diff --git a/qiskit/algorithms/minimum_eigen_solvers/falqon.py b/qiskit/algorithms/minimum_eigen_solvers/falqon.py
new file mode 100644
index 000000000000..3d1ff8b0f9b0
--- /dev/null
+++ b/qiskit/algorithms/minimum_eigen_solvers/falqon.py
@@ -0,0 +1,56 @@
+from qiskit.opflow import StateFn, CircuitSampler, PauliExpectation, PauliSumOp, H
+from qiskit.circuit import ParameterVector
+from qiskit.circuit.library import PauliEvolutionGate
+
+from qiskit.quantum_info import SparsePauliOp
+
+class FALQON:
+    def __init__(self, cost_h, comm_h, driver_h=None):
+        self.cost_h = cost_h
+        self.comm_h = comm_h
+        self.n_qubits = cost_h.num_qubits
+        if driver_h is None:
+            self.driver_h = PauliSumOp(
+                SparsePauliOp.from_sparse_list([("X", [i], 1) for i in range(self.n_qubits)], num_qubits=self.n_qubits))
+        else:
+            self.driver_h = driver_h
+
+    def build_maxclique_ansatz(self, delta_t, betas):
+        circ = (H ^ self.cost_h.num_qubits).to_circuit()
+        params = ParameterVector("beta", length=len(betas))
+        for param in params:
+            circ.append(PauliEvolutionGate(self.cost_h, time=delta_t), circ.qubits)
+            circ.append(PauliEvolutionGate(self.driver_h, time=delta_t * param), circ.qubits)
+        return circ
+
+    def expval_circuit(self, ansatz, betas, measurement, sampler):
+        params = dict(zip(ansatz.parameters, betas))
+        composed = measurement.compose(StateFn(ansatz))
+        exp = PauliExpectation().convert(composed)
+        return sampler.convert(exp, params).eval()
+
+    def run(self, n, backend, delta_t=0.03, beta_0=0.0, callback=None):
+        comm_statefn = StateFn(self.comm_h).adjoint()
+        cost_statefn = StateFn(self.cost_h).adjoint()
+
+        betas = [beta_0]
+        energies = []
+        states = []
+
+        sampler = CircuitSampler(backend=backend)
+        for i in range(n):
+            ansatz = self.build_maxclique_ansatz(delta_t, betas)
+            beta = -1 * self.expval_circuit(ansatz, betas, comm_statefn, sampler)
+            betas.append(beta)
+
+            ansatz = self.build_maxclique_ansatz(delta_t, betas)
+            energy = self.expval_circuit(ansatz, betas, cost_statefn, sampler)
+            energies.append(energy)
+
+            state = StateFn(ansatz).bind_parameters(dict(zip(ansatz.parameters, betas))).eval()
+            states.append(state.primitive.data)
+
+            if callback is not None:
+                callback([betas, energies, states])
+
+        return energies, betas, states[-1]
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