{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "2c935a4a-aa7d-499a-b358-3ef7fac417c2",
   "metadata": {},
   "source": [
    "# Obtaining the deuteron energy descibed on two qubits (Dumitrescu et al., PRL 120, 210501 (2018))\n",
    "\n",
    "Our starting point is the 2‑qubit Hamiltonian\n",
    "\n",
    "$H_2 = 5.906709\\, I + 0.218291\\, Z_0 - 6.125\\, Z_1\n",
    "      - 2.143304\\left(X_0X_1 + Y_0Y_1\\right).$\n",
    "      \n",
    "The trial state is \n",
    "$\n",
    "|\\psi(\\theta)\\rangle =\n",
    "e^{\\,i\\frac{\\theta}{2}\\left(X_0 Y_1 - X_1 Y_0\\right)} |00\\rangle,$\n",
    "\n",
    "1. Define the Hamiltonian and the two qubit circuit\n",
    "2. For a given theta, prepare the ansatz |\\psi(\\theta)\\rangle\n",
    "3. Compute the expectation values for $Z_0$, $Z_1$, $X_0X_1$, $Y_0Y_1$ with a finite number of measurements.  \n",
    "4. Deduce the expectation value of $E(\\theta)=\\langle H_2\\rangle$\n",
    "5. Then reproduce the Fig. 2 of (Dumitrescu et al., PRL 120, 210501 (2018)) where the different Pauli strings are shown as a function of $\\theta$, show also $E(\\theta)$ as a function of $theta$, and deduce the ground state energy\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4766d432-a17d-4e44-8f69-1734e11c0ff6",
   "metadata": {},
   "source": [
    "## 0. Imports\n",
    "\n",
    "- `QuantumCircuit` to build circuits\n",
    "- `StatevectorSampler` for **shot-based** counts (like running the circuit many times)\n",
    "- `Statevector` for exact (ideal) checks (no shot noise)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "09303518",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import QuantumCircuit\n",
    "from qiskit.quantum_info import Statevector\n",
    "from qiskit.primitives import StatevectorSampler\n",
    "from qiskit.visualization import plot_histogram\n",
    "import numpy as np\n",
    "\n",
    "# for vizualization \n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import display\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae79692c-9c5b-4cf1-bcd1-049d2d064d72",
   "metadata": {},
   "source": [
    "## 1. Circuit for the trial state vector\n",
    "\n",
    "The trial state is \n",
    "\\[\n",
    "|\\psi(\\theta)\\rangle =\n",
    "e^{\\,i\\frac{\\theta}{2}\\left(X_0 Y_1 - X_1 Y_0\\right)} |00\\rangle,\n",
    "\\]\n",
    "It could be prepared by \n",
    "1) performing a X gate on the first qubit\n",
    "2) a Y-rotation with angle \\( theta \\) on the first qubit\n",
    "3) a CNOT where 1 control 0\n",
    "\n",
    "**Task: For a fixed $\\theta$, make the circuit and perform measurements by counts** "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "47e471f4-5345-405d-91cf-c474a4257ecb",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 454.517x284.278 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Counts: {'10': 261, '01': 739}\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "theta = np.pi/3\n",
    "qc = QuantumCircuit(2, 2, name=\"Trial_state\")\n",
    "qc.ry(theta, 1)     # 1) Y-rotation on qubit 0\n",
    "qc.x(0)             # 2) X on qubit 1\n",
    "qc.cx(1, 0)         # 3) CNOT: control 0 -> target 1\n",
    "\n",
    "# --- Add measurement (shots require measurements) ---\n",
    "qc.measure([0, 1], [0, 1])\n",
    "\n",
    "# Draw circuit\n",
    "fig = qc.draw(output=\"mpl\")\n",
    "display(fig)\n",
    "\n",
    "# --- Run 1000 shots (local sampling) ---\n",
    "sampler = StatevectorSampler()\n",
    "shots = 1000\n",
    "\n",
