From 9af5138209202926b10e8ff4fdc5a376bc1a2876 Mon Sep 17 00:00:00 2001
From: Julia Plewa <juliadplewa@gmail.com>
Date: Fri, 17 Dec 2021 20:29:35 +0100
Subject: [PATCH 1/2] Add option to run MLAE circuits separately

---
 .../algorithms/amplitude_estimators/mlae.py   | 20 ++++++++++---
 .../algorithms/test_amplitude_estimators.py   | 30 +++++++++++++++++++
 2 files changed, 46 insertions(+), 4 deletions(-)

diff --git a/qiskit/algorithms/amplitude_estimators/mlae.py b/qiskit/algorithms/amplitude_estimators/mlae.py
index 378512fefa4f..db3e07a1ea95 100644
--- a/qiskit/algorithms/amplitude_estimators/mlae.py
+++ b/qiskit/algorithms/amplitude_estimators/mlae.py
@@ -53,6 +53,7 @@ def __init__(
         evaluation_schedule: Union[List[int], int],
         minimizer: Optional[MINIMIZER] = None,
         quantum_instance: Optional[Union[QuantumInstance, BaseBackend, Backend]] = None,
+        run_circuits_as_one_job: bool = True,
     ) -> None:
         r"""
         Args:
@@ -66,6 +67,9 @@ def __init__(
                 argument and a list of (float, float) tuples (as bounds) as second argument and
                 returns a single float which is the found minimum.
             quantum_instance: Quantum Instance or Backend
+            run_circuits_as_one_job: If set to True, the necessary circuits will be submitted as
+                one job. Otherwise, each circuit will be run separately. This is useful for
+                backends that don't support multi-circuit experiments.
 
         Raises:
             ValueError: If the number of oracle circuits is smaller than 1.
@@ -99,6 +103,8 @@ def default_minimizer(objective_fn, bounds):
         else:
             self._minimizer = minimizer
 
+        self._run_circuits_as_one_job = run_circuits_as_one_job
+
     @property
     def quantum_instance(self) -> Optional[QuantumInstance]:
         """Get the quantum instance.
@@ -286,12 +292,18 @@ def estimate(
             result.shots = 1
 
         else:
-            # run circuit on QASM simulator
+            # construct circuits
             circuits = self.construct_circuits(estimation_problem, measurement=True)
-            ret = self._quantum_instance.execute(circuits)
 
-            # get counts and construct MLE input
-            result.circuit_results = [ret.get_counts(circuit) for circuit in circuits]
+            # run circuit on QASM simulator, get counts, and construct MLE input
+            if self._run_circuits_as_one_job:
+                ret = self._quantum_instance.execute(circuits)
+                result.circuit_results = [ret.get_counts(circuit) for circuit in circuits]
+            else:
+                rets = [self._quantum_instance.execute(circuit) for circuit in circuits]
+                result.circuit_results = [
+                    ret.get_counts(circuit) for ret, circuit in zip(rets, circuits)
+                ]
 
             # to count the number of Q-oracle calls
             result.shots = self._quantum_instance._run_config.shots
diff --git a/test/python/algorithms/test_amplitude_estimators.py b/test/python/algorithms/test_amplitude_estimators.py
index e1351651ec53..a69f1efb4a06 100644
--- a/test/python/algorithms/test_amplitude_estimators.py
+++ b/test/python/algorithms/test_amplitude_estimators.py
@@ -547,5 +547,35 @@ def is_good_state(bitstr):
         self.assertAlmostEqual(result.estimation, expect, places=5)
 
 
+@ddt
+class TestMaximumLikelihoodAmplitudeEstimation(QiskitAlgorithmsTestCase):
+    """Specific tests for Maximum Likelihood AE."""
+
+    def test_sequential_circuit_submission(self):
+        """Test that the results are correct when circuits are submitted separately."""
+        prob = 0.2
+        a_op = BernoulliStateIn(prob)
+        q_op = BernoulliGrover(prob)
+        problem = EstimationProblem(a_op, objective_qubits=[0], grover_operator=q_op)
+
+        # construct algo
+        quantum_instance = QuantumInstance(
+            backend=BasicAer.get_backend("qasm_simulator"),
+            shots=1000,
+            seed_simulator=2,
+            seed_transpiler=2,
+        )
+        mlae = MaximumLikelihoodAmplitudeEstimation(
+            evaluation_schedule=5,
+            quantum_instance=quantum_instance,
+            run_circuits_as_one_job=False,
+        )
+
+        # run the algo
+        result = mlae.estimate(problem)
+
+        self.assertAlmostEqual(prob, result.estimation, places=3, msg=f"estimate failed")
+
+
 if __name__ == "__main__":
     unittest.main()

From 068d56f2d619c7d39cc42d9ba6623e890adc2ed1 Mon Sep 17 00:00:00 2001
From: Julia Plewa <juliadplewa@gmail.com>
Date: Fri, 17 Dec 2021 21:05:30 +0100
Subject: [PATCH 2/2] Fix lint error

---
 test/python/algorithms/test_amplitude_estimators.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/python/algorithms/test_amplitude_estimators.py b/test/python/algorithms/test_amplitude_estimators.py
index a69f1efb4a06..33c28f7c9236 100644
--- a/test/python/algorithms/test_amplitude_estimators.py
+++ b/test/python/algorithms/test_amplitude_estimators.py
@@ -574,7 +574,7 @@ def test_sequential_circuit_submission(self):
         # run the algo
         result = mlae.estimate(problem)
 
-        self.assertAlmostEqual(prob, result.estimation, places=3, msg=f"estimate failed")
+        self.assertAlmostEqual(prob, result.estimation, places=3, msg="estimate failed")
 
 
 if __name__ == "__main__":