add detail about QAE algorithms in class docstring
@@ -36,6 +36,13 @@ class AmplitudeEstimationAlgorithm(QuantumAlgorithm):
where the amplitude `a` (in [0, 1]) is approximated, and |psi_0> and |psi_1> are two
normalized, not necessarily orthogonal, states.
+ In the QAE algorithms, the Grover operator Q is used, which is defined as
+
+ Q = -A S_0 A^{-1} S_psi0,
+
+ where S_0 reflects about the |0>_n state and S_psi0 reflects about |psi_0>_n.
+
+ See https://arxiv.org/abs/quant-ph/0005055 for more detail about QAE.
"""
@abstractmethod
@@ -75,9 +82,10 @@ class AmplitudeEstimationAlgorithm(QuantumAlgorithm):
"""
Get the Q operator, or Grover-operator for the Amplitude Estimation algorithm, i.e.
- Q = - A S_0 A^{-1} S_psi
+ Q = -A S_0 A^{-1} S_psi0,
- see https://arxiv.org/abs/quant-ph/0005055 for more detail.
+ where S_0 reflects about the |0>_n state and S_psi0 reflects about |psi_0>_n.
+ See https://arxiv.org/abs/quant-ph/0005055 for more detail.
If the Q operator is not set, we try to build it from the A operator.
If neither the A operator is set, None is returned.
