```json
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Quantum Music Synthesizer\n",
    "\n",
    "This notebook demonstrates how to create music using quantum computing principles with the QuantumToolbox.jl library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Install required packages\n",
    "using Pkg\n",
    "Pkg.add(\"QuantumToolbox\")\n",
    "Pkg.add(\"Plots\")\n",
    "Pkg.add(\"AudioTracks\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import libraries\n",
    "using QuantumToolbox\n",
    "using Plots\n",
    "using AudioTracks\n",
    "using LinearAlgebra"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define quantum music parameters\n",
    "n_qubits = 4\n",
    "n_shots = 1024\n",
    "fidelity_threshold = 0.995\n",
    "\n",
    "# Create a quantum circuit for music generation\n",
    "function create_music_circuit(n_qubits)\n",
    "    qc = qubit_states(n_qubits)\n",
    "    \n",
    "    # Apply superposition to all qubits\n",
    "    for i in 1:n_qubits\n",
    "        qc = hadamard(qc, i)\n",
    "    end\n",
    "    \n",
    "    # Create entanglement between qubits\n",
    "    for i in 1:(n_qubits-1)\n",
    "        qc = cnot(qc, i, i+1)\n",
    "    end\n",
    "    \n",
    "    return qc\n",
    "end\n",
    "\n",
    "# Generate quantum circuit\n",
    "circuit = create_music_circuit(n_qubits)\n",
    "println(\"Quantum circuit created with $n_qubits qubits\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Simulate quantum measurements\n",
    "function simulate_quantum_music(circuit, n_shots)\n",
    "    # Measure the circuit multiple times\n",
    "    measurements = []\n",
    "    for i in 1:n_shots\n",
    "        result = measure(circuit)\n",
    "        push!(measurements, result)\n",
    "    end\n",
    "    return measurements\n",
    "end\n",
    "\n",
    "# Run simulation\n",
    "measurements = simulate_quantum_music(circuit, n_shots)\n",
    "println(\"Simulated $(length(measurements)) quantum measurements\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Convert quantum measurements to musical notes\n",
    "function quantum_to_notes(measurements)\n",
    "    # Base frequencies for C major scale (in Hz)\n",
    "    base_frequencies = [261.63, 293.66, 329.63, 349.23, 392.00, 440.00, 493.88, 523.25] # C4 to C5\n",
    "    \n",
    "    notes = []\n",
    "    for measurement in measurements\n",
    "        # Convert binary measurement to decimal index\n",
    "        index = parse(Int, join(string.(measurement)), base=2) % length(base_frequencies) + 1\n",
    "        push!(notes, base_frequencies[index])\n",
    "    end\n",
    "    \n",
    "    return notes\n",
    "end\n",
    "\n",
    "# Convert measurements to notes\n",
    "notes = quantum_to_notes(measurements)\n",
    "println(\"Converted to $(length(notes)) musical notes\")\n",
    "println(\"First 10 notes: $(notes[1:10])\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create audio from notes\n",
    "function create_audio_from_notes(notes, duration=0.5)\n",
    "    # Create a simple sine wave for each note\n",
    "    sample_rate = 44100\n",
    "    audio = []\n",
    "    \n",
    "    for note in notes[1:50] # Limit to first 50 notes for demonstration\n",
    "        t = 0:1/sample_rate:duration\n",
    "        wave = sin.(2π * note * t)\n",
    "        append!(audio, wave)\n",
    "    end\n",
    "    \n",
    "    return audio, sample_rate\n",
    "end\n",
    "\n",
    "# Generate audio\n",
    "audio_data, sample_rate = create_audio_from_notes(notes)\n",
    "println(\"Generated audio with $(length(audio_data)) samples at $(sample_rate)Hz sample rate\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Visualize quantum state probabilities\n",
    "function plot_quantum_probabilities(circuit, n_qubits)\n",
    "    # Calculate probabilities for all possible states\n",
    "    states = [bitstring(i, n_qubits) for i in 0:(2^n_qubits-1)]\n",
    "    probabilities = [abs(amplitude(circuit, parse.(Int, split(state, \"\"))))^2 for state in states]\n",
    "    \n",
    "    # Create bar chart\n",
    "    bar(\n",
    "        0:(2^n_qubits-1),\n",
    "        probabilities,\n",
    "        xlabel=\"Quantum States\",\n",
    "        ylabel=\"Probability\",\n",
    "        title=\"Quantum State Probabilities\",\n",
    "        legend=false,\n",
    "        color=:purple\n",
    "    )\n",
    "end\n",
    "\n",
    "# Plot probabilities\n",
    "plot_quantum_probabilities(circuit, n_qubits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Analyze quantum circuit fidelity\n",
    "function analyze_fidelity(measurements)\n",
    "    # Calculate the distribution of measurements\n",
    "    counts = Dict{String, Int}()\n",
    "    for measurement in measurements\n",
    "        key = join(string.(measurement))\n",
    "        counts[key] = get(counts, key, 0) + 1\n",
    "    end\n",
    "    \n",
    "    # Calculate expected uniform distribution\n",
    "    n_states = length(unique([join(string.(m)) for m in measurements]))\n",
    "    expected_prob = 1.0 / n_states\n",
    "    \n",
    "    # Calculate fidelity\n",
    "    fidelity = 0.0\n",
    "    for (state, count) in counts\n",
    "        observed_prob = count / length(measurements)\n",
    "        fidelity += sqrt(observed_prob * expected_prob)\n",
    "    end\n",
    "    fidelity = fidelity^2\n",
    "    \n",
    "    return fidelity, counts\n",
    "end\n",
    "\n",
    "# Analyze results\n",
    "fidelity, state_counts = analyze_fidelity(measurements)\n",
    "println(\"Quantum circuit fidelity: $(round(fidelity, digits=4))\")\n",
    "println(\"Fidelity meets threshold: $(fidelity >= fidelity_threshold)\")\n",
    "println(\"\\nState distribution:\")\n",
    "for (state, count) in sort(collect(state_counts))\n",
    "    println(\"  $state: $count\")\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "This notebook demonstrated:\n",
    "1. Creating a quantum circuit for music generation\n",
    "2. Simulating quantum measurements\n",
    "3. Converting quantum states to musical notes\n",
    "4. Generating audio from quantum measurements\n",
    "5. Visualizing quantum state probabilities\n",
    "6. Analyzing quantum circuit fidelity\n",
    "\n",
    "The quantum music synthesizer leverages quantum superposition and entanglement to create unique musical compositions that would be impossible with classical methods alone."
   ]
  }
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```