Sorts gate array to have deterministic gate selection (#16139)

* sorts gate array to have deterministic gate selection

* changes array return and add test case

* updates test case to generate expected result

* running fmt and adding bugfix note

* update bugfix notes

Author: amruthpremjith

qiskit/circuit/random/utils.py

@@ -708,7 +708,7 @@ def random_clifford_circuit(num_qubits, num_gates, gates="all", seed=None):
         QuantumCircuit: constructed circuit
     """
 
-    gates_1q = list(set(_BASIS_1Q.keys()) - {"v", "w", "id", "iden", "sinv"})
+    gates_1q = [gate for gate in _BASIS_1Q if gate not in {"v", "w", "id", "iden", "sinv"}]
     gates_2q = list(_BASIS_2Q.keys())
 
     if gates == "all":

releasenotes/notes/return-consistent-random-clifford-ckt-4b3be73ea202c87c.yaml

@@ -0,0 +1,7 @@
+---
+fixes:
+  - |
+    Fixed :func:`.random_clifford_circuit` to produce deterministic results across multiple runs given the same ``seed``.
+
+    Fixes `#16138 <https://github.com/Qiskit/qiskit/issues/16138>`__.
+

test/python/quantum_info/operators/symplectic/test_clifford.py

@@ -13,6 +13,11 @@
 
 """Tests for Clifford class."""
 
+from collections import OrderedDict
+import os
+import subprocess
+import sys
+import textwrap
 import unittest
 import itertools
 import numpy as np
@@ -174,6 +179,29 @@ def test_append_1_qubit_gate(self):
                     np.all(np.array(value_destabilizer == [target_destabilizer[gate_name]]))
                 )
 
+    @combine(hash_seed=["1", "2", "10", "100"])
+    def test_random_clifford_circuit_with_same_seed(self, hash_seed):
+        random_clifford = random_clifford_circuit(
+            num_qubits=10, num_gates=100, gates="all", seed=0
+        ).count_ops()
+
+        env = os.environ.copy()
+        env["PYTHONHASHSEED"] = hash_seed
+
+        test_script = textwrap.dedent(
+            """
+        from qiskit.circuit.random.utils import random_clifford_circuit
+        cliff_circuit = random_clifford_circuit(num_qubits=10, num_gates=100, gates="all", seed=0)
+        print(cliff_circuit.count_ops(),end="")
+        """
+        )
+
+        result = subprocess.run(
+            [sys.executable, "-c", test_script], env=env, capture_output=True, text=True, check=True
+        )
+
+        self.assertEqual(result.stdout, random_clifford.__str__())
+
     @combine(
         gate=[
             IGate(),