diff --git a/algorithms/bernstein_vazirani/bernstein_vazirani.ipynb b/algorithms/bernstein_vazirani/bernstein_vazirani.ipynb
index b42406f3e..b59aa49a8 100644
--- a/algorithms/bernstein_vazirani/bernstein_vazirani.ipynb
+++ b/algorithms/bernstein_vazirani/bernstein_vazirani.ipynb
@@ -141,12 +141,12 @@
     "@qfunc\n",
     "def bv_function(a: CInt, x: QArray):\n",
     "    aux = QBit()\n",
+    "    allocate(aux)\n",
     "    within_apply(\n",
     "        lambda: hadamard_transform(x),\n",
-    "        lambda: within_apply(\n",
-    "            lambda: (allocate(aux), X(aux), H(aux)), lambda: bv_predicate(a, x, aux)\n",
-    "        ),\n",
-    "    )"
+    "        lambda: within_apply(lambda: (X(aux), H(aux)), lambda: bv_predicate(a, x, aux)),\n",
+    "    )\n",
+    "    free(aux)"
    ]
   },
   {
diff --git a/algorithms/bernstein_vazirani/bernstein_vazirani.qmod b/algorithms/bernstein_vazirani/bernstein_vazirani.qmod
index b8286ab3c..55878b707 100644
--- a/algorithms/bernstein_vazirani/bernstein_vazirani.qmod
+++ b/algorithms/bernstein_vazirani/bernstein_vazirani.qmod
@@ -8,17 +8,18 @@ qperm bv_predicate(a: int, const x: qbit[], res: qbit) {
 
 qfunc bv_function(a: int, x: qbit[]) {
   aux: qbit;
+  allocate(aux);
   within {
     hadamard_transform(x);
   } apply {
     within {
-      allocate(aux);
       X(aux);
       H(aux);
     } apply {
       bv_predicate(a, x, aux);
     }
   }
+  free(aux);
 }
 
