diff --git a/docs/_toc.yml b/docs/_toc.yml
index 28b04f2..9923605 100644
--- a/docs/_toc.yml
+++ b/docs/_toc.yml
@@ -13,6 +13,7 @@ parts:
   - caption: Use-Cases
     chapters:
       - file: use-cases/ssh_model
+      - file: use-cases/adiabatic
     #  - file: ../examples/pulser-myqlm-conversion
   - caption: Theory
     chapters:
diff --git a/docs/use-cases/adiabatic.ipynb b/docs/use-cases/adiabatic.ipynb
new file mode 100644
index 0000000..e724c51
--- /dev/null
+++ b/docs/use-cases/adiabatic.ipynb
@@ -0,0 +1,163 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Quantum Adiabatic Pulses\n",
+    "\n",
+    "Here we prepare a ground state of a Hamiltonian using an adiabatic pulse. See [...] for more details on the adiabatic theorem."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Recall the Rydberg Hamiltonian is\n",
+    "\n",
+    "$$\n",
+    "H = \\frac{\\hbar \\Omega(t)}{2} \\sum_i  X_i - \\hbar \\delta(t) \\sum_i  N_i + \\sum_{i<j} \\frac{C_6}{r_{ij}^6}N_i N_j \n",
+    "$$\n",
+    "\n",
+    "where $\\Omega$ is the Rabi frequency, $\\delta$ is the detuning, $C_6$ is a device specific constant and $r_{ij}$ is the distance between qubits $i$ and $j$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We will choose the signals so that the initial Hamiltonian will be\n",
+    "\n",
+    "$$\n",
+    "H_i = - \\hbar \\delta_i \\sum_i  N_i + \\sum_{i<j} \\frac{C_6}{r_{ij}^6}N_i N_j \n",
+    "$$\n",
+    "by choosing a suitably negative value for $\\delta_i$ we ensure the ground state of the $H_i$ is the all $0$ state, which is the state we start in.\n",
+    "\n",
+    "\n",
+    "We will choose the signals so that the final Hamiltonian will be\n",
+    "\n",
+    "$$\n",
+    "H_f = \\frac{\\hbar \\Omega_f}{2} \\sum_i  X_i + \\sum_{i<j} \\frac{C_6}{r_{ij}^6}N_i N_j \n",
+    "$$\n",
+    "and this is the Hamiltonian's whose ground state we want to prepare."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import qse\n",
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "delta_initial = -2.0\n",
+    "omega_final = 2.0\n",
+    "\n",
+    "r_b = qse.calc.blockade_radius(omega_final * 0.5)\n",
+    "qbits = qse.lattices.ring(r_b, 8)\n",
+    "qbits.draw(radius=\"nearest\", units=\"µm\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "duration = 5000  # ns\n",
+    "amplitude = qse.Signal(np.linspace(0, omega_final, duration))\n",
+    "detuning = qse.Signal(np.linspace(delta_initial, 0, duration))\n",
+    "\n",
+    "plt.plot(amplitude.values, label=\"Amplitude\")\n",
+    "plt.plot(detuning.values, label=\"Detuning\")\n",
+    "plt.xlabel(\"Time (ns)\")\n",
+    "plt.ylabel(\"Signal (rad/µs)\")\n",
+    "plt.axhline(y=0, ls=\"--\", c=\"k\")\n",
+    "plt.legend()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "calc = qse.calc.Qutip(qbits, amplitude, detuning)\n",
+    "\n",
+    "# We get the initial and final hamiltonians\n",
+    "h_i = calc.get_hamiltonian(amplitude[0], detuning[0])\n",
+    "h_f = calc.get_hamiltonian(amplitude[-1], detuning[-1])\n",
+    "\n",
+    "# We compute the expectations of both Hamiltonians\n",
+    "results = calc.calculate(e_ops=[h_i, h_f])\n",
+    "\n",
+    "# Let's compute the groun-state energies of the initial and final hamiltonians\n",
+    "e_i = h_i.eigenenergies()[0]\n",
+    "e_f = h_f.eigenenergies()[0]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "plt.plot(results[\"expectations\"][:, 0], label=r\"$\\langle H_i \\rangle$\")\n",
+    "plt.axhline(e_i, ls=\"--\", label=r\"$e_i$\")\n",
+    "\n",
+    "plt.plot(results[\"expectations\"][:, 1], label=r\"$\\langle H_f \\rangle$\")\n",
+    "plt.axhline(e_f, ls=\"--\", c=\"C1\", label=r\"$e_f$\")\n",
+    "\n",
+    "plt.ylabel(\"Energy\")\n",
+    "plt.xlabel(\"Time (ns)\")\n",
+    "plt.legend()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "probs = np.real(np.conj(results[\"state\"]) * results[\"state\"]).flatten()\n",
+    "probs_dict = {f\"{np.binary_repr(c, qbits.nqbits)}\": p for c, p in enumerate(probs)}\n",
+    "probs_dict = {\n",
+    "    w: probs_dict[w] for w in sorted(probs_dict, key=probs_dict.get, reverse=True)\n",
+    "}\n",
+    "fig = qse.vis.bar(probs_dict, ylabel=\"Probability\", cutoff=0.011)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "qse",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.12.13"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/qse/calc/qutip.py b/qse/calc/qutip.py
index 841383d..63ec571 100644
--- a/qse/calc/qutip.py
+++ b/qse/calc/qutip.py
@@ -48,7 +48,7 @@ def calculate(self, e_ops=None):
 
         result = {"state": state.full()}
         if e_ops is not None:
-            result["expectations" : np.array(exps)]
+            result["expectations"] = np.array(exps)
 
         return result