From 4aa9130c8cfbf246d724d2a0670aab23d62a3afa Mon Sep 17 00:00:00 2001
From: woodsp-ibm <woodsp@us.ibm.com>
Date: Tue, 17 Oct 2023 16:36:53 -0400
Subject: [PATCH] Fix State Fidelity cache key

---
 qiskit_algorithms/state_fidelities/base_state_fidelity.py  | 7 ++++---
 .../notes/fix_fidelity_cache-3a4cc328344716e0.yaml         | 7 +++++++
 2 files changed, 11 insertions(+), 3 deletions(-)
 create mode 100644 releasenotes/notes/fix_fidelity_cache-3a4cc328344716e0.yaml

diff --git a/qiskit_algorithms/state_fidelities/base_state_fidelity.py b/qiskit_algorithms/state_fidelities/base_state_fidelity.py
index 1909e63f..3a293107 100644
--- a/qiskit_algorithms/state_fidelities/base_state_fidelity.py
+++ b/qiskit_algorithms/state_fidelities/base_state_fidelity.py
@@ -21,6 +21,7 @@
 
 from qiskit import QuantumCircuit
 from qiskit.circuit import ParameterVector
+from qiskit.primitives.utils import _circuit_key
 
 from ..algorithm_job import AlgorithmJob
 from .state_fidelity_result import StateFidelityResult
@@ -173,8 +174,8 @@ def _construct_circuits(
         circuits = []
         for (circuit_1, circuit_2) in zip(circuits_1, circuits_2):
 
-            # TODO: improve caching, what if the circuit is modified without changing the id?
-            circuit = self._circuit_cache.get((id(circuit_1), id(circuit_2)))
+            # Use the same key for circuits as qiskit.primitives use.
+            circuit = self._circuit_cache.get((_circuit_key(circuit_1), _circuit_key(circuit_2)))
 
             if circuit is not None:
                 circuits.append(circuit)
@@ -193,7 +194,7 @@ def _construct_circuits(
                 )
                 circuits.append(circuit)
                 # update cache
-                self._circuit_cache[id(circuit_1), id(circuit_2)] = circuit
+                self._circuit_cache[_circuit_key(circuit_1), _circuit_key(circuit_2)] = circuit
 
         return circuits
 
diff --git a/releasenotes/notes/fix_fidelity_cache-3a4cc328344716e0.yaml b/releasenotes/notes/fix_fidelity_cache-3a4cc328344716e0.yaml
new file mode 100644
index 00000000..fe6443cc
--- /dev/null
+++ b/releasenotes/notes/fix_fidelity_cache-3a4cc328344716e0.yaml
@@ -0,0 +1,7 @@
+---
+fixes:
+  - |
+    Fixes internal cache used by state fidelities so that circuits are cached
+    using the same generated key method as that used by the reference primitives.
+    This avoids a potential incorrect result that could have occurred with the
+    key as it was before when id() was used.