{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "76613054",
   "metadata": {},
   "source": [
    "# 02 - Bell States\n",
    "\n",
    "Create all four Bell states — the simplest examples of quantum entanglement.\n",
    "\n",
    "**Concepts:** Entanglement, CNOT, Hadamard, Bell states"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a1644f41",
   "metadata": {},
   "outputs": [],
   "source": [
    "import quantsdk as qs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6267ce48",
   "metadata": {},
   "source": [
    "## Bell State |Phi+>\n",
    "\n",
    "$$|\\Phi^+\\rangle = \\frac{1}{\\sqrt{2}}(|00\\rangle + |11\\rangle)$$\n",
    "\n",
    "Two gates: Hadamard + CNOT."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d11b44f3",
   "metadata": {},
   "outputs": [],
   "source": [
    "phi_plus = qs.Circuit(2, name=\"Phi+\").h(0).cx(0, 1).measure_all()\n",
    "\n",
    "result = qs.run(phi_plus, shots=2000, seed=42)\n",
    "print(f\"|Phi+> counts: {result.counts}\")\n",
    "print(f\"Probabilities: {result.probabilities}\")\n",
    "print(\"\\nNotice: only |00> and |11> — qubits are perfectly correlated!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4212fb9",
   "metadata": {},
   "source": [
    "## All Four Bell States"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5ac8a398",
   "metadata": {},
   "outputs": [],
   "source": [
    "# |Phi+> = (|00> + |11>) / sqrt(2)\n",
    "phi_plus = qs.Circuit(2, name=\"Phi+\").h(0).cx(0, 1).measure_all()\n",
    "\n",
    "# |Phi-> = (|00> - |11>) / sqrt(2)\n",
    "phi_minus = qs.Circuit(2, name=\"Phi-\").h(0).z(0).cx(0, 1).measure_all()\n",
    "\n",
    "# |Psi+> = (|01> + |10>) / sqrt(2)\n",
    "psi_plus = qs.Circuit(2, name=\"Psi+\").h(0).x(1).cx(0, 1).measure_all()\n",
    "\n",
    "# |Psi-> = (|01> - |10>) / sqrt(2)\n",
    "psi_minus = qs.Circuit(2, name=\"Psi-\").h(0).z(0).x(1).cx(0, 1).measure_all()\n",
    "\n",
    "bell_states = {\n",
    "    \"|Phi+>\": phi_plus,\n",
    "    \"|Phi->\": phi_minus,\n",
    "    \"|Psi+>\": psi_plus,\n",
    "    \"|Psi->\": psi_minus,\n",
    "}\n",
    "\n",
    "for name, circuit in bell_states.items():\n",
    "    result = qs.run(circuit, shots=2000, seed=42)\n",
    "    print(f\"{name}: {result.counts}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11864911",
   "metadata": {},
   "source": [
    "## Circuit Details"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8e38b985",
   "metadata": {},
   "outputs": [],
   "source": [
    "circuit = qs.Circuit(2, name=\"Bell\").h(0).cx(0, 1).measure_all()\n",
    "\n",
    "print(f\"Depth: {circuit.depth}\")\n",
    "print(f\"Gate count: {circuit.gate_count}\")\n",
    "print(f\"Operations: {circuit.count_ops()}\")\n",
    "print(f\"\\nCircuit drawing:\")\n",
    "print(circuit.draw())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d9a0c779",
   "metadata": {},
   "source": [
    "## Statistical Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4c467017",
   "metadata": {},
   "outputs": [],
   "source": [
    "result = qs.run(phi_plus, shots=10000, seed=123)\n",
    "\n",
    "print(f\"Top results: {result.top_k(2)}\")\n",
    "print(f\"\\nSummary:\\n{result.summary()}\")"
   ]
  }
 ],
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