diff --git a/challenge-2023.04-apr/challenge-2023.04-apr.ipynb b/challenge-2023.04-apr/challenge-2023.04-apr.ipynb
index 8662b68..28ea912 100644
--- a/challenge-2023.04-apr/challenge-2023.04-apr.ipynb
+++ b/challenge-2023.04-apr/challenge-2023.04-apr.ipynb
@@ -82,7 +82,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 1,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -109,7 +109,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -120,56 +120,391 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [],
    "source": [
-    "def Knapsack(values,weights, max_weight):\n",
+    "def Knapsack(values, weights, max_weight):\n",
     "    \n",
     "    #init a model\n",
-    "\n",
+    "    mdl = Model(\"Basic Problem using maximize\")\n",
+    "    \n",
     "    # indicate the binary variables \n",
-    "\n",
+    "    n_vars = len(values) # Number of variables\n",
+    "    x = mdl.binary_var_list(n_vars, name=\"x\")  # Using binary variables for this model\n",
+    "    \n",
     "    # define the objective function\n",
+    "    obj_func = 0\n",
+    "    for i in range(len(weights)):\n",
+    "        obj_func = weights[i]*x[i]\n",
+    "        # obj_func = weights[0]*x[0] + weights[1]*x[1] + weights[2]*x[2] + weights[3]*x[3] + weights[4]*x[4]\n",
+    "    mdl.maximize(obj_func)\n",
     "\n",
     "    # add  the constraints\n",
-    "    return  #return model, check FromDocplex2IsingModel"
+    "    mdl.add_constraint(obj_func <= max_weight)\n",
+    "    \n",
+    "    return  mdl #return model, check FromDocplex2IsingModel"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 4,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>terms</th>\n",
+       "      <th>weights</th>\n",
+       "      <th>constant</th>\n",
+       "      <th>n</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>[4, 5]</td>\n",
+       "      <td>10.0</td>\n",
+       "      <td>190.5</td>\n",
+       "      <td>9</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>[4, 6]</td>\n",
+       "      <td>20.0</td>\n",
+       "      <td>190.5</td>\n",
+       "      <td>9</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>[4, 7]</td>\n",
+       "      <td>40.0</td>\n",
+       "      <td>190.5</td>\n",
+       "      <td>9</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>[8, 4]</td>\n",
+       "      <td>60.0</td>\n",
+       "      <td>190.5</td>\n",
+       "      <td>9</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>[5, 6]</td>\n",
+       "      <td>5.0</td>\n",
+       "      <td>190.5</td>\n",
+       "      <td>9</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>5</th>\n",
+       "      <td>[5, 7]</td>\n",
+       "      <td>10.0</td>\n",
+       "      <td>190.5</td>\n",
+       "      <td>9</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>6</th>\n",
+       "      <td>[8, 5]</td>\n",
+       "      <td>15.0</td>\n",
+       "      <td>190.5</td>\n",
+       "      <td>9</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>7</th>\n",
+       "      <td>[6, 7]</td>\n",
+       "      <td>20.0</td>\n",
+       "      <td>190.5</td>\n",
+       "      <td>9</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>8</th>\n",
+       "      <td>[8, 6]</td>\n",
+       "      <td>30.0</td>\n",
+       "      <td>190.5</td>\n",
+       "      <td>9</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>9</th>\n",
+       "      <td>[8, 7]</td>\n",
+       "      <td>60.0</td>\n",
+       "      <td>190.5</td>\n",
+       "      <td>9</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>10</th>\n",
+       "      <td>[0]</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>190.5</td>\n",
+       "      <td>9</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>11</th>\n",
+       "      <td>[1]</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>190.5</td>\n",
+       "      <td>9</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>12</th>\n",
