From 63786e1fca7d25dc4685323bdb04db453bfe8610 Mon Sep 17 00:00:00 2001
From: Tomasz <tpecyna@man.poznan.pl>
Date: Mon, 20 Feb 2023 11:01:47 +0100
Subject: [PATCH] implement MinimumEigensolver interface

---
 .../minimum_eigensolvers/__init__.py          |  2 +
 .../algorithms/minimum_eigensolvers/falqon.py | 71 +++++++++++++++++++
 2 files changed, 73 insertions(+)
 create mode 100644 qiskit/algorithms/minimum_eigensolvers/falqon.py

diff --git a/qiskit/algorithms/minimum_eigensolvers/__init__.py b/qiskit/algorithms/minimum_eigensolvers/__init__.py
index d7406c09860b..f277cf8c1af3 100644
--- a/qiskit/algorithms/minimum_eigensolvers/__init__.py
+++ b/qiskit/algorithms/minimum_eigensolvers/__init__.py
@@ -48,6 +48,7 @@
 from .sampling_mes import SamplingMinimumEigensolver, SamplingMinimumEigensolverResult
 from .sampling_vqe import SamplingVQE, SamplingVQEResult
 from .qaoa import QAOA
+from .falqon import FALQON
 
 __all__ = [
     "AdaptVQE",
@@ -63,4 +64,5 @@
     "SamplingVQE",
     "SamplingVQEResult",
     "QAOA",
+    "FALQON"
 ]
diff --git a/qiskit/algorithms/minimum_eigensolvers/falqon.py b/qiskit/algorithms/minimum_eigensolvers/falqon.py
new file mode 100644
index 000000000000..9f0f6b14f34b
--- /dev/null
+++ b/qiskit/algorithms/minimum_eigensolvers/falqon.py
@@ -0,0 +1,71 @@
+from collections.abc import Sequence
+
+from qiskit.primitives import BaseEstimator
+
+import numpy as np
+
+from .minimum_eigensolver import MinimumEigensolver, MinimumEigensolverResult
+from ..list_or_dict import ListOrDict
+from ...opflow import PauliSumOp, H, commutator
+from ...quantum_info import SparsePauliOp
+from ...quantum_info.operators.base_operator import BaseOperator
+from ...circuit import ParameterVector
+from ...circuit.library import PauliEvolutionGate
+
+
+class FALQON(MinimumEigensolver):
+
+    def __init__(self,
+                 estimator: BaseEstimator,
+                 n: int = 1,
+                 delta_t: float = 0.3,
+                 initial_point: Sequence[float] = None
+                 ):
+        super().__init__()
+
+        self.estimator = estimator
+        self.n = n
+        self.delta_t = delta_t
+        self.initial_point = initial_point
+
+    def build_ansatz(self, operator, driver_h, betas):
+        circ = (H ^ operator.num_qubits).to_circuit()
+        params = ParameterVector("beta", length=len(betas))
+        for param in params:
+            circ.append(PauliEvolutionGate(operator, time=self.delta_t), circ.qubits)
+            circ.append(PauliEvolutionGate(driver_h, time=self.delta_t * param), circ.qubits)
+        return circ
+
+    def compute_minimum_eigenvalue(self,
+                                   operator: BaseOperator | PauliSumOp,
+                                   aux_operators: ListOrDict[BaseOperator | PauliSumOp] | None = None
+                                   ) -> "MinimumEigensolverResult":
+
+        n_qubits = operator.num_qubits
+        driver_h = PauliSumOp(SparsePauliOp.from_sparse_list([("X", [i], 1) for i in range(n_qubits)],
+                                                             num_qubits=n_qubits))
+        comm_h = (complex(0, 1) * commutator(driver_h, operator)).reduce()
+
+        if self.initial_point is None:
+            betas = [0.0]
+        else:
+            betas = self.initial_point
+
+        energies = []
+
+        for i in range(self.n):
+            ansatz = self.build_ansatz(operator, driver_h, betas)
+            beta = -1 * self.estimator.run(ansatz, comm_h, betas).result().values[0]
+            betas.append(beta)
+
+            ansatz = self.build_ansatz(operator, driver_h, betas)
+            energy = self.estimator.run(ansatz, operator, betas).result().values[0]
+            energies.append(energy)
+
+        return self._build_falqon_result(energies)
+
+    def _build_falqon_result(self, energies):
+        result = MinimumEigensolverResult()
+        result.aux_operators_evaluated = None
+        result.eigenvalue = np.min(np.asarray(energies))
+        return result