diff --git a/test/python/algorithms/eigensolvers/test_vqd.py b/test/python/algorithms/eigensolvers/test_vqd.py
index 295308ca0aff..16652a259ebd 100644
--- a/test/python/algorithms/eigensolvers/test_vqd.py
+++ b/test/python/algorithms/eigensolvers/test_vqd.py
@@ -10,7 +10,7 @@
 # copyright notice, and modified files need to carry a notice indicating
 # that they have been altered from the originals.
 
-""" Test VQD """
+"""Test VQD"""
 
 import unittest
 from test.python.algorithms import QiskitAlgorithmsTestCase
@@ -19,13 +19,9 @@
 from ddt import data, ddt
 
 from qiskit import QuantumCircuit
-from qiskit.algorithms.eigensolvers import VQD
+from qiskit.algorithms.eigensolvers import VQD, VQDResult
 from qiskit.algorithms import AlgorithmError
-from qiskit.algorithms.optimizers import (
-    COBYLA,
-    L_BFGS_B,
-    SLSQP,
-)
+from qiskit.algorithms.optimizers import COBYLA, L_BFGS_B, SLSQP, SPSA
 from qiskit.algorithms.state_fidelities import ComputeUncompute
 from qiskit.circuit.library import TwoLocal, RealAmplitudes
 from qiskit.opflow import PauliSumOp
@@ -207,6 +203,7 @@ def store_intermediate_result(eval_count, parameters, mean, metadata, step):
     @data(H2_PAULI, H2_OP, H2_SPARSE_PAULI)
     def test_vqd_optimizer(self, op):
         """Test running same VQD twice to re-use optimizer, then switch optimizer"""
+
         vqd = VQD(
             estimator=self.estimator,
             fidelity=self.fidelity,
@@ -231,6 +228,17 @@ def run_check():
             vqd.optimizer = L_BFGS_B()
             run_check()
 
+        with self.subTest("Batched optimizer replace"):
+            vqd.optimizer = SLSQP(maxiter=60, max_evals_grouped=10)
+            run_check()
+
+        with self.subTest("SPSA replace"):
+            # SPSA takes too long to converge, so we will
+            # only check that it runs with no errors.
+            vqd.optimizer = SPSA(maxiter=5, learning_rate=0.01, perturbation=0.01)
+            result = vqd.compute_eigenvalues(operator=op)
+            self.assertIsInstance(result, VQDResult)
+
     @data(H2_PAULI, H2_OP, H2_SPARSE_PAULI)
     def test_optimizer_list(self, op):
         """Test sending an optimizer list"""
diff --git a/test/python/algorithms/gradients/test_estimator_gradient.py b/test/python/algorithms/gradients/test_estimator_gradient.py
index ae6dbfa2930d..c84450313b61 100644
--- a/test/python/algorithms/gradients/test_estimator_gradient.py
+++ b/test/python/algorithms/gradients/test_estimator_gradient.py
@@ -1,6 +1,6 @@
 # This code is part of Qiskit.
 #
-# (C) Copyright IBM 2019, 2023.
+# (C) Copyright IBM 2019, 2021.
 #
 # This code is licensed under the Apache License, Version 2.0. You may
 # obtain a copy of this license in the LICENSE.txt file in the root directory
@@ -14,7 +14,7 @@
 """Test Estimator Gradients"""
 
 import unittest
-from test.python.algorithms.gradients.logging_primitives import LoggingEstimator
+
 import numpy as np
 from ddt import ddt, data, unpack
 
@@ -35,6 +35,8 @@
 from qiskit.quantum_info.random import random_pauli_list
 from qiskit.test import QiskitTestCase
 
+from .logging_primitives import LoggingEstimator
+
 gradient_factories = [
     lambda estimator: FiniteDiffEstimatorGradient(estimator, epsilon=1e-6, method="central"),
     lambda estimator: FiniteDiffEstimatorGradient(estimator, epsilon=1e-6, method="forward"),
diff --git a/test/python/algorithms/gradients/test_qgt.py b/test/python/algorithms/gradients/test_qgt.py
index df8eecdd8478..74f22d462d7c 100644
--- a/test/python/algorithms/gradients/test_qgt.py
+++ b/test/python/algorithms/gradients/test_qgt.py
@@ -14,7 +14,6 @@
 """Test QGT."""
 