    "result = sampler.run([qc], shots=shots).result()\n",
    "counts = result[0].data.c.get_counts()\n",
    "\n",
    "print(\"Counts:\", counts)\n",
    "\n",
    "# --- Plot histogram ---\n",
    "fig2 = plot_histogram(counts, title=f\"Trial_state counts (shots={shots}, theta={theta:.3f})\")\n",
    "display(fig2)\n",
    "plt.close(fig2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1a86c0e-08a2-468f-8c8f-7782c1289d2d",
   "metadata": {},
   "source": [
    "## 3. Computing expectation values of observables for one single angle value \n",
    "\n",
    "To measure on one qubit:\n",
    "\n",
    "- **Z**: do nothing, measure in computational basis\n",
    "- **X**: apply **H**, then measure Z\n",
    "- **Y**: apply **Sdg** then **H**, then measure Z\n",
    "\n",
    "For two-qubit Pauli strings (like \\(X_0X_1\\)), apply the rule on each qubit.\n",
    "\n",
    "### From counts to expectation values\n",
    "\n",
    "Eigenvalues:\n",
    "- bit `0` → +1\n",
    "- bit `1` → −1\n",
    "\n",
    "Qiskit bitstrings are shown as `'b1b0'` (highest classical bit on the left). \n",
    "Tips: you need to convert counts to expectation values, for this you can use a similar \n",
    "routine used in the two-qubit tutorial. Examples of routines are also given below.  \n",
    "\n",
    "**Task: For a fixed $\\theta$, make the circuits and computes the differen expectation values ** "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "63288326-c79b-4d9c-9e3a-b62473ee9ec2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "counts_z : {'10': 1000}\n",
      "counts_xx: {'10': 254, '11': 256, '00': 284, '01': 206}\n",
      "counts_yy: {'11': 247, '01': 259, '10': 252, '00': 242}\n",
      "\n",
      "Expectation values (from shots):\n",
      "<Z0>   = 1.0\n",
      "<Z1>   = -1.0\n",
      "<X0X1> = 0.08\n",
      "<Y0Y1> = -0.022\n"
     ]
    }
   ],
   "source": [
    "sampler = StatevectorSampler()\n",
    "Nshot = 1000\n",
    "\n",
    "# -----------------------\n",
    "# 1) Define circuits independently\n",
    "# -----------------------\n",
    "\n",
    "# Z0 and Z1 measurement (computational basis)\n",
    "qc_z = QuantumCircuit(2, 2, name=\"Measure_Z0Z1\")\n",
    "qc_z.ry(theta, 1)\n",
    "qc_z.x(0)\n",
    "qc_z.cx(1, 0)\n",
    "qc_z.measure([0, 1], [0, 1])\n",
    "\n",
    "# X0X1 measurement: rotate to X basis with H on both qubits, then measure\n",
    "qc_xx = QuantumCircuit(2, 2, name=\"Measure_XX\")\n",
    "qc_xx.ry(theta, 1)\n",
    "qc_xx.x(0)\n",
    "qc_xx.cx(1, 0)\n",
    "qc_xx.h(1)\n",
    "qc_xx.h(0)\n",
    "qc_xx.measure([0, 1], [0, 1])\n",
    "\n",
    "# Y0Y1 measurement: rotate to Y basis with Sdg then H on both qubits, then measure\n",
    "qc_yy = QuantumCircuit(2, 2, name=\"Measure_YY\")\n",
    "qc_yy.ry(theta, 1)\n",
    "qc_yy.x(0)\n",
    "qc_yy.cx(1, 0)\n",
    "qc_yy.sdg(0); qc_yy.h(0)\n",
    "qc_yy.sdg(1); qc_yy.h(1)\n",
    "qc_yy.measure([0, 1], [0, 1])\n",
    "\n",
    "# -----------------------\n",
    "# 2) Run shots and get counts\n",
    "# -----------------------\n",
    "sampler = StatevectorSampler()\n",
    "\n",
    "counts_z  = sampler.run([qc_z],  shots=Nshot).result()[0].data.c.get_counts()\n",
    "counts_xx = sampler.run([qc_xx], shots=Nshot).result()[0].data.c.get_counts()\n",
    "counts_yy = sampler.run([qc_yy], shots=Nshot).result()[0].data.c.get_counts()\n",
    "\n",
    "print(\"counts_z :\", counts_z)\n",
    "print(\"counts_xx:\", counts_xx)\n",
    "print(\"counts_yy:\", counts_yy)\n",
    "\n",
