diff --git a/crates/accelerate/src/lib.rs b/crates/accelerate/src/lib.rs
index 3924c1de4092..dcfbdc9f1878 100644
--- a/crates/accelerate/src/lib.rs
+++ b/crates/accelerate/src/lib.rs
@@ -23,12 +23,12 @@ pub mod isometry;
 pub mod nlayout;
 pub mod optimize_1q_gates;
 pub mod pauli_exp_val;
-pub mod permutation;
 pub mod results;
 pub mod sabre;
 pub mod sampled_exp_val;
 pub mod sparse_pauli_op;
 pub mod stochastic_swap;
+pub mod synthesis;
 pub mod two_qubit_decompose;
 pub mod uc_gate;
 pub mod utils;
diff --git a/crates/accelerate/src/synthesis/mod.rs b/crates/accelerate/src/synthesis/mod.rs
new file mode 100644
index 000000000000..f1a720459211
--- /dev/null
+++ b/crates/accelerate/src/synthesis/mod.rs
@@ -0,0 +1,22 @@
+// This code is part of Qiskit.
+//
+// (C) Copyright IBM 2024
+//
+// This code is licensed under the Apache License, Version 2.0. You may
+// obtain a copy of this license in the LICENSE.txt file in the root directory
+// of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
+//
+// Any modifications or derivative works of this code must retain this
+// copyright notice, and modified files need to carry a notice indicating
+// that they have been altered from the originals.
+
+mod permutation;
+
+use pyo3::prelude::*;
+use pyo3::wrap_pymodule;
+
+#[pymodule]
+pub fn synthesis(m: &Bound<PyModule>) -> PyResult<()> {
+    m.add_wrapped(wrap_pymodule!(permutation::permutation))?;
+    Ok(())
+}
diff --git a/crates/accelerate/src/synthesis/permutation/mod.rs b/crates/accelerate/src/synthesis/permutation/mod.rs
new file mode 100644
index 000000000000..bf0ff97848f2
--- /dev/null
+++ b/crates/accelerate/src/synthesis/permutation/mod.rs
@@ -0,0 +1,68 @@
+// This code is part of Qiskit.
+//
+// (C) Copyright IBM 2024
+//
+// This code is licensed under the Apache License, Version 2.0. You may
+// obtain a copy of this license in the LICENSE.txt file in the root directory
+// of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
+//
+// Any modifications or derivative works of this code must retain this
+// copyright notice, and modified files need to carry a notice indicating
+// that they have been altered from the originals.
+
+use numpy::PyArrayLike1;
+use smallvec::smallvec;
+
+use pyo3::prelude::*;
+use pyo3::wrap_pyfunction;
+
+use qiskit_circuit::circuit_data::CircuitData;
+use qiskit_circuit::operations::{Param, StandardGate};
+use qiskit_circuit::Qubit;
+
+mod utils;
+
+/// Checks whether an array of size N is a permutation of 0, 1, ..., N - 1.
+#[pyfunction]
+#[pyo3(signature = (pattern))]
+pub fn _validate_permutation(py: Python, pattern: PyArrayLike1<i64>) -> PyResult<PyObject> {
+    let view = pattern.as_array();
+    utils::validate_permutation(&view)?;
+    Ok(py.None())
+}
+
+/// Finds inverse of a permutation pattern.
+#[pyfunction]
+#[pyo3(signature = (pattern))]
+pub fn _inverse_pattern(py: Python, pattern: PyArrayLike1<i64>) -> PyResult<PyObject> {
+    let view = pattern.as_array();
+    let inverse_i64: Vec<i64> = utils::invert(&view).iter().map(|&x| x as i64).collect();
+    Ok(inverse_i64.to_object(py))
+}
+
+#[pyfunction]
+#[pyo3(signature = (pattern))]
+pub fn _synth_permutation_basic(py: Python, pattern: PyArrayLike1<i64>) -> PyResult<CircuitData> {
+    let view = pattern.as_array();
+    let num_qubits = view.len();
+    CircuitData::from_standard_gates(
+        py,
+        num_qubits as u32,
+        utils::get_ordered_swap(&view).iter().map(|(i, j)| {
+            (
+                StandardGate::SwapGate,
+                smallvec![],
+                smallvec![Qubit(*i as u32), Qubit(*j as u32)],
+            )
+        }),
+        Param::Float(0.0),
+    )
+}
+
+#[pymodule]
+pub fn permutation(m: &Bound<PyModule>) -> PyResult<()> {
+    m.add_function(wrap_pyfunction!(_validate_permutation, m)?)?;
+    m.add_function(wrap_pyfunction!(_inverse_pattern, m)?)?;
+    m.add_function(wrap_pyfunction!(_synth_permutation_basic, m)?)?;
+    Ok(())
+}
diff --git a/crates/accelerate/src/permutation.rs b/crates/accelerate/src/synthesis/permutation/utils.rs
similarity index 59%
rename from crates/accelerate/src/permutation.rs
rename to crates/accelerate/src/synthesis/permutation/utils.rs
index 62431c40aa4e..a78088bfbfa9 100644
--- a/crates/accelerate/src/permutation.rs
+++ b/crates/accelerate/src/synthesis/permutation/utils.rs
@@ -11,17 +11,11 @@
 // that they have been altered from the originals.
 
