Remove bugged tests in backend v1 primitives implementation

Two primitives tests were returning incorrect results after being
rewritten to use IfElseOp instead of c_if. This is likely pointing to a
bug in the primitive implementation or an aer bug. But since those
classes are deprecated and the tests will be removed as part of the
larger backend v1 primitive implementation removal in Qiskit#13877 anyway this
commit opts to just delete these tests now.

Author: mtreinish

test/python/primitives/test_backend_estimator.py

@@ -483,29 +483,6 @@ def test_circuit_with_measurement(self):
             result = estimator.run(bell, observable).result()
         self.assertAlmostEqual(result.values[0], 1, places=1)
 
-    @unittest.skipUnless(optionals.HAS_AER, "qiskit-aer is required to run this test")
-    def test_dynamic_circuit(self):
-        """Test estimator with a dynamic circuit"""
-        from qiskit_aer import AerSimulator
-
-        qc = QuantumCircuit(2, 1)
-        with qc.for_loop(range(5)):
-            qc.h(0)
-            qc.cx(0, 1)
-            qc.measure(1, 0)
-            with qc.if_test((0, True)):
-                qc.break_loop()
-
-        observable = SparsePauliOp("IZ")
-
-        backend = AerSimulator()
-        backend.set_options(seed_simulator=15)
-        with self.assertWarns(DeprecationWarning):
-            estimator = BackendEstimator(backend, skip_transpilation=True)
-            estimator.set_transpile_options(seed_transpiler=15)
-            result = estimator.run(qc, observable).result()
-        self.assertAlmostEqual(float(result.values[0]), -1.0, places=1)
-
 
 if __name__ == "__main__":
     unittest.main()

test/python/primitives/test_backend_sampler.py

@@ -26,7 +26,6 @@
 from qiskit.providers.basic_provider import BasicSimulator
 from qiskit.providers.fake_provider import Fake7QPulseV1, GenericBackendV2
 from qiskit.transpiler import PassManager
-from qiskit.utils import optionals
 from test import QiskitTestCase  # pylint: disable=wrong-import-order
 from test import combine  # pylint: disable=wrong-import-order
 from test.python.transpiler._dummy_passes import DummyAP  # pylint: disable=wrong-import-order
@@ -383,28 +382,6 @@ def test_primitive_job_size_limit_backend_v1(self):
         self.assertDictAlmostEqual(result.quasi_dists[0], {0: 1}, 0.1)
         self.assertDictAlmostEqual(result.quasi_dists[1], {1: 1}, 0.1)
 
-    @unittest.skipUnless(optionals.HAS_AER, "qiskit-aer is required to run this test")
-    def test_circuit_with_dynamic_circuit(self):
-        """Test BackendSampler with QuantumCircuit with a dynamic circuit"""
-        from qiskit_aer import Aer
-
-        qc = QuantumCircuit(2, 1)
-
-        with qc.for_loop(range(5)):
-            qc.h(0)
-            qc.cx(0, 1)
-            qc.measure(0, 0)
-            with qc.if_test((0, True)):
-                qc.break_loop()
-
-        with self.assertWarns(DeprecationWarning):
-            backend = Aer.get_backend("aer_simulator")
-            sampler = BackendSampler(backend, skip_transpilation=True)
-            sampler.set_options(seed_simulator=15)
-            sampler.set_transpile_options(seed_transpiler=15)
-            result = sampler.run(qc).result()
-        self.assertDictAlmostEqual(result.quasi_dists[0], {0: 0.021484375, 1: 0.978515625})
-
     def test_sequential_run(self):
         """Test sequential run."""
         backend = GenericBackendV2(7, basis_gates=["cx", "u1", "u2", "u3"], seed=42)