    "# -----------------------\n",
    "# 3) Convert counts -> expectation values\n",
    "# -----------------------\n",
    "def bit_to_ev(b: int) -> int:\n",
    "    # Z-eigenvalue mapping\n",
    "    return 1 if b == 0 else -1\n",
    "\n",
    "def exp_Z0(counts: dict, shots: int) -> float:\n",
    "    # Qiskit bitstrings are 'b1b0' (bit 1 left, bit 0 right)\n",
    "    return sum(bit_to_ev(int(s[1])) * c for s, c in counts.items()) / shots\n",
    "\n",
    "def exp_Z1(counts: dict, shots: int) -> float:\n",
    "    return sum(bit_to_ev(int(s[0])) * c for s, c in counts.items()) / shots\n",
    "\n",
    "def exp_two_qubit_product(counts: dict, shots: int) -> float:\n",
    "    # After basis rotations, Z-measurement corresponds to X or Y measurement.\n",
    "    # The product eigenvalue is (ev on qubit0) * (ev on qubit1).\n",
    "    total = 0.0\n",
    "    for s, c in counts.items():\n",
    "        b1 = int(s[0])\n",
    "        b0 = int(s[1])\n",
    "        total += (bit_to_ev(b0) * bit_to_ev(b1)) * c\n",
    "    return total / shots\n",
    "\n",
    "Z0 = exp_Z0(counts_z, Nshot)\n",
    "Z1 = exp_Z1(counts_z, Nshot)\n",
    "XX = exp_two_qubit_product(counts_xx, Nshot)\n",
    "YY = exp_two_qubit_product(counts_yy, Nshot)\n",
    "\n",
    "print(\"\\nExpectation values (from shots):\")\n",
    "print(\"<Z0>   =\", Z0)\n",
    "print(\"<Z1>   =\", Z1)\n",
    "print(\"<X0X1> =\", XX)\n",
    "print(\"<Y0Y1> =\", YY)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f647fec-3bbe-4311-8e78-9d8aeca8e207",
   "metadata": {},
   "source": [
    "## 3. Computing expectation values of observables for a set of angles\n",
    "\n",
    "Tips: \n",
    "\n",
    "### Making loops on $\\theta$\n",
    "\n",
    "- You should define a list of angle values and make a loop on the angles, for instance:  \n",
    " \n",
    "``` \n",
    "n_theta = 41  # number of theta points\n",
    "theta_list = np.linspace(-np.pi, np.pi, n_theta)\n",
    "```\n",
    "\n",
    "### Example of useful routines for the $\\langle Z_0 \\rangle $ expectation value\n",
    "\n",
    "- Prior to the loop, you can define a routine that builds the circuit for a given $\\theta$ value. \n",
    "An example of such a circuit to measure $Z_0$ (or $Z_1$) is \n",
    "\n",
    "```\n",
    "def circuit_z(theta: float) -> QuantumCircuit:\n",
    "    qc = QuantumCircuit(2, 2, name=\"Measure_Z0Z1\")\n",
    "    qc.ry(theta, 1)\n",
    "    qc.x(0)\n",
    "    qc.cx(1, 0)\n",
    "    qc.measure([0, 1], [0, 1])\n",
    "    return qc\n",
    "```\n",
    "\n",
    "The routine can be called in a loop on $\\theta$ value for instance using the syntax\n",
    "  \n",
    "```\n",
    "counts_z  = sampler.run([circuit_z(theta)],  shots=Nshot).result()[0].data.c.get_counts()\n",
    "```\n",
    "\n",
    "### Storing\n",
    "\n",
    "To store results as a function of $\\theta$ this could be done by defining a list: \n",
    "\n",
    "```\n",
    "Z0_list = []\n",
    "```\n",
    "\n",
    "Results could be stored in the $\\theta$ loop using \n",
    "\n",
    "```\n",
    "    Z0_list.append(exp_Z0(counts_z, Nshot))\n",
    "```\n",
    "\n",
    "with `exp_Z0` the routine to transform bits into qubits and compute expectation values (given below).  \n",
    "After the loop, you do \n",
    "```\n",
    "Z0_list = np.array(Z0_list)\n",
    "```\n",
    "that are the $\\langle Z_0 \\rangle$ results.\n",
    "\n",
