diff --git a/releasenotes/notes/fix_save_expval_truncation-2ea6b9224b22956e.yaml b/releasenotes/notes/fix_save_expval_truncation-2ea6b9224b22956e.yaml
new file mode 100644
index 0000000000..41b1a9c8e4
--- /dev/null
+++ b/releasenotes/notes/fix_save_expval_truncation-2ea6b9224b22956e.yaml
@@ -0,0 +1,4 @@
+---
+fixes:
+  - |
+    Fixes a small bug preventing the expval truncation mechanism from activating correctly.
diff --git a/src/framework/circuit.hpp b/src/framework/circuit.hpp
index eab35cd514..ef79862ee7 100644
--- a/src/framework/circuit.hpp
+++ b/src/framework/circuit.hpp
@@ -420,13 +420,14 @@ void Circuit::reset_metadata() {
 void Circuit::add_op_metadata(const Op &op) {
   has_conditional |= op.conditional;
   opset_.insert(op);
-  if (!qubitset_.empty() &&
-      (op.type == OpType::save_expval || op.type == OpType::save_expval_var)) {
+  if (op.type == OpType::save_expval || op.type == OpType::save_expval_var) {
     for (int_t j = 0; j < op.expval_params.size(); j++) {
       const std::string &pauli = std::get<0>(op.expval_params[j]);
       for (int_t i = 0; i < op.qubits.size(); i++) {
         // add qubit with non-I operator
-        if (pauli[pauli.size() - 1 - i] != 'I') {
+        // we also add one qubit if the qubitset is empty to prevent edge cases
+        // with empty circuits
+        if (qubitset_.empty() || pauli[pauli.size() - 1 - i] != 'I') {
           qubitset_.insert(op.qubits[i]);
         }
       }
@@ -693,6 +694,7 @@ void Circuit::remap_qubits(Op &op) const {
       }
       pauli = new_pauli;
     }
+    op.qubits.resize(qubitmap_.size());
     for (int_t i = 0; i < qubitmap_.size(); i++) {
       op.qubits[i] = i;
     }
diff --git a/test/terra/primitives/test_estimator_v2.py b/test/terra/primitives/test_estimator_v2.py
index 988d8dc743..8c08d013f1 100644
--- a/test/terra/primitives/test_estimator_v2.py
+++ b/test/terra/primitives/test_estimator_v2.py
@@ -445,6 +445,33 @@ def test_truncate(self):
             result_5[0].data["evs"][0], result_2[0].data["evs"][0], delta=self._rtol
         )
 
+    def test_truncate_large_backends(self):
+        """Test truncation allows us to run few-qubit circuits on many-qubit backends"""
+        N = 12
+        qc = QuantumCircuit(N)
+
+        qc.x(range(N))
+        qc.h(range(N))
+
+        for kk in range(N // 2, 0, -1):
+            qc.ch(kk, kk - 1)
+        for kk in range(N // 2, N - 1):
+            qc.ch(kk, kk + 1)
+
+        op = SparsePauliOp("Z" * N)
+        backend_127 = GenericBackendV2(num_qubits=127)
+        pm = generate_preset_pass_manager(backend=backend_127, optimization_level=1)
+        isa_circuit = pm.run(qc)
+        mapped_observable = op.apply_layout(isa_circuit.layout)
+
+        ref_est = StatevectorEstimator()
+        ref_result = ref_est.run(pubs=[(qc, op)]).result()
+
+        est = EstimatorV2()
+        res = est.run(pubs=[(isa_circuit, mapped_observable)]).result()
+
+        self.assertAlmostEqual(ref_result[0].data.evs, res[0].data.evs)
+
 
 if __name__ == "__main__":
     unittest.main()