diff --git a/src/circuit_json.rs b/src/circuit_json.rs
index 35b48fb..74111a4 100644
--- a/src/circuit_json.rs
+++ b/src/circuit_json.rs
@@ -180,9 +180,15 @@ pub struct Command<P = String> {
     pub opgroup: Option<String>,
 }
 
-/// A permutation of the elements of a register.
+/// A classic basis state permutation.
+/// Used when defining Toffoli boxes.
 #[derive(Deserialize, Serialize, Clone, Debug, PartialEq, Eq, Hash)]
-pub struct Permutation(pub Register, pub Register);
+#[serde(transparent)]
+pub struct Permutation(pub Vec<(Vec<bool>, Vec<bool>)>);
+
+/// An implicit permutation of the elements of a register.
+#[derive(Deserialize, Serialize, Clone, Debug, PartialEq, Eq, Hash)]
+pub struct ImplicitPermutation(pub Register, pub Register);
 
 /// Pytket canonical serialized circuit
 #[derive(Deserialize, Serialize, Clone, Debug, PartialEq)]
@@ -199,7 +205,7 @@ pub struct SerialCircuit<P = String> {
     /// Input bit registers.
     pub bits: Vec<Register>,
     /// Implicit permutation of the output qubits.
-    pub implicit_permutation: Vec<Permutation>,
+    pub implicit_permutation: Vec<ImplicitPermutation>,
 }
 
 impl<P> Default for Operation<P> {