` pulse followed by a flux pulse of varying amplitude and duration, applied to the qubit with the highest frequency in the pair.
+The initial :math:`pi` pulse brings the qubit into the state :math:`\ket{1}` while the flux pulse detunes its frequency near resonance with the second qubit. The implementation of the iSWAP gate leverages the avoided crossing between the states :math:`\ket{10}` and :math:`\ket{01}`.
+
+The expected population oscillation pattern follows:
+.. math::
+	p_e(t, \delta) = \frac{\Delta^2}{\Delta^2 + 4g^2} + {4g^2}{\Delta^2 + 4g^2}\cos^2\left(\frac{\sqrt{\Delta^2 + 4g^2}}{2}t\right)
+
+where :math:`\Delta=\omega_1 - \omega_2`,  and :math:`g` is the coupling constant for the two qubits.
+
+The pulse sequence used to calibrate the CZ gate is the same as the one for the iSWAP gate, with the addition of an initial :math:`\pi` pulse applied to the qubit with the lower frequency so that both qubits are initially prepared in the :math:`\ket{1}`. With this sequence the CZ gate is implemented leveraging the avoided crossing between the states :math:`\ket{11}` and :math:`\ket{20}`.
+
 Parameters
 ^^^^^^^^^^
 
@@ -28,3 +42,8 @@ Below is an example runcard for this experiment.
 The expected output is the following:
 
 .. image:: chevron.png
+
+The plot represents the probability of measuring qubit 1 in the excited state as a function of the flux pulse parameters.
+The characteristic shape of the plot, known as a Chevron pattern, appears as a consequence of the interaction of the two qubits through their coupling, leading to population exchange.
+
+Before running the Chevron routine it may be useful to run a Cryoscope experiment in order to correct possible distortions in the flux pulse.