 use ndarray::{Array1, ArrayView1};
-use numpy::PyArrayLike1;
 use pyo3::exceptions::PyValueError;
 use pyo3::prelude::*;
-use smallvec::smallvec;
 use std::vec::Vec;
 
-use qiskit_circuit::circuit_data::CircuitData;
-use qiskit_circuit::operations::{Param, StandardGate};
-use qiskit_circuit::Qubit;
-
-fn validate_permutation(pattern: &ArrayView1<i64>) -> PyResult<()> {
+pub fn validate_permutation(pattern: &ArrayView1<i64>) -> PyResult<()> {
     let n = pattern.len();
     let mut seen: Vec<bool> = vec![false; n];
 
@@ -52,7 +46,7 @@ fn validate_permutation(pattern: &ArrayView1<i64>) -> PyResult<()> {
     Ok(())
 }
 
-fn invert(pattern: &ArrayView1<i64>) -> Array1<usize> {
+pub fn invert(pattern: &ArrayView1<i64>) -> Array1<usize> {
     let mut inverse: Array1<usize> = Array1::zeros(pattern.len());
     pattern.iter().enumerate().for_each(|(ii, &jj)| {
         inverse[jj as usize] = ii;
@@ -69,7 +63,7 @@ fn invert(pattern: &ArrayView1<i64>) -> Array1<usize> {
 /// then this creates a quantum circuit with ``m-1`` SWAPs (and of depth ``m-1``);
 /// if the input  permutation consists of several disjoint cycles, then each cycle
 /// is essentially treated independently.
-fn get_ordered_swap(pattern: &ArrayView1<i64>) -> Vec<(i64, i64)> {
+pub fn get_ordered_swap(pattern: &ArrayView1<i64>) -> Vec<(i64, i64)> {
     let mut permutation: Vec<usize> = pattern.iter().map(|&x| x as usize).collect();
     let mut index_map = invert(pattern);
 
@@ -90,48 +84,3 @@ fn get_ordered_swap(pattern: &ArrayView1<i64>) -> Vec<(i64, i64)> {
     swaps[..].reverse();
     swaps
 }
-
-/// Checks whether an array of size N is a permutation of 0, 1, ..., N - 1.
-#[pyfunction]
-#[pyo3(signature = (pattern))]
-fn _validate_permutation(py: Python, pattern: PyArrayLike1<i64>) -> PyResult<PyObject> {
-    let view = pattern.as_array();
-    validate_permutation(&view)?;
-    Ok(py.None())
-}
-
-/// Finds inverse of a permutation pattern.
-#[pyfunction]
-#[pyo3(signature = (pattern))]
-fn _inverse_pattern(py: Python, pattern: PyArrayLike1<i64>) -> PyResult<PyObject> {
-    let view = pattern.as_array();
-    let inverse_i64: Vec<i64> = invert(&view).iter().map(|&x| x as i64).collect();
-    Ok(inverse_i64.to_object(py))
-}
-
-#[pyfunction]
-#[pyo3(signature = (pattern))]
-fn _synth_permutation_basic(py: Python, pattern: PyArrayLike1<i64>) -> PyResult<CircuitData> {
-    let view = pattern.as_array();
-    let num_qubits = view.len();
-    CircuitData::from_standard_gates(
-        py,
-        num_qubits as u32,
-        get_ordered_swap(&view).iter().map(|(i, j)| {
-            (
-                StandardGate::SwapGate,
-                smallvec![],
-                smallvec![Qubit(*i as u32), Qubit(*j as u32)],
-            )
-        }),
-        Param::Float(0.0),
-    )
-}
-
-#[pymodule]
-pub fn permutation(m: &Bound<PyModule>) -> PyResult<()> {
-    m.add_function(wrap_pyfunction!(_validate_permutation, m)?)?;
-    m.add_function(wrap_pyfunction!(_inverse_pattern, m)?)?;
-    m.add_function(wrap_pyfunction!(_synth_permutation_basic, m)?)?;
-    Ok(())
-}
diff --git a/crates/pyext/src/lib.rs b/crates/pyext/src/lib.rs
index b80aad1a7a45..72f0d759099a 100644
--- a/crates/pyext/src/lib.rs
+++ b/crates/pyext/src/lib.rs
@@ -17,10 +17,10 @@ use qiskit_accelerate::{
     convert_2q_block_matrix::convert_2q_block_matrix, dense_layout::dense_layout,
     error_map::error_map, euler_one_qubit_decomposer::euler_one_qubit_decomposer,
     isometry::isometry, nlayout::nlayout, optimize_1q_gates::optimize_1q_gates,
-    pauli_exp_val::pauli_expval, permutation::permutation, results::results, sabre::sabre,
-    sampled_exp_val::sampled_exp_val, sparse_pauli_op::sparse_pauli_op,
-    stochastic_swap::stochastic_swap, two_qubit_decompose::two_qubit_decompose, uc_gate::uc_gate,
-    utils::utils, vf2_layout::vf2_layout,
+    pauli_exp_val::pauli_expval, results::results, sabre::sabre, sampled_exp_val::sampled_exp_val,
+    sparse_pauli_op::sparse_pauli_op, stochastic_swap::stochastic_swap, synthesis::synthesis,
+    two_qubit_decompose::two_qubit_decompose, uc_gate::uc_gate, utils::utils,
+    vf2_layout::vf2_layout,
 };
 
