{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "fd407eed",
   "metadata": {},
   "source": [
    "# 03 - GHZ State\n",
    "\n",
    "Create a Greenberger-Horne-Zeilinger (GHZ) state — multi-qubit entanglement.\n",
    "\n",
    "$$|GHZ\\rangle = \\frac{1}{\\sqrt{2}}(|000\\rangle + |111\\rangle)$$\n",
    "\n",
    "**Concepts:** Multi-qubit entanglement, scaling, circuit depth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "868f8761",
   "metadata": {},
   "outputs": [],
   "source": [
    "import quantsdk as qs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "995bc7ad",
   "metadata": {},
   "source": [
    "## 3-Qubit GHZ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fa05b2ee",
   "metadata": {},
   "outputs": [],
   "source": [
    "ghz3 = qs.Circuit(3, name=\"GHZ-3\")\n",
    "ghz3.h(0).cx(0, 1).cx(0, 2).measure_all()\n",
    "\n",
    "result = qs.run(ghz3, shots=2000, seed=42)\n",
    "print(f\"3-qubit GHZ: {result.counts}\")\n",
    "print(f\"Only |000> and |111> — all qubits entangled!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b1ab380",
   "metadata": {},
   "source": [
    "## Scaling GHZ to N Qubits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a4f1e9d5",
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_ghz(n: int) -> qs.Circuit:\n",
    "    \"\"\"Create an n-qubit GHZ state.\"\"\"\n",
    "    circuit = qs.Circuit(n, name=f\"GHZ-{n}\")\n",
    "    circuit.h(0)\n",
    "    for i in range(1, n):\n",
    "        circuit.cx(0, i)\n",
    "    circuit.measure_all()\n",
    "    return circuit\n",
    "\n",
    "for n in [3, 5, 8, 10]:\n",
    "    circuit = make_ghz(n)\n",
    "    result = qs.run(circuit, shots=1000, seed=42)\n",
    "    all_zeros = '0' * n\n",
    "    all_ones = '1' * n\n",
    "    p0 = result.counts.get(all_zeros, 0) / 1000\n",
    "    p1 = result.counts.get(all_ones, 0) / 1000\n",
    "    print(f\"GHZ-{n:2d}: P({all_zeros})={p0:.3f}, P({all_ones})={p1:.3f}, depth={circuit.depth}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7bc281f",
   "metadata": {},
   "source": [
    "## W State (Alternative Entanglement)\n",
    "\n",
    "The W state distributes entanglement differently:\n",
    "\n",
    "$$|W\\rangle = \\frac{1}{\\sqrt{3}}(|001\\rangle + |010\\rangle + |100\\rangle)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4228d23f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "\n",
    "# Approximate 3-qubit W state\n",
    "w_state = qs.Circuit(3, name=\"W-state\")\n",
    "w_state.ry(0, 2 * math.acos(math.sqrt(1/3)))  # P(|1>) = 1/3\n",
    "w_state.ch(0, 1)                                # Controlled-H\n",
    "w_state.cx(1, 2)                                # Spread entanglement\n",
    "w_state.cx(0, 1)                                # Correct state\n",
    "w_state.x(0)                                    # Flip q0\n",
    "w_state.measure_all()\n",
    "\n",
    "result = qs.run(w_state, shots=3000, seed=42)\n",
    "print(f\"W state: {result.counts}\")\n",
    "print(f\"Probabilities: {result.probabilities}\")"
   ]
  }
 ],
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