+       "      <td>[2]</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>190.5</td>\n",
+       "      <td>9</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>13</th>\n",
+       "      <td>[3]</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>190.5</td>\n",
+       "      <td>9</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>14</th>\n",
+       "      <td>[4]</td>\n",
+       "      <td>92.0</td>\n",
+       "      <td>190.5</td>\n",
+       "      <td>9</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>15</th>\n",
+       "      <td>[5]</td>\n",
+       "      <td>22.5</td>\n",
+       "      <td>190.5</td>\n",
+       "      <td>9</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>16</th>\n",
+       "      <td>[6]</td>\n",
+       "      <td>45.0</td>\n",
+       "      <td>190.5</td>\n",
+       "      <td>9</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>17</th>\n",
+       "      <td>[7]</td>\n",
+       "      <td>90.0</td>\n",
+       "      <td>190.5</td>\n",
+       "      <td>9</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>18</th>\n",
+       "      <td>[8]</td>\n",
+       "      <td>135.0</td>\n",
+       "      <td>190.5</td>\n",
+       "      <td>9</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "     terms  weights  constant  n\n",
+       "0   [4, 5]     10.0     190.5  9\n",
+       "1   [4, 6]     20.0     190.5  9\n",
+       "2   [4, 7]     40.0     190.5  9\n",
+       "3   [8, 4]     60.0     190.5  9\n",
+       "4   [5, 6]      5.0     190.5  9\n",
+       "5   [5, 7]     10.0     190.5  9\n",
+       "6   [8, 5]     15.0     190.5  9\n",
+       "7   [6, 7]     20.0     190.5  9\n",
+       "8   [8, 6]     30.0     190.5  9\n",
+       "9   [8, 7]     60.0     190.5  9\n",
+       "10     [0]      0.0     190.5  9\n",
+       "11     [1]      0.0     190.5  9\n",
+       "12     [2]      0.0     190.5  9\n",
+       "13     [3]      0.0     190.5  9\n",
+       "14     [4]     92.0     190.5  9\n",
+       "15     [5]     22.5     190.5  9\n",
+       "16     [6]     45.0     190.5  9\n",
+       "17     [7]     90.0     190.5  9\n",
+       "18     [8]    135.0     190.5  9"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
-    "knapsack =  Knapsack(values,weights, max_weight)\n",
+    "# Converting the Docplex model into its qubo representation\n",
+    "mdl = Knapsack(values, weights, max_weight)\n",
+    "qubo = FromDocplex2IsingModel(mdl)\n",
     "\n",
-    "# Ising encoding of the QUBO problem for binpacking problem\n",
+    "# Ising encoding of the QUBO problem\n",
+    "ising_encoding = qubo.ising_model  \n",
     "\n",
+    "# Print in a df the ising encoding (we need to remove keys: 'problem_instance' and 'metadata')) \n",
+    "ising_encoding_dict = ising_encoding.asdict(exclude_keys=['problem_instance', 'metadata'])\n",
+    "pd.DataFrame(ising_encoding_dict)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "// This file has been generated by DOcplex\n",
+      "// model name is: Copy of Copy of Basic Problem using maximize\n",
+      "// var contrainer section\n",
+      "dvar bool x[5];\n",
+      "dvar bool slack_C0[4];\n",
+      "\n",
+      "// single vars section\n",
+      "dvar bool x_0;\n",
+      "dvar bool x_1;\n",
+      "dvar bool x_2;\n",
+      "dvar bool x_3;\n",
+      "dvar bool x_4;\n",
+      "dvar bool slack_C0_0;\n",
+      "dvar bool slack_C0_1;\n",
+      "dvar bool slack_C0_2;\n",
+      "dvar bool slack_C0_3;\n",
+      "\n",
+      "minimize\n",
+      " - 524 x_4 - 130 slack_C0_0 - 260 slack_C0_1 - 520 slack_C0_2 - 780 slack_C0_3\n",
+      " [ 80 x_4^2 + 40 x_4*slack_C0_0 + 80 x_4*slack_C0_1 + 160 x_4*slack_C0_2\n",
+      " + 240 x_4*slack_C0_3 + 5 slack_C0_0^2 + 20 slack_C0_0*slack_C0_1\n",
+      " + 40 slack_C0_0*slack_C0_2 + 60 slack_C0_0*slack_C0_3 + 20 slack_C0_1^2\n",