    "- As an intermediate step, just do the code that shows the expectation value of $\\langle Z_0 \\rangle$ and display this expectation value as a function of $\\theta$ and display it\n",
    "\n",
    "To display the result, use matplotib standard routines. For instance, a minimal script is:\n",
    "\n",
    "```\n",
    "fig, ax = plt.subplots(figsize=(6.0, 4.0))\n",
    "ax.plot(theta_list, Z_0_list, marker = 'o', label=r\"$\\langle Z_0\\rangle$\")\n",
    "ax.legend()\n",
    "fig.tight_layout()\n",
    "plt.show()\n",
    "```\n",
    "\n",
    "- Then, do the same for $\\langle Z_1 \\rangle$, $\\langle X_0X_1\\rangle $ and $\\langle Y_0Y_1\\rangle $.\n",
    "- Note that, while for $\\langle Z_1 \\rangle$, the same circuit can be used,for $\\langle X_0X_1\\rangle $ and $\\langle Y_0Y_1 \\rangle$ additional circuit should be built with proper rotations before measurements.   \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "cbbd0d97-b74c-4fb3-9e3b-3bc89749a707",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Nshot = 1000\n",
    "n_theta = 41  # number of theta points\n",
    "theta_list = np.linspace(-np.pi, np.pi, n_theta)\n",
    "\n",
    "sampler = StatevectorSampler()\n",
    "\n",
    "# -----------------------\n",
    "# Helpers: counts -> expectation values\n",
    "# -----------------------\n",
    "def bit_to_ev(b: int) -> int:\n",
    "    # Z-eigenvalue mapping\n",
    "    return 1 if b == 0 else -1\n",
    "\n",
    "def exp_Z0(counts: dict, shots: int) -> float:\n",
    "    # Qiskit bitstrings are 'b1b0' (bit 1 left, bit 0 right)\n",
    "    return sum(bit_to_ev(int(s[1])) * c for s, c in counts.items()) / shots\n",
    "\n",
    "def exp_Z1(counts: dict, shots: int) -> float:\n",
    "    return sum(bit_to_ev(int(s[0])) * c for s, c in counts.items()) / shots\n",
    "\n",
    "def exp_two_qubit_product(counts: dict, shots: int) -> float:\n",
    "    # After basis rotations, Z-measurement corresponds to X or Y measurement.\n",
    "    total = 0.0\n",
    "    for s, c in counts.items():\n",
    "        b1 = int(s[0])\n",
    "        b0 = int(s[1])\n",
    "        total += (bit_to_ev(b0) * bit_to_ev(b1)) * c\n",
    "    return total / shots\n",
    "\n",
    "# -----------------------\n",
    "# Circuit builders (independent, no compose)\n",
    "# -----------------------\n",
    "def circuit_z(theta: float) -> QuantumCircuit:\n",
    "    qc = QuantumCircuit(2, 2, name=\"Measure_Z0Z1\")\n",
    "    qc.ry(theta, 1)\n",
    "    qc.x(0)\n",
    "    qc.cx(1, 0)\n",
    "    qc.measure([0, 1], [0, 1])\n",
    "    return qc\n",
    "\n",
    "def circuit_xx(theta: float) -> QuantumCircuit:\n",
    "    qc = QuantumCircuit(2, 2, name=\"Measure_XX\")\n",
    "    qc.ry(theta, 1)\n",
    "    qc.x(0)\n",
    "    qc.cx(1, 0)\n",
    "    qc.h(0); qc.h(1)         # X basis on both\n",
    "    qc.measure([0, 1], [0, 1])\n",
    "    return qc\n",
    "\n",
    "def circuit_yy(theta: float) -> QuantumCircuit:\n",
    "    qc = QuantumCircuit(2, 2, name=\"Measure_YY\")\n",
    "    qc.ry(theta, 1)\n",
    "    qc.x(0)\n",
    "    qc.cx(1, 0)\n",
    "    qc.sdg(0); qc.h(0)        # Y basis on qubit 0\n",
    "    qc.sdg(1); qc.h(1)        # Y basis on qubit 1\n",
    "    qc.measure([0, 1], [0, 1])\n",
    "    return qc\n",
    "\n",
    "# -----------------------\n",
    "# Loop over theta\n",
    "# -----------------------\n",
    "Z0_list, Z1_list, XX_list, YY_list = [], [], [], []\n",
    "\n",
    "for theta in theta_list:\n",
    "    counts_z  = sampler.run([circuit_z(theta)],  shots=Nshot).result()[0].data.c.get_counts()\n",
