Producing correct QFT circuits over linear connectivity with 32 or more qubits (#16004)

In the debug more, the previous code panicked (attempt to multiply with overflow) when raising 2_u32 to power 32 or more.
And in the release mode, I believe, it silently produced incorrect circuits.

Author: alexanderivrii

crates/synthesis/src/qft/qft_decompose_lnn.rs

@@ -74,7 +74,7 @@ pub fn synth_qft_line(
         for j in i..num_qubits - 1 {
             let q0 = num_qubits - j + i - 1;
             let q1 = num_qubits - j + i - 2;
-            let phase = PI / (2_u32.pow((j - i + 2) as u32) as f64);
+            let phase = PI / 2.0_f64.powi((j - i + 2) as i32);
 
             if j - i + 2 < num_qubits - approximation_degree + 1 {
                 append_phase(&mut instructions, q0, phase);

releasenotes/notes/fix-qft-lnn-9d01e4ecc4995953.yaml

@@ -0,0 +1,5 @@
+---
+fixes:
+  - |
+    Fixed :func:`.synth_qft_line` to correctly synthesize circuits with
+    32 or more qubits.

test/python/synthesis/test_qft_synthesis.py

@@ -58,6 +58,12 @@ def test_qft_lnn_approximated(self, num_qubits, do_swaps, approximation_degree):
         with self.subTest(msg="synthesized QFT circuit do not have LNN connectivity"):
             self.assertTrue(check_lnn_connectivity(qft_lnn))
 
+    @data(50, 100, 1000)
+    def test_create_large_circuit(self, num_qubits):
+        """Test creating large QFT circuits."""
+        qft = synth_qft_line(num_qubits)
+        self.assertEqual(set(qft.count_ops()), {"p", "cx", "h"})
+
 
 @ddt
 class TestQFTFull(QiskitTestCase):
@@ -111,6 +117,12 @@ def test_synthesis_name(self, num_qubits):
         synthesized = synth_qft_full(num_qubits, name="SomeRandomName")
         self.assertEqual(original.name, synthesized.name)
 
+    @data(50, 100, 1000)
+    def test_create_large_circuit(self, num_qubits):
+        """Test creating large QFT circuits."""
+        qft = synth_qft_full(num_qubits)
+        self.assertEqual(set(qft.count_ops()), {"cp", "h", "swap"})
+
 
 if __name__ == "__main__":
     unittest.main()