 qfunc main(output x: qnum<5>) {
diff --git a/algorithms/simon/simon.ipynb b/algorithms/simon/simon.ipynb
index f78755064..5da5a5bdf 100644
--- a/algorithms/simon/simon.ipynb
+++ b/algorithms/simon/simon.ipynb
@@ -72,7 +72,7 @@
    "source": [
     "### Quantum Part\n",
     "\n",
-    "The quantum part of the algorithm is rather simple, calling the quantum implementation of $f(x)$, between two calls of the hadamard transform. The call of $f$ is done out-of-place, onto a quantum variable $y$, whereas only the final state of $x$ is relevant to the classical postprocess to follow. "
+    "The quantum part of the algorithm is rather simple, calling the quantum implementation of $f(x)$, between two calls of the hadamard transform. The call of $f$ is done out-of-place, onto a quantum variable $res$, whereas only the final state of $x$ is relevant to the classical postprocess to follow. "
    ]
   },
   {
@@ -86,8 +86,7 @@
     "\n",
     "\n",
     "@qfunc\n",
-    "def simon_qfunc(f_qfunc: QCallable[QNum, Output[QNum]], x: QNum):\n",
-    "    res = QNum()\n",
+    "def simon_qfunc(f_qfunc: QCallable[QNum, Output[QNum]], x: QNum, res: Output[QNum]):\n",
     "    within_apply(lambda: hadamard_transform(x), lambda: f_qfunc(x, res))"
    ]
   },
@@ -376,9 +375,9 @@
     "\n",
     "\n",
     "@qfunc\n",
-    "def main(x: Output[QNum[NUM_QUBITS]]):\n",
+    "def main(x: Output[QNum[NUM_QUBITS]], res: Output[QNum]):\n",
     "    allocate(x)\n",
-    "    simon_qfunc(lambda x, res: simon_qfunc_simple(S_SECRET, x, res), x)\n",
+    "    simon_qfunc(lambda x, res: simon_qfunc_simple(S_SECRET, x, res), x, res)\n",
     "\n",
     "\n",
     "qmod_2 = create_model(\n",
@@ -411,7 +410,7 @@
     "with ExecutionSession(qprog_2, execution_preferences=prefs_more_shots) as es:\n",
     "    result_2 = es.sample()\n",
     "\n",
-    "bitstrings = result_2.dataframe[\"bitstring\"].tolist()\n",
+    "bitstrings = [f\"{x:0{NUM_QUBITS}b}\" for x in result_2.dataframe[\"x\"].tolist()]\n",
     "reversed_bitstrings = [b[::-1] for b in bitstrings]\n",
     "samples = [[int(bit) for bit in b] for b in reversed_bitstrings]"
    ]
@@ -602,9 +601,11 @@
    "outputs": [],
    "source": [
     "@qfunc\n",
-    "def main(x: Output[QNum[NUM_QUBITS]]):\n",
+    "def main(x: Output[QNum[NUM_QUBITS]], res: Output[QNum]):\n",
     "    allocate(x)\n",
-    "    simon_qfunc(lambda x, res: simon_qfunc_with_bipartite_s(PARTITION_INDEX, x, res), x)\n",
+    "    simon_qfunc(\n",
+    "        lambda x, res: simon_qfunc_with_bipartite_s(PARTITION_INDEX, x, res), x, res\n",
+    "    )\n",
     "\n",
     "\n",
     "qmod_4 = create_model(main)\n",
@@ -643,7 +644,7 @@
     "with ExecutionSession(qprog_4, execution_preferences=prefs_more_shots) as es:\n",
     "    result_4 = es.sample()\n",
     "\n",
-    "bitstrings = result_4.dataframe[\"bitstring\"].tolist()\n",
+    "bitstrings = [f\"{x:0{NUM_QUBITS}b}\" for x in result_4.dataframe[\"x\"].tolist()]\n",
     "reversed_bitstrings = [b[::-1] for b in bitstrings]\n",
     "samples = [[int(bit) for bit in b] for b in reversed_bitstrings]"
    ]
diff --git a/algorithms/simon/simon_example.qmod b/algorithms/simon/simon_example.qmod
index 834053981..81159bfce 100644
--- a/algorithms/simon/simon_example.qmod
+++ b/algorithms/simon/simon_example.qmod
@@ -1,5 +1,4 @@
-qfunc simon_qfunc(f_qfunc: qfunc (qnum, output qnum), x: qnum) {
-  res: qnum;
+qfunc simon_qfunc(f_qfunc: qfunc (qnum, output qnum), x: qnum, output res: qnum) {
   within {
     hadamard_transform(x);
   } apply {
@@ -11,9 +10,9 @@ qperm simon_qfunc_simple(s: int, const x: qnum, output res: qnum) {
   res = min(x, x ^ s);
 }
 
-qfunc main(output x: qnum<5>) {
+qfunc main(output x: qnum<5>, output res: qnum) {
   allocate(x);
   simon_qfunc(lambda(x, res) {
     simon_qfunc_simple(6, x, res);
-  }, x);
+  }, x, res);
 }
diff --git a/algorithms/simon/simon_shallow_example.qmod b/algorithms/simon/simon_shallow_example.qmod
index d9305ae38..e34984140 100644
--- a/algorithms/simon/simon_shallow_example.qmod
+++ b/algorithms/simon/simon_shallow_example.qmod
@@ -1,5 +1,4 @@
-qfunc simon_qfunc(f_qfunc: qfunc (qnum, output qnum), x: qnum) {
-  res: qnum;
+qfunc simon_qfunc(f_qfunc: qfunc (qnum, output qnum), x: qnum, output res: qnum) {
   within {
     hadamard_transform(x);
   } apply {
@@ -18,9 +17,9 @@ qperm simon_qfunc_with_bipartite_s(partition_index: int, const x: qbit[], output
   }
 }
 
-qfunc main(output x: qnum<6>) {
+qfunc main(output x: qnum<6>, output res: qnum) {
   allocate(x);
   simon_qfunc(lambda(x, res) {
     simon_qfunc_with_bipartite_s(4, x, res);
-  }, x);
+  }, x, res);
 }