 import unittest
-from test.python.algorithms.gradients.logging_primitives import LoggingEstimator
 from ddt import ddt, data
 
 import numpy as np
@@ -26,6 +25,8 @@
 from qiskit.primitives import Estimator
 from qiskit.test import QiskitTestCase
 
+from .logging_primitives import LoggingEstimator
+
 
 @ddt
 class TestQGT(QiskitTestCase):
diff --git a/test/python/algorithms/gradients/test_sampler_gradient.py b/test/python/algorithms/gradients/test_sampler_gradient.py
index 2c9f93a9f17e..b4caac078502 100644
--- a/test/python/algorithms/gradients/test_sampler_gradient.py
+++ b/test/python/algorithms/gradients/test_sampler_gradient.py
@@ -1,6 +1,6 @@
 # This code is part of Qiskit.
 #
-# (C) Copyright IBM 2019, 2023.
+# (C) Copyright IBM 2019, 2021.
 #
 # This code is licensed under the Apache License, Version 2.0. You may
 # obtain a copy of this license in the LICENSE.txt file in the root directory
@@ -15,9 +15,10 @@
 
 import unittest
 from typing import List
-from test.python.algorithms.gradients.logging_primitives import LoggingSampler
+
 import numpy as np
 from ddt import ddt, data
+
 from qiskit import QuantumCircuit
 from qiskit.algorithms.gradients import (
     FiniteDiffSamplerGradient,
@@ -32,6 +33,8 @@
 from qiskit.result import QuasiDistribution
 from qiskit.test import QiskitTestCase
 
+from .logging_primitives import LoggingSampler
+
 gradient_factories = [
     lambda sampler: FiniteDiffSamplerGradient(sampler, epsilon=1e-6, method="central"),
     lambda sampler: FiniteDiffSamplerGradient(sampler, epsilon=1e-6, method="forward"),
diff --git a/test/python/algorithms/minimum_eigensolvers/test_sampling_vqe.py b/test/python/algorithms/minimum_eigensolvers/test_sampling_vqe.py
index 27cf6c46cfb0..8e364e3800c4 100644
--- a/test/python/algorithms/minimum_eigensolvers/test_sampling_vqe.py
+++ b/test/python/algorithms/minimum_eigensolvers/test_sampling_vqe.py
@@ -1,6 +1,6 @@
 # This code is part of Qiskit.
 #
-# (C) Copyright IBM 2018, 2023.
+# (C) Copyright IBM 2018, 2021.
 #
 # This code is licensed under the Apache License, Version 2.0. You may
 # obtain a copy of this license in the LICENSE.txt file in the root directory
@@ -12,6 +12,7 @@
 
 """Test the Sampler VQE."""
 
+
 import unittest
 from functools import partial
 from test.python.algorithms import QiskitAlgorithmsTestCase
diff --git a/test/python/algorithms/time_evolvers/variational/test_var_qite.py b/test/python/algorithms/time_evolvers/variational/test_var_qite.py
index 636798d7947e..9c79a0024885 100644
--- a/test/python/algorithms/time_evolvers/variational/test_var_qite.py
+++ b/test/python/algorithms/time_evolvers/variational/test_var_qite.py
@@ -99,8 +99,8 @@ def test_run_d_1_with_aux_ops(self):
             var_qite = VarQITE(
                 ansatz, init_param_values, var_principle, estimator, num_timesteps=25
             )
-
             evolution_result = var_qite.evolve(evolution_problem)
+
             aux_ops = evolution_result.aux_ops_evaluated
 
             parameter_values = evolution_result.parameter_values[-1]
@@ -128,6 +128,7 @@ def test_run_d_1_with_aux_ops(self):
                 ansatz, init_param_values, var_principle, estimator, num_timesteps=25
             )
             evolution_result = var_qite.evolve(evolution_problem)
+
             aux_ops = evolution_result.aux_ops_evaluated
 
