Fixed sign bug in docs in LinCombEstimatorGradient. (#9113)

qiskit/algorithms/gradients/lin_comb_estimator_gradient.py

@@ -64,9 +64,9 @@ class LinCombEstimatorGradient(BaseEstimatorGradient):
                 ``DerivativeType.IMAG``, or ``DerivativeType.COMPLEX``. Defaults to
                 ``DerivativeType.REAL``.
 
-                    - ``DerivativeType.REAL`` computes :math:`2 \mathrm{Re}[(dω⟨ψ(ω)|)O(θ)|ψ(ω)〉]`.
-                    - ``DerivativeType.IMAG`` computes :math:`2 \mathrm{Im}[(dω⟨ψ(ω)|)O(θ)|ψ(ω)〉]`.
-                    - ``DerivativeType.COMPLEX`` computes :math:`2 (dω⟨ψ(ω)|)O(θ)|ψ(ω)〉`.
+                    - ``DerivativeType.REAL`` computes :math:`2 \mathrm{Re}[⟨ψ(ω)|O(θ)|dω ψ(ω)〉]`.
+                    - ``DerivativeType.IMAG`` computes :math:`2 \mathrm{Im}[⟨ψ(ω)|O(θ)|dω ψ(ω)〉]`.
+                    - ``DerivativeType.COMPLEX`` computes :math:`2 ⟨ψ(ω)|O(θ)|dω ψ(ω)〉`.
 
             options: Primitive backend runtime options used for circuit execution.
                 The order of priority is: options in ``run`` method > gradient's

releasenotes/notes/fix-complex-gradient-sign-25f153b5a53ae259.yaml

@@ -0,0 +1,9 @@
+---
+fixes:
+  - |
+    Fixed the documentation in :class:`.LinCombEstimatorGradient` to correctly 
+    show the derivative applied on the ket-side of the expectation 
+    value. Previously, the derivative had been documented in the bra-side, which
+    led to a sign swap for gradients in the ``IMAG`` and ``COMPLEX`` 
+    cases of the :class:`.DerivativeType`.
+

test/python/algorithms/gradients/test_estimator_gradient.py

@@ -17,7 +17,7 @@ import unittest
 from test import combine
 
 import numpy as np
-from ddt import ddt
+from ddt import ddt, data, unpack
 
 from qiskit import QuantumCircuit
 from qiskit.algorithms.gradients import (
@@ -25,12 +25,13 @@ from qiskit.algorithms.gradients import (
     LinCombEstimatorGradient,
     ParamShiftEstimatorGradient,
     SPSAEstimatorGradient,
+    DerivativeType,
 )
 from qiskit.circuit import Parameter
 from qiskit.circuit.library import EfficientSU2, RealAmplitudes
 from qiskit.circuit.library.standard_gates import RXXGate, RYYGate, RZXGate, RZZGate
 from qiskit.primitives import Estimator
-from qiskit.quantum_info import Operator, SparsePauliOp
+from qiskit.quantum_info import Operator, SparsePauliOp, Pauli
 from qiskit.quantum_info.random import random_pauli_list
 from qiskit.test import QiskitTestCase
 
@@ -374,6 +375,17 @@ class TestEstimatorGradient(QiskitTestCase):
             rtol=1e-4,
         )
 
+    @data((DerivativeType.IMAG, -1.0), (DerivativeType.COMPLEX, -1.0j))
+    @unpack
+    def test_lin_comb_imag_gradient(self, derivative_type, expected_gradient_value):
+        """Tests if the ``LinCombEstimatorGradient`` has the correct value."""
+        estimator = Estimator()
+        gradient = LinCombEstimatorGradient(estimator, derivative_type=derivative_type)
+        c = QuantumCircuit(1)
+        c.rz(Parameter("p"), 0)
+        result = gradient.run([c], [Pauli("I")], [[0.0]]).result()
+        self.assertAlmostEqual(result.gradients[0][0], expected_gradient_value)
+
     @combine(
         grad=[
             FiniteDiffEstimatorGradient,