From 625ff98f68ea1903862c41e9d714f55ce7965a15 Mon Sep 17 00:00:00 2001
From: Julien Gacon <gaconju@gmail.com>
Date: Wed, 27 Jul 2022 19:19:44 +0200
Subject: [PATCH] Fix converting VectorStateFn to a CircuitStateFn (#8405)

---
 qiskit/opflow/state_fns/circuit_state_fn.py   |  5 ++---
 ...vector-to-circuit-fn-02cb3424269fa733.yaml | 21 +++++++++++++++++++
 .../python/opflow/test_state_op_meas_evals.py | 13 ++++++++++++
 3 files changed, 36 insertions(+), 3 deletions(-)
 create mode 100644 releasenotes/notes/fix-opflow-vector-to-circuit-fn-02cb3424269fa733.yaml

diff --git a/qiskit/opflow/state_fns/circuit_state_fn.py b/qiskit/opflow/state_fns/circuit_state_fn.py
index 9f959e8718c8..7d5b3a2957de 100644
--- a/qiskit/opflow/state_fns/circuit_state_fn.py
+++ b/qiskit/opflow/state_fns/circuit_state_fn.py
@@ -20,8 +20,7 @@
 from qiskit import BasicAer, ClassicalRegister, QuantumCircuit, transpile
 from qiskit.circuit import Instruction, ParameterExpression
 from qiskit.circuit.exceptions import CircuitError
-from qiskit.circuit.library import IGate
-from qiskit.extensions import Initialize
+from qiskit.circuit.library import IGate, StatePreparation
 from qiskit.opflow.exceptions import OpflowError
 from qiskit.opflow.list_ops.composed_op import ComposedOp
 from qiskit.opflow.list_ops.list_op import ListOp
@@ -123,7 +122,7 @@ def from_vector(statevector: np.ndarray) -> "CircuitStateFn":
         """
         normalization_coeff = np.linalg.norm(statevector)
         normalized_sv = statevector / normalization_coeff
-        return CircuitStateFn(Initialize(normalized_sv), coeff=normalization_coeff)
+        return CircuitStateFn(StatePreparation(normalized_sv), coeff=normalization_coeff)
 
     def primitive_strings(self) -> Set[str]:
         return {"QuantumCircuit"}
diff --git a/releasenotes/notes/fix-opflow-vector-to-circuit-fn-02cb3424269fa733.yaml b/releasenotes/notes/fix-opflow-vector-to-circuit-fn-02cb3424269fa733.yaml
new file mode 100644
index 000000000000..d101486d0fa9
--- /dev/null
+++ b/releasenotes/notes/fix-opflow-vector-to-circuit-fn-02cb3424269fa733.yaml
@@ -0,0 +1,21 @@
+---
+fixes:
+  - |
+    Previously it was not possible to adjoint a :class:`.CircuitStateFn` that has been
+    constructed from a :class:`.VectorStateFn`. That's because the statevector has been 
+    converted to a circuit with the :class:`~qiskit.extensions.Initialize` instruction, which
+    is not unitary. This problem is now fixed by instead using the :class:`.StatePreparation`
+    instruction, which can be used since the state is assumed to start out in the all 0 state.
+
+    For example we can now do::
+
+        from qiskit import QuantumCircuit
+        from qiskit.opflow import StateFn
+
+        left = StateFn([0, 1])
+        left_circuit = left.to_circuit_op().primitive
+
+        right_circuit = QuantumCircuit(1)
+        right_circuit.x(0)
+
+        overlap = left_circuit.inverse().compose(right_circuit)  # this line raised an error before!
diff --git a/test/python/opflow/test_state_op_meas_evals.py b/test/python/opflow/test_state_op_meas_evals.py
index 937065ca691d..d5b36f7d89f4 100644
--- a/test/python/opflow/test_state_op_meas_evals.py
+++ b/test/python/opflow/test_state_op_meas_evals.py
@@ -24,6 +24,7 @@
 from qiskit.utils import QuantumInstance
 from qiskit.opflow import StateFn, Zero, One, H, X, I, Z, Plus, Minus, CircuitSampler, ListOp
 from qiskit.opflow.exceptions import OpflowError
+from qiskit.quantum_info import Statevector
 
 
 @ddt
@@ -217,6 +218,18 @@ def test_quantum_instance_with_backend_shots(self):
         res = sampler.convert(~Plus @ Plus).eval()
         self.assertAlmostEqual(res, 1 + 0j, places=2)
 
+    def test_adjoint_vector_to_circuit_fn(self):
+        """Test it is possible to adjoint a VectorStateFn that was converted to a CircuitStateFn."""
+        left = StateFn([0, 1])
+        left_circuit = left.to_circuit_op().primitive
+
+        right_circuit = QuantumCircuit(1)
+        right_circuit.x(0)
+
+        circuit = left_circuit.inverse().compose(right_circuit)
+
+        self.assertTrue(Statevector(circuit).equiv([1, 0]))
+
 
 if __name__ == "__main__":
     unittest.main()