+      " + 80 slack_C0_1*slack_C0_2 + 120 slack_C0_1*slack_C0_3 + 80 slack_C0_2^2\n",
+      " + 240 slack_C0_2*slack_C0_3 + 180 slack_C0_3^2 ] + 845;\n",
+      " \n",
+      "subject to {\n",
+      "\n",
+      "}\n"
+     ]
+    }
+   ],
+   "source": [
+    "knapsack =  Knapsack(values, weights, max_weight)\n",
     "\n",
-    "# Docplex encoding of the QUBO problem for binpacking problem\n",
+    "# Ising encoding of the QUBO problem for binpacking problem\n",
+    "# Converting the Docplex model of binpacking into its qubo representation\n",
+    "qubo_bin = FromDocplex2IsingModel(knapsack) \n",
     "\n",
+    "# Ising encoding of the QUBO problem for binpacking problem\n",
+    "ising_encoding_bin = qubo_bin.ising_model\n",
     "\n",
+    "# Docplex encoding of the QUBO problem for binpacking problem\n",
+    "mdl_qubo_docplex = qubo_bin.qubo_docplex\n",
     "\n",
     "mdl_qubo_docplex.prettyprint()"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 6,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>solutions_bitstrings</th>\n",
+       "      <th>bitstrings_energies</th>\n",
+       "      <th>probabilities</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>100011101</td>\n",
+       "      <td>-4.0</td>\n",
+       "      <td>0.001661</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>010011101</td>\n",
+       "      <td>-4.0</td>\n",
+       "      <td>0.001661</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>000011101</td>\n",
+       "      <td>-4.0</td>\n",
+       "      <td>0.001661</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>111111101</td>\n",
+       "      <td>-4.0</td>\n",
+       "      <td>0.001661</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>011111101</td>\n",
+       "      <td>-4.0</td>\n",
+       "      <td>0.001661</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "  solutions_bitstrings  bitstrings_energies  probabilities\n",
+       "0            100011101                 -4.0       0.001661\n",
+       "1            010011101                 -4.0       0.001661\n",
+       "2            000011101                 -4.0       0.001661\n",
+       "3            111111101                 -4.0       0.001661\n",
+       "4            011111101                 -4.0       0.001661"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "# Initilize the QAOA object\n",
     "qaoa = QAOA()\n",
     "\n",
     "# Set the parameters to work the QAOA algorithm\n",
     "# where n_shots =1024 and  seed_simulator=1\n",
-    "\n",
+    "qaoa.set_backend_properties(n_shots=1024, seed_simulator=1)\n",
     "\n",
     "#p = 1, a custom type and range from 0 to pi\n",
-    "\n",
-    "qaoa.compile(ising_encoding)\n",
+    "rep = 1 \n",
+    "qaoa.set_circuit_properties(p=rep, init_type=\"custom\", variational_params_dict={\"betas\":rep*[0.01*np.pi],\"gammas\":rep*[0.01*np.pi]})\n",
+    "qaoa.compile(ising_encoding_bin)\n",
     "\n",
     "# Run the QAOA algorithm\n",
     "qaoa.optimize()\n",
@@ -179,13 +514,40 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 7,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(-4.0,\n",
+       " ['000011101',\n",
+       "  '100011101',\n",
+       "  '010011101',\n",
+       "  '110011101',\n",
+       "  '001011101',\n",
+       "  '101011101',\n",
+       "  '011011101',\n",
+       "  '111011101',\n",
+       "  '000111101',\n",
+       "  '100111101',\n",
+       "  '010111101',\n",
+       "  '110111101',\n",
+       "  '001111101',\n",
+       "  '101111101',\n",
+       "  '011111101',\n",
+       "  '111111101'])"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "# To find the correct answer using ground_state_hamiltonian\n",
     "# and  the paremeter is a cost_hamiltonian\n",
-    "correct_solution = \n",
+    "correct_solution = ground_state_hamiltonian(qaoa.cost_hamil)\n",
     "correct_solution"
    ]
   },
