diff --git a/pytket/phir/routing.py b/pytket/phir/routing.py
new file mode 100644
index 0000000..eaabb46
--- /dev/null
+++ b/pytket/phir/routing.py
@@ -0,0 +1,34 @@
+# Copyright (c) 2023 Quantinuum LLC.
+# INSERT LICENSE HERE
+"""
+Routing functions. For simulation we don't need to create a sequence of
+transport operations; we are only interested in the time cost to transport from
+one state to another.
+"""
+
+from __future__ import annotations
+
+
+def inverse(lst: list[int]) -> list[int]:
+    """Inverse of a permutation list. If a[i] = x, then inverse(a)[x] = i."""
+    inv = [-1] * len(lst)
+    for (i, elem) in enumerate(lst):
+        if not 0 <= elem < len(lst):
+            raise ValueError(f"List contains element not in range: {elem}")
+        if inv[elem] != -1:
+            raise ValueError(f"List contains duplicate elements: {lst}")
+        inv[elem] = i
+    return inv
+
+def transport_cost(init: list[int], goal: list[int], swap_cost: float) -> float:
+    """Cost of transport from init to goal.
+
+    This is based on the number of parallel swaps performed by Odd-Even
+    Transposition Sort, which is the maximum distance that any qubit travels.
+    """
+    if len(init) != len(goal):
+        raise ValueError(
+            f"init and goal lists have different lengths: {len(init)} vs. {len(goal)}"
+        )
+    n_swaps = max(abs(g - i) for (i, g) in zip(inverse(init), inverse(goal)))
+    return n_swaps * swap_cost