diff --git a/circom_circuits/ledger/notes.circom b/circom_circuits/ledger/notes.circom
index d3b4c59..a4013ed 100644
--- a/circom_circuits/ledger/notes.circom
+++ b/circom_circuits/ledger/notes.circom
@@ -14,4 +14,22 @@ template derive_public_key(){
     hash.inp[0] <== dst.out;
     hash.inp[1] <== secret_key;
     out <== hash.out;
+}
+
+template derive_note_id(){
+    signal input op_id;
+    signal input output_number;
+    signal input value;
+    signal input pk;
+
+    component note_id = Poseidon2_hash(5);
+    component note_id_v1 = NOTE_ID_V1();
+    note_id.inp[0] <== note_id_v1.out;
+    note_id.inp[1] <== op_id;
+    note_id.inp[2] <== output_number;
+    note_id.inp[3] <== value;
+    note_id.inp[4] <== pk;
+
+    signal output out;
+    out <== note_id.out;
 }
\ No newline at end of file
diff --git a/circom_circuits/ledger/update_state.circom b/circom_circuits/ledger/update_state.circom
new file mode 100644
index 0000000..0c31719
--- /dev/null
+++ b/circom_circuits/ledger/update_state.circom
@@ -0,0 +1,104 @@
+//test
+pragma circom 2.1.9;
+
+include "../hash_bn/poseidon2_hash.circom";
+include "../hash_bn/poseidon2_perm.circom";
+include "../misc/constants.circom";
+include "notes.circom";
+include "../hash_bn/merkle.circom";
+
+
+template update_state_with_one_note(merkle_depth){
+    signal input merkle_root;
+    signal input old_value;
+    signal input old_pk;
+    signal input new_value;
+    signal input new_pk;
+    signal input selectors[merkle_depth];
+    signal input path[merkle_depth];
+
+    //Get the old note ID
+    component old_note_id = derive_note_id();
+    old_note_id.op_id <== 0;
+    old_note_id.output_number <== 0;
+    old_note_id.value <== old_value;
+    old_note_id.pk <== old_pk;
+
+    // Check that the note is in the tree
+            //First check selectors are indeed bits
+    for(var i = 0; i < merkle_depth; i++){
+        selectors[i] * (1 - selectors[i]) === 0;
+    }
+            //Then check the note id is in the tree
+    component old_membership = proof_of_membership(merkle_depth);
+    for(var i = 0; i < merkle_depth; i++){
+        old_membership.nodes[i] <== path[i];
+        old_membership.selector[i] <== selectors[i];
+    }
+    old_membership.root <== merkle_root;
+    old_membership.leaf <== old_note_id.out;
+    old_membership.out === 1;
+
+    // Then update the root with the new note replacing the old one
+            // First derive the new note ID
+    component new_note_id = derive_note_id();
+    new_note_id.op_id <== 0;
+    new_note_id.output_number <== 0;
+    new_note_id.value <== new_value;
+    new_note_id.pk <== new_pk;
+            // Then update the Merkle root
+    component new_root = compute_merkle_root(merkle_depth);
+    for(var i = 0; i< merkle_depth; i++) {
+        new_root.nodes[i] <== path[i];
+        new_root.selector[i] <== selectors[i];
+    }
+    new_root.leaf <== new_note_id.out;
+
+    // Output
+    signal output updated_root;
+    updated_root <== new_root.root;
+}
+
+template update_state_with_several_notes(merkle_depth, batch_size){
+    signal input previous_root;
+    signal input previous_note_values[batch_size];
+    signal input previous_note_pk[batch_size];
+    signal input new_note_values[batch_size];
+    signal input new_note_pk[batch_size];
+    signal input merkle_paths[batch_size][merkle_depth];
+    signal input merkle_selectors[batch_size][merkle_depth];
+
+    signal output new_root;
+
+    component update[batch_size];
+
+    // Update with the first note
+    update[0] = update_state_with_one_note(merkle_depth);
+    update[0].merkle_root <== previous_root;
+    update[0].old_value <== previous_note_values[0];
+    update[0].old_pk <== previous_note_pk[0];
+    update[0].new_value <== new_note_values[0];
+    update[0].new_pk <== new_note_pk[0];
+    for(var i = 0; i < merkle_depth; i++){
+        update[0].selectors[i] <== merkle_selectors[0][i];
+        update[0].path[i] <== merkle_paths[0][i];
+    }
+
+    // Update all the other notes
+    for(var i = 1; i < batch_size; i++){
+        update[i] = update_state_with_one_note(merkle_depth);
+        update[i].merkle_root <== update[i-1].updated_root;
+        update[i].old_value <== previous_note_values[i];
+        update[i].old_pk <== previous_note_pk[i];
+        update[i].new_value <== new_note_values[i];
+        update[i].new_pk <== new_note_pk[i];
+        for(var j = 0; j < merkle_depth; j++){
+            update[i].selectors[j] <== merkle_selectors[i][j];
+            update[i].path[j] <== merkle_paths[i][j];
+        }
+    }
+
+    new_root <== update[batch_size -1].updated_root;
+}
+
+component main {public [previous_root,previous_note_values,new_note_values]}= update_state_with_several_notes(32,3);
\ No newline at end of file
diff --git a/circom_circuits/mantle/pol_lib.circom b/circom_circuits/mantle/pol_lib.circom
index 38dd6c6..0cc7fba 100644
--- a/circom_circuits/mantle/pol_lib.circom
+++ b/circom_circuits/mantle/pol_lib.circom
@@ -72,14 +72,11 @@ template would_win_leadership(merkle_depth){
 
 
     // Derive the note id
-    component note_id = Poseidon2_hash(5);
-    component dst_note_id = NOTE_ID_V1();
-    note_id.inp[0] <== dst_note_id.out;
-    note_id.inp[1] <== transaction_hash;
-    note_id.inp[2] <== output_number;
-    note_id.inp[3] <== value;
-    note_id.inp[4] <== pk.out;
-
+    component note_id = derive_note_id();
+    note_id.op_id <== transaction_hash;
+    note_id.output_number <== output_number;
+    note_id.value <== value;
+    note_id.pk <== pk.out;
 
     // Check the note ID is aged enough
             //First check selectors are indeed bits