@@ -198,9 +560,27 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 8,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "objective: -4.000\n",
+      "status: OPTIMAL_SOLUTION(2)\n",
+      "  x_0=0\n",
+      "  x_1=0\n",
+      "  x_2=0\n",
+      "  x_3=0\n",
+      "  x_4=1\n",
+      "  slack_C0_0=1\n",
+      "  slack_C0_1=1\n",
+      "  slack_C0_2=0\n",
+      "  slack_C0_3=1\n"
+     ]
+    }
+   ],
    "source": [
     "## docplex solution\n",
     "sol = mdl_qubo_docplex.solve()\n",
@@ -225,14 +605,25 @@
     "## implementation\n",
     "\n",
     "# Initilize the QAOA object and use a device\n",
-    "device = create_device(\"local\", 'qiskit.qasm_simulator')\n",
-    "\n",
-    "\n",
+    "device = create_device(\"local\", 'qiskit.aer_simulator')\n",
     "qaoa = QAOA(device)\n",
     "\n",
     "# Set the parameters to work the QAOA algorithm\n",
     "# play with the parameters values\n",
+    "knapsack =  Knapsack(values, weights, max_weight)\n",
+    "\n",
+    "# Ising encoding of the QUBO problem for binpacking problem\n",
+    "# Converting the Docplex model of binpacking into its qubo representation\n",
+    "qubo_bin = FromDocplex2IsingModel(knapsack) \n",
     "\n",
+    "# Ising encoding of the QUBO problem for binpacking problem\n",
+    "ising_encoding_bin = qubo_bin.ising_model\n",
+    "\n",
+    "qaoa.set_backend_properties(n_shots=1024, seed_simulator=1)\n",
+    "\n",
+    "rep = 5\n",
+    "qaoa.set_circuit_properties(p=rep, init_type=\"custom\", variational_params_dict={\"betas\":rep*[0.01*np.pi],\"gammas\":rep*[0.01*np.pi]})\n",
+    "qaoa.compile(ising_encoding_bin)\n",
     "\n",
     "# Run the QAOA algorithm\n",
     "qaoa.optimize()\n",
@@ -251,9 +642,84 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 20,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>solutions_bitstrings</th>\n",
+       "      <th>bitstrings_energies</th>\n",
+       "      <th>probabilities</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>101111101</td>\n",
+       "      <td>-4.0</td>\n",
+       "      <td>0.02</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>100111101</td>\n",
+       "      <td>-4.0</td>\n",
+       "      <td>0.01</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>000111101</td>\n",
+       "      <td>-4.0</td>\n",
+       "      <td>0.01</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>001011101</td>\n",
+       "      <td>-4.0</td>\n",
+       "      <td>0.01</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>010111101</td>\n",
+       "      <td>-4.0</td>\n",
+       "      <td>0.01</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "  solutions_bitstrings  bitstrings_energies  probabilities\n",
+       "0            101111101                 -4.0           0.02\n",
+       "1            100111101                 -4.0           0.01\n",
+       "2            000111101                 -4.0           0.01\n",
+       "3            001011101                 -4.0           0.01\n",
+       "4            010111101                 -4.0           0.01"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "## implementation using a noise model using qiskit \n",
     "\n",
@@ -271,6 +737,8 @@
     "qaoa = QAOA(device)\n",
     "\n",
     "# Set the parameters to work the QAOA algorithm\n",
+    "rep = 1\n",
+    "qaoa.set_circuit_properties(p=rep, init_type=\"custom\", variational_params_dict={\"betas\":rep*[0.01*np.pi],\"gammas\":rep*[0.01*np.pi]})\n",
     "\n",
     "\n",
     "qaoa.compile(ising_encoding)\n",
@@ -395,9 +863,9 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "mitiq-qaoa",
+   "display_name": "Python 3 [OpenQAOA]",
    "language": "python",
-   "name": "mitiq-qaoa"
+   "name": "python3_openqaoa_fozpr5"
   },
   "language_info": {
    "codemirror_mode": {
@@ -409,7 +877,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.8"
+   "version": "3.9.10"
   }
  },
  "nbformat": 4,