quantum.js

class QuantumSystem {
  constructor() {
    this.state = {
      superposition: {
        active: false,
        states: new Array(8).fill(0).map(() => Math.random())
      },
      gates: {
        hadamard: false,
        phase: 0
      },
      search: {
        iterations: 0,
        target: Math.floor(Math.random() * 100),
        probability: 0
      },
      walk: {
        active: false,
        position: 0,
        history: []
      }
    };
    
    this.metrics = {
      coherence: 1.0,
      entanglement: 0.0,
      efficiency: 0.0
    };
  }

  // Superposition methods
  toggleSuperposition() {
    this.state.superposition.active = !this.state.superposition.active;
    if (this.state.superposition.active) {
      this.state.superposition.states = this.state.superposition.states.map(
        () => Math.random() * Math.exp(2 * Math.PI * Math.random())
      );
    }
    this.updateMetrics();
    return this.state.superposition;
  }

  // Gate operations
  applyHadamard() {
    this.state.gates.hadamard = !this.state.gates.hadamard;
    if (this.state.gates.hadamard) {
      this.state.superposition.states = this.state.superposition.states.map(x => 
        (x + (x * -1)) / Math.sqrt(2)
      );
    }
    this.updateMetrics();
    return this.state.gates;
  }

  applyPhaseGate() {
    this.state.gates.phase += Math.PI / 4;
    // Using proper complex number math with real and imaginary parts
    this.state.superposition.states = this.state.superposition.states.map(x => {
      const phase = this.state.gates.phase;
      // Multiply by e^(iφ) = cos(φ) + i*sin(φ)
      return x * Math.cos(phase); // Simplified for visualization - only showing real part
    });
    this.updateMetrics();
    return this.state.gates;
  }

  // Grover's search simulation
  runGroverSearch() {
    const N = 100;
    const iterations = Math.floor(Math.PI/4 * Math.sqrt(N));
    
    this.state.search.iterations++;
    this.state.search.probability = Math.pow(
      Math.sin((2 * this.state.search.iterations + 1) * Math.asin(1/Math.sqrt(N))),
      2
    );
    
    this.updateMetrics();
    return this.state.search;
  }

  // Quantum walk simulation
  startQuantumWalk() {
    if (this.state.walk.active) return;
    
    this.state.walk.active = true;
    this.state.walk.interval = setInterval(() => {
      // Quantum walk uses superposition of left and right steps
      const step = (Math.random() - 0.5) * 2 * Math.sqrt(2);
      this.state.walk.position += step;
      this.state.walk.history.push(this.state.walk.position);
      this.updateMetrics();
      // Trigger visualization update
      if (typeof updateVisualizations === 'function') {
        updateVisualizations();
      }
    }, 100);
    
    return this.state.walk;
  }

  stopQuantumWalk() {
    this.state.walk.active = false;
    if (this.state.walk.interval) {
      clearInterval(this.state.walk.interval);
    }
    return this.state.walk;
  }

  // Metrics calculation
  updateMetrics() {
    // Coherence decays with operations
    this.metrics.coherence = Math.exp(-0.1 * this.state.search.iterations);
    
    // Entanglement increases with superposition and operations
    if (this.state.superposition.active) {
      this.metrics.entanglement = Math.min(
        1, 
        this.metrics.entanglement + 0.1
      );
    } else {
      this.metrics.entanglement *= 0.9; // Decay when not in superposition
    }
    
    // Efficiency based on search progress and walk stability
    const searchEfficiency = 1 - 1/(1 + this.state.search.iterations);
    const walkEfficiency = this.state.walk.active ? 
      Math.exp(-Math.abs(this.state.walk.position) / 10) : 1;
    this.metrics.efficiency = (searchEfficiency + walkEfficiency) / 2;
  }

  getState() {
    return {
      state: this.state,
      metrics: this.metrics
    };
  }
}

// Initialize quantum system
const quantumSystem = new QuantumSystem();

// UI Event handlers
function toggleSuperposition() {
  quantumSystem.toggleSuperposition();
  updateVisualizations();
}

function applyHadamard() {
  quantumSystem.applyHadamard();
  updateVisualizations();
}

function applyPhaseGate() {
  quantumSystem.applyPhaseGate();
  updateVisualizations(); 
}

function runGroverSearch() {
  quantumSystem.runGroverSearch();
  updateVisualizations();
}

function startQuantumWalk() {
  quantumSystem.startQuantumWalk();
}

function stopQuantumWalk() {
  quantumSystem.stopQuantumWalk();
}