    "    counts_xx = sampler.run([circuit_xx(theta)], shots=Nshot).result()[0].data.c.get_counts()\n",
    "    counts_yy = sampler.run([circuit_yy(theta)], shots=Nshot).result()[0].data.c.get_counts()\n",
    "\n",
    "    Z0_list.append(exp_Z0(counts_z, Nshot))\n",
    "    Z1_list.append(exp_Z1(counts_z, Nshot))\n",
    "    XX_list.append(exp_two_qubit_product(counts_xx, Nshot))\n",
    "    YY_list.append(exp_two_qubit_product(counts_yy, Nshot))\n",
    "\n",
    "Z0_list = np.array(Z0_list)\n",
    "Z1_list = np.array(Z1_list)\n",
    "XX_list = np.array(XX_list)\n",
    "YY_list = np.array(YY_list)\n",
    "\n",
    "# -----------------------\n",
    "# APS-like plotting style (no manual colors)\n",
    "# -----------------------\n",
    "plt.rcParams.update({\n",
    "    \"font.family\": \"serif\",\n",
    "    \"font.size\": 12,\n",
    "    \"mathtext.fontset\": \"stix\",\n",
    "    \"axes.linewidth\": 1.0,\n",
    "    \"xtick.direction\": \"in\",\n",
    "    \"ytick.direction\": \"in\",\n",
    "    \"xtick.minor.visible\": True,\n",
    "    \"ytick.minor.visible\": True,\n",
    "    \"xtick.top\": True,\n",
    "    \"ytick.right\": True,\n",
    "    \"legend.frameon\": False,\n",
    "})\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(6.0, 4.0))\n",
    "ax.plot(theta_list, Z0_list, marker ='o',label=r\"$\\langle Z_0\\rangle$\")\n",
    "ax.plot(theta_list, Z1_list, marker ='x',label=r\"$\\langle Z_1\\rangle$\")\n",
    "ax.plot(theta_list, XX_list, marker ='d',label=r\"$\\langle X_0X_1\\rangle$\")\n",
    "ax.plot(theta_list, YY_list, marker ='o',label=r\"$\\langle Y_0Y_1\\rangle$\")\n",
    "\n",
    "ax.set_xlabel(r\"$\\theta$\")\n",
    "ax.set_ylabel(\"Expectation value\")\n",
    "ax.set_xlim(-np.pi, np.pi)\n",
    "ax.set_ylim(-1.05, 1.05)\n",
    "\n",
    "# Nice tick labels at -pi, 0, +pi\n",
    "ax.set_xticks([-np.pi, 0, np.pi])\n",
    "ax.set_xticklabels([r\"$-\\pi$\", r\"$0$\", r\"$\\pi$\"])\n",
    "\n",
    "ax.legend()\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "970f568b-3ee4-417a-b34d-115b78f04765",
   "metadata": {},
   "source": [
    "## 4. Expectation value of $H_2$ from measurements as a function of $\\theta$\n",
    "\n",
    "From the different expectation values above, compute the expectation value of $\\langle H_2 \\rangle$ \n",
    "as a list and display the result as a function of $\\theta$.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "e1fe9799-f4b7-4102-a9ea-b71d8f609454",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# --- Compute <H2>(theta) from the measured expectations ---\n",
    "c0 = 5.906709\n",
    "cZ0 = 0.218291\n",
    "cZ1 = -6.125\n",
    "cXX_YY = -2.143304\n",
    "\n",
    "H2_list = c0 + cZ0*Z0_list + cZ1*Z1_list + cXX_YY*(XX_list + YY_list)\n",
    "\n",
    "# --- Plot <H2> vs theta (APS-like style, same rcParams as before) ---\n",
    "fig, ax = plt.subplots(figsize=(6.0, 4.0))\n",
    "ax.plot(theta_list, H2_list, marker = 'o', label=r\"$\\langle H_2\\rangle$\")\n",
    "\n",
    "ax.set_xlabel(r\"$\\theta$\")\n",
    "ax.set_ylabel(r\"$\\langle H_2\\rangle$\")\n",
    "ax.set_xlim(-np.pi, np.pi)\n",
    "\n",
    "# Tick labels at -pi, 0, +pi\n",
    "ax.set_xticks([-np.pi, 0, np.pi])\n",
    "ax.set_xticklabels([r\"$-\\pi$\", r\"$0$\", r\"$\\pi$\"])\n",
    "\n",
    "ax.legend()\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "73c1c50a-56b6-4cf1-8a8f-e817f0d02529",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
