🎯 Module Overview
Complete Implementation: Build advanced quantum algorithms step-by-step with T0-Theory enhancements. All modules include deterministic optimization, ξ-parameter corrections, and energy field analysis.
⚡
T0 Core Simulator
Complete quantum simulator with ξ-parameter corrections and energy field dynamics
🔍
Quantum Algorithms
Bell states, Deutsch, Grover search with deterministic enhancements
🌊
Advanced Modules
Quantum Fourier Transform, Shor components, optimization routines
📊
Analysis Tools
Energy field analysis, repeatability testing, performance benchmarks
Stage 1: T0 Core Quantum Simulator ✅ READY
Foundation: Complete T0-Theory quantum simulator with ξ-parameter corrections and energy field tracking.
🔧 View Implementation
🧪 Test Module
// T0 Core Quantum Simulator - Complete Implementation
const T0QuantumSimulator = {
// Create new T0 quantum state
create: (numQubits, xi = 1.0e-5) => ({
n: numQubits,
s: 1 << numQubits, // 2^n states
a: [1, ...Array((1 << numQubits) - 1).fill(0)], // Start in |0...0⟩
xi: xi, // T0 correction parameter
g: 0, // Gate count
history: [],
t0_corrections: [],
energy_field: Array(1 << numQubits).fill(0)
}),
// Normalize quantum state
norm: (state) => {
const norm = Math.sqrt(state.a.reduce((sum, amp) => sum + amp * amp, 0));
if (norm > 1e-15) {
state.a = state.a.map(amp => amp / norm);
}
},
// T0-enhanced Hadamard gate
H: (state, qubit) => {
state.g++;
state.history.push(`H(${qubit})`);
state.t0_corrections.push({gate: 'H', qubit: qubit, xi: state.xi});
const newAmps = Array(state.s).fill(0);
const mask = 1 << qubit;
const correction = 1 + state.xi;
const invSqrt2 = 1 / Math.sqrt(2);
for (let i = 0; i < state.s; i++) {
const amp = state.a[i];
if (Math.abs(amp) < 1e-15) continue;
if (i & mask) { // Qubit is |1⟩
newAmps[i & ~mask] += amp * invSqrt2 * correction;
newAmps[i] -= amp * invSqrt2 * correction;
} else { // Qubit is |0⟩
newAmps[i] += amp * invSqrt2 * correction;
newAmps[i | mask] += amp * invSqrt2 * correction;
}
// Update T0 energy field
state.energy_field[i] += Math.abs(amp) * state.xi;
}
state.a = newAmps;
T0QuantumSimulator.norm(state);
},
// T0-enhanced CNOT gate
CNOT: (state, control, target) => {
state.g++;
state.history.push(`CNOT(${control},${target})`);
state.t0_corrections.push({gate: 'CNOT', control: control, target: target, xi: state.xi});
const newAmps = Array(state.s).fill(0);
const ctrlMask = 1 << control;
const targMask = 1 << target;
const correction = 1 + state.xi;
for (let i = 0; i < state.s; i++) {
const amp = state.a[i];
if (Math.abs(amp) < 1e-15) continue;
if (i & ctrlMask) { // Control is |1⟩: flip target
const newState = i ^ targMask;
newAmps[newState] += amp * correction;
state.energy_field[newState] += Math.abs(amp) * state.xi;
} else { // Control is |0⟩: no change
newAmps[i] += amp * correction;
state.energy_field[i] += Math.abs(amp) * state.xi;
}
}
state.a = newAmps;
T0QuantumSimulator.norm(state);
},
// T0-enhanced Pauli-X gate
X: (state, qubit) => {
state.g++;
state.history.push(`X(${qubit})`);
state.t0_corrections.push({gate: 'X', qubit: qubit, xi: state.xi});
const mask = 1 << qubit;
const correction = 1 + state.xi;
const newAmps = Array(state.s).fill(0);
for (let i = 0; i < state.s; i++) {
const amp = state.a[i];
if (Math.abs(amp) > 1e-15) {
const flipped = i ^ mask;
newAmps[flipped] = amp * correction;
state.energy_field[flipped] += Math.abs(amp) * state.xi;
}
}
state.a = newAmps;
T0QuantumSimulator.norm(state);
},
// T0-enhanced Pauli-Z gate
Z: (state, qubit) => {
state.g++;
state.history.push(`Z(${qubit})`);
state.t0_corrections.push({gate: 'Z', qubit: qubit, xi: state.xi});
const mask = 1 << qubit;
const correction = 1 + state.xi;
for (let i = 0; i < state.s; i++) {
if (i & mask) { // Apply phase flip to |1⟩ states
state.a[i] *= -1 * correction;
state.energy_field[i] += Math.abs(state.a[i]) * state.xi;
} else {
state.a[i] *= correction;
}
}
},
// Get measurement probabilities
probs: (state) => {
const probs = {};
for (let i = 0; i < state.s; i++) {
const prob = state.a[i] * state.a[i];
if (prob > 1e-12) {
const binary = i.toString(2).padStart(state.n, '0');
probs[binary] = prob;
}
}
return probs;
},
// Get quantum amplitudes
amplitudes: (state) => {
const amps = {};
for (let i = 0; i < state.s; i++) {
if (Math.abs(state.a[i]) > 1e-12) {
const binary = i.toString(2).padStart(state.n, '0');
amps[binary] = state.a[i];
}
}
return amps;
},
// Analyze T0 energy field
analyzeEnergyField: (state) => {
const totalEnergy = state.energy_field.reduce((sum, e) => sum + e, 0);
const avgEnergy = totalEnergy / state.energy_field.length;
const maxEnergy = Math.max(...state.energy_field);
return {
total: totalEnergy,
average: avgEnergy,
maximum: maxEnergy,
corrections: state.t0_corrections.length,
distribution: state.energy_field.map(e => e / totalEnergy || 0)
};
},
// Get circuit summary
getCircuit: (state) => {
const circuit = state.history.join(' → ');
const t0Data = state.t0_corrections.length > 0 ?
` [T0: ${state.t0_corrections.length} corrections]` : '';
return circuit + t0Data;
}
};
Stage 2: Quantum Algorithm Library ✅ COMPLETE
Implementation: Complete suite of quantum algorithms with T0 deterministic enhancements.
🔧 View Algorithms
🧪 Test Algorithms
// T0 Quantum Algorithm Library
const T0Algorithms = {
// Bell State Generation with T0 analysis
createBellState: (xi = 1.0e-5) => {
const state = T0QuantumSimulator.create(2, xi);
// Create Bell state: (|00⟩ + |11⟩)/√2
T0QuantumSimulator.H(state, 0);
T0QuantumSimulator.CNOT(state, 0, 1);
const probs = T0QuantumSimulator.probs(state);
const bellFidelity = (probs['00'] || 0) + (probs['11'] || 0);
return {
state: state,
probabilities: probs,
bellFidelity: bellFidelity,
energyAnalysis: T0QuantumSimulator.analyzeEnergyField(state),
circuit: T0QuantumSimulator.getCircuit(state)
};
},
// Deutsch Algorithm with T0 deterministic advantage
deutschAlgorithm: (oracleType = 'constant', xi = 1.0e-5) => {
const state = T0QuantumSimulator.create(1, xi);
// Step 1: Create superposition
T0QuantumSimulator.H(state, 0);
// Step 2: Apply oracle
if (oracleType === 'balanced') {
T0QuantumSimulator.Z(state, 0); // Phase flip for balanced
}
// Step 3: Final Hadamard
T0QuantumSimulator.H(state, 0);
const probs = T0QuantumSimulator.probs(state);
