fix: Fix rabi fitting by including phase in period estimate

Fixes #656 but it requires more tests.

src/qibocal/protocols/characterization/rabi/amplitude.py

@@ -150,7 +150,7 @@ def _fit(data: RabiAmplitudeData) -> RabiAmplitudeResults:
         index = local_maxima[0] if len(local_maxima) > 0 else None
         # 0.5 hardcoded guess for less than one oscillation
         f = x[index] / (x[1] - x[0]) if index is not None else 0.5
-        pguess = [0.5, 0.5, 1 / f, np.pi / 2]
+        pguess = [0.5, 0.5, 1 / f, 0]
         try:
             popt, perr = curve_fit(
                 utils.rabi_amplitude_function,
@@ -165,7 +165,7 @@ def _fit(data: RabiAmplitudeData) -> RabiAmplitudeResults:
                 sigma=qubit_data.error,
             )
             perr = np.sqrt(np.diag(perr))
-            pi_pulse_parameter = np.abs(popt[2] / 2)
+            pi_pulse_parameter = utils.correct_period(period=popt[2], phase=popt[3])
 
         except:
             log.warning("rabi_fit: the fitting was not succesful")

src/qibocal/protocols/characterization/rabi/amplitude_signal.py

@@ -155,7 +155,9 @@ def _fit(data: RabiAmplitudeVoltData) -> RabiAmplitudeVoltResults:
                 popt[2] * (x_max - x_min),
                 popt[3] - 2 * np.pi * x_min / (x_max - x_min) / popt[2],
             ]
-            pi_pulse_parameter = np.abs((translated_popt[2]) / 2)
+            pi_pulse_parameter = utils.correct_period(
+                period=translated_popt[2], phase=translated_popt[3]
+            )
 
         except:
             log.warning("rabi_fit: the fitting was not succesful")

src/qibocal/protocols/characterization/rabi/length.py

@@ -169,7 +169,7 @@ def _fit(data: RabiLengthData) -> RabiLengthResults:
                 sigma=qubit_data.error,
             )
             perr = np.sqrt(np.diag(perr))
-            pi_pulse_parameter = np.abs(popt[2] / 2)
+            pi_pulse_parameter = utils.correct_period(period=popt[2], phase=popt[3])
         except:
             log.warning("rabi_fit: the fitting was not succesful")
             pi_pulse_parameter = 0

src/qibocal/protocols/characterization/rabi/length_signal.py

@@ -161,7 +161,10 @@ def _fit(data: RabiLengthVoltData) -> RabiLengthVoltResults:
                 popt[3] - 2 * np.pi * x_min / popt[2] / (x_max - x_min),
                 popt[4] / (x_max - x_min),
             ]
-            pi_pulse_parameter = np.abs(translated_popt[2] / 2)
+            pi_pulse_parameter = utils.correct_period(
+                period=translated_popt[2], phase=translated_popt[3]
+            )
+
         except:
             log.warning("rabi_fit: the fitting was not succesful")
             pi_pulse_parameter = 0

src/qibocal/protocols/characterization/rabi/utils.py

@@ -12,7 +12,7 @@ def rabi_amplitude_function(x, offset, amplitude, period, phase):
     Args:
         x: Input data.
     """
-    return offset + amplitude * np.sin(2 * np.pi * x / period + phase)
+    return offset + amplitude * np.cos(2 * np.pi * x / period + phase)
 
 
 def rabi_length_function(x, offset, amplitude, period, phase, t2_inv):
@@ -190,3 +190,17 @@ def extract_rabi(data):
     if "RabiLength" in data.__class__.__name__:
         return "length", "Time [ns]", rabi_length_function
     raise RuntimeError("Data has to be a data structure of the Rabi routines.")
+
+
+def correct_period(period: float, phase: float):
+    """Correct period by taking phase into account.
+
+    https://github.com/qiboteam/qibocal/issues/656
+    """
+
+    naive_half_period = period / 2
+    # solution of cos (2 pi x / period + phase) = +/- 1 for k in [-2,2]
+    solutions = [naive_half_period * (k - phase / np.pi) for k in [-2, -1, 0, 1, 2]]
+    # chose solution closest to naive_half period
+
+    return solutions[np.argmin(np.abs(solutions - naive_half_period))]