             parameter_values = evolution_result.parameter_values[-1]
diff --git a/test/python/algorithms/time_evolvers/variational/test_var_qrte.py b/test/python/algorithms/time_evolvers/variational/test_var_qrte.py
index 1682c60b842b..b7dfaf59f12b 100644
--- a/test/python/algorithms/time_evolvers/variational/test_var_qrte.py
+++ b/test/python/algorithms/time_evolvers/variational/test_var_qrte.py
@@ -131,6 +131,7 @@ def test_run_d_1_with_aux_ops(self):
                 ansatz, init_param_values, var_principle, estimator, num_timesteps=25
             )
             evolution_result = var_qrte.evolve(evolution_problem)
+
             aux_ops = evolution_result.aux_ops_evaluated
 
             parameter_values = evolution_result.parameter_values[-1]
@@ -158,6 +159,7 @@ def test_run_d_1_with_aux_ops(self):
                 ansatz, init_param_values, var_principle, estimator, num_timesteps=25
             )
             evolution_result = var_qrte.evolve(evolution_problem)
+
             aux_ops = evolution_result.aux_ops_evaluated
 
             parameter_values = evolution_result.parameter_values[-1]
diff --git a/test/python/circuit/library/test_qft.py b/test/python/circuit/library/test_qft.py
index 49e34736616d..fa5305aa3631 100644
--- a/test/python/circuit/library/test_qft.py
+++ b/test/python/circuit/library/test_qft.py
@@ -13,6 +13,7 @@
 """Test library of QFT circuits."""
 
 import unittest
+import warnings
 import numpy as np
 from ddt import ddt, data, unpack
 
@@ -184,11 +185,18 @@ def __init__(self, *_args, **_kwargs):
         # We don't want to issue a warning on mutation until we know that the values are
         # finalised; this is because a user might want to mutate the number of qubits and the
         # approximation degree.  In these cases, wait until we try to build the circuit.
-        with self.assertWarns(DeprecationWarning):
+        with warnings.catch_warnings(record=True) as caught_warnings:
+            warnings.filterwarnings(
+                "always",
+                category=RuntimeWarning,
+                module=r"qiskit\..*",
+                message=r".*precision loss in QFT.*",
+            )
             qft = QFT()
             # Even with the approximation this will trigger the warning.
             qft.num_qubits = 1080
             qft.approximation_degree = 20
+        self.assertFalse(caught_warnings)
 
         # Short-circuit the build method so it exits after input validation, but without actually
         # spinning the CPU to build a huge, useless object.
diff --git a/test/python/opflow/opflow_test_case.py b/test/python/opflow/opflow_test_case.py
index ebd0d5d6b377..ef8d8c6824c7 100644
--- a/test/python/opflow/opflow_test_case.py
+++ b/test/python/opflow/opflow_test_case.py
@@ -1,6 +1,6 @@
 # This code is part of Qiskit.
 #
-# (C) Copyright IBM 2018, 2023.
+# (C) Copyright IBM 2018, 2020.
 #
 # This code is licensed under the Apache License, Version 2.0. You may
 # obtain a copy of this license in the LICENSE.txt file in the root directory
@@ -12,7 +12,6 @@
 
 """Opflow Test Case"""
 
-import warnings
 from qiskit.test import QiskitTestCase
 
 
diff --git a/test/python/primitives/test_estimator.py b/test/python/primitives/test_estimator.py
index 73f20f449d71..4a9209e7fa8a 100644
--- a/test/python/primitives/test_estimator.py
+++ b/test/python/primitives/test_estimator.py
@@ -1,6 +1,6 @@
 # This code is part of Qiskit.
 #
-# (C) Copyright IBM 2022, 2023.
+# (C) Copyright IBM 2022.
 #
 # This code is licensed under the Apache License, Version 2.0. You may
 # obtain a copy of this license in the LICENSE.txt file in the root directory
@@ -13,6 +13,7 @@
 """Tests for Estimator."""
 
 import unittest
+
 import numpy as np
 from ddt import data, ddt, unpack