diff --git a/qiskit_experiments/library/randomized_benchmarking/clifford_utils.py b/qiskit_experiments/library/randomized_benchmarking/clifford_utils.py
index 8dae210f42..666f8b0cc9 100644
--- a/qiskit_experiments/library/randomized_benchmarking/clifford_utils.py
+++ b/qiskit_experiments/library/randomized_benchmarking/clifford_utils.py
@@ -46,6 +46,7 @@
 _valid_sparse_indices = _clifford_compose_2q_data["valid_sparse_indices"]
 # map a clifford number to the index of _CLIFFORD_COMPOSE_2Q_DENSE
 _clifford_num_to_dense_index = {idx: ii for ii, idx in enumerate(_valid_sparse_indices)}
+_CLIFFORD_TENSOR_1Q = np.load(f"{_DATA_FOLDER}/clifford_tensor_1q.npz")["table"]
 
 # Transpilation utilities
 def _transpile_clifford_circuit(
@@ -740,12 +741,6 @@ def _layer_indices_from_num(num: Integral) -> Tuple[Integral, Integral, Integral
     return idx0, idx1, idx2
 
 
-@lru_cache(maxsize=24 * 24)
-def _product_1q_nums(first: Integral, second: Integral) -> Integral:
-    """Return the 2-qubit Clifford integer that represents the product of 1-qubit Cliffords."""
-    qc0 = CliffordUtils.clifford_1_qubit_circuit(first)
-    qc1 = CliffordUtils.clifford_1_qubit_circuit(second)
-    qc = QuantumCircuit(2)
-    qc.compose(qc0, qubits=(0,), inplace=True)
-    qc.compose(qc1, qubits=(1,), inplace=True)
-    return num_from_2q_circuit(qc)
+def _tensor_1q_nums(first: Integral, second: Integral) -> Integral:
+    """Return the 2-qubit Clifford integer that is the tensor product of 1-qubit Cliffords."""
+    return _CLIFFORD_TENSOR_1Q[first, second]
diff --git a/qiskit_experiments/library/randomized_benchmarking/data/clifford_tensor_1q.npz b/qiskit_experiments/library/randomized_benchmarking/data/clifford_tensor_1q.npz
new file mode 100644
index 0000000000..7725682f70
Binary files /dev/null and b/qiskit_experiments/library/randomized_benchmarking/data/clifford_tensor_1q.npz differ
diff --git a/qiskit_experiments/library/randomized_benchmarking/data/generate_clifford_data.py b/qiskit_experiments/library/randomized_benchmarking/data/generate_clifford_data.py
index 7ebd45dcab..5193dc35d8 100644
--- a/qiskit_experiments/library/randomized_benchmarking/data/generate_clifford_data.py
+++ b/qiskit_experiments/library/randomized_benchmarking/data/generate_clifford_data.py
@@ -59,7 +59,7 @@ def _hash_cliff(cliff):
 
 
 def gen_clifford_inverse_1q():
-    """Generate table data for integer 1Q Clifford inversion"""
+    """Generate data for integer 1Q Clifford inversion table"""
     invs = np.empty(NUM_CLIFFORD_1Q, dtype=int)
     for i, cliff_i in _CLIFF_1Q.items():
         invs[i] = _TO_INT_1Q[_hash_cliff(cliff_i.adjoint())]
@@ -68,7 +68,7 @@ def gen_clifford_inverse_1q():
 
 
 def gen_clifford_compose_1q():
-    """Generate table data for integer 1Q Clifford composition."""
+    """Generate data for integer 1Q Clifford composition table"""
     products = np.empty((NUM_CLIFFORD_1Q, NUM_CLIFFORD_1Q), dtype=int)
     for i, cliff_i in _CLIFF_1Q.items():
         for j, cliff_j in _CLIFF_1Q.items():
@@ -83,7 +83,7 @@ def gen_clifford_compose_1q():
 
 
 def gen_clifford_inverse_2q():
-    """Generate table data for integer 2Q Clifford inversion"""
+    """Generate data for integer 2Q Clifford inversion table"""
     invs = np.empty(NUM_CLIFFORD_2Q, dtype=int)
     for i, cliff_i in _CLIFF_2Q.items():
         invs[i] = _TO_INT_2Q[_hash_cliff(cliff_i.adjoint())]
@@ -191,6 +191,16 @@ def gen_cliff_single_2q_gate_map():
     return table
 
 
+def gen_clifford_tensor_1q():
+    """Generate data for 2Q integer Clifford table of the tensor product of 1Q integer Cliffords."""
+    products = np.empty((NUM_CLIFFORD_1Q, NUM_CLIFFORD_1Q), dtype=int)
+    for i, cliff_i in _CLIFF_1Q.items():
+        for j, cliff_j in _CLIFF_1Q.items():
+            cliff = cliff_i.tensor(cliff_j)
+            products[i, j] = _TO_INT_2Q[_hash_cliff(cliff)]
+    return products
+
+
 if __name__ == "__main__":
     if _CLIFF_SINGLE_GATE_MAP_1Q != gen_cliff_single_1q_gate_map():
         raise Exception(
@@ -212,3 +222,5 @@ def gen_cliff_single_2q_gate_map():
         table=_CLIFFORD_COMPOSE_2Q_DENSE,
         valid_sparse_indices=valid_sparse_indices,
     )
+
+    np.savez_compressed("clifford_tensor_1q.npz", table=gen_clifford_tensor_1q())
diff --git a/qiskit_experiments/library/randomized_benchmarking/layer_fidelity.py b/qiskit_experiments/library/randomized_benchmarking/layer_fidelity.py
index 6dbd80d5c0..40c5247f87 100644
--- a/qiskit_experiments/library/randomized_benchmarking/layer_fidelity.py
+++ b/qiskit_experiments/library/randomized_benchmarking/layer_fidelity.py
@@ -40,7 +40,7 @@
     inverse_1q,
     inverse_2q,
     num_from_2q_circuit,
-    _product_1q_nums,
+    _tensor_1q_nums,
     _clifford_1q_int_to_instruction,
     _clifford_2q_int_to_instruction,
     _decompose_clifford_ops,
@@ -403,8 +403,11 @@ def __circuit_body(
             for j, qpair in enumerate(two_qubit_layer):
                 # sample product of two 1q-Cliffords as 2q interger Clifford
                 samples = rng.integers(NUM_1Q_CLIFFORD, size=2)
-                cliffs_2q[j] = compose_2q(cliffs_2q[j], _product_1q_nums(*samples))
-                for sample, q in zip(samples, qpair):
+                cliffs_2q[j] = compose_2q(cliffs_2q[j], _tensor_1q_nums(*samples))
+                # For Clifford 1 (x) Clifford 2, in its circuit representation,
+                # Clifford 1 acts on the 2nd qubit and Clifford 2 acts on the 1st qubit.
+                # That's why the qpair is reversed here.
+                for sample, q in zip(samples, reversed(qpair)):
                     circ._append(_to_gate_1q(sample), (circ.qubits[q],), ())
             for k, q in enumerate(one_qubits):
                 sample = rng.integers(NUM_1Q_CLIFFORD)