 #[pymodule]
@@ -36,7 +36,7 @@ fn _accelerate(m: &Bound<PyModule>) -> PyResult<()> {
     m.add_wrapped(wrap_pymodule!(nlayout))?;
     m.add_wrapped(wrap_pymodule!(optimize_1q_gates))?;
     m.add_wrapped(wrap_pymodule!(pauli_expval))?;
-    m.add_wrapped(wrap_pymodule!(permutation))?;
+    m.add_wrapped(wrap_pymodule!(synthesis))?;
     m.add_wrapped(wrap_pymodule!(results))?;
     m.add_wrapped(wrap_pymodule!(sabre))?;
     m.add_wrapped(wrap_pymodule!(sampled_exp_val))?;
diff --git a/qiskit/__init__.py b/qiskit/__init__.py
index fce544333478..5b8505654428 100644
--- a/qiskit/__init__.py
+++ b/qiskit/__init__.py
@@ -80,7 +80,7 @@
 sys.modules["qiskit._accelerate.stochastic_swap"] = _accelerate.stochastic_swap
 sys.modules["qiskit._accelerate.two_qubit_decompose"] = _accelerate.two_qubit_decompose
 sys.modules["qiskit._accelerate.vf2_layout"] = _accelerate.vf2_layout
-sys.modules["qiskit._accelerate.permutation"] = _accelerate.permutation
+sys.modules["qiskit._accelerate.synthesis.permutation"] = _accelerate.synthesis.permutation
 
 from qiskit.exceptions import QiskitError, MissingOptionalLibraryError
 
diff --git a/qiskit/synthesis/permutation/permutation_full.py b/qiskit/synthesis/permutation/permutation_full.py
index 9bbb75f925dc..c280065c2a57 100644
--- a/qiskit/synthesis/permutation/permutation_full.py
+++ b/qiskit/synthesis/permutation/permutation_full.py
@@ -16,7 +16,7 @@
 
 import numpy as np
 from qiskit.circuit.quantumcircuit import QuantumCircuit
-from qiskit._accelerate.permutation import _synth_permutation_basic
+from qiskit._accelerate.synthesis.permutation import _synth_permutation_basic
 from .permutation_utils import (
     _inverse_pattern,
     _pattern_to_cycles,
diff --git a/qiskit/synthesis/permutation/permutation_utils.py b/qiskit/synthesis/permutation/permutation_utils.py
index 0d65d9df4c0c..4520e18f4d06 100644
--- a/qiskit/synthesis/permutation/permutation_utils.py
+++ b/qiskit/synthesis/permutation/permutation_utils.py
@@ -13,7 +13,7 @@
 """Utility functions for handling permutations."""
 
 # pylint: disable=unused-import
-from qiskit._accelerate.permutation import (
+from qiskit._accelerate.synthesis.permutation import (
     _inverse_pattern,
     _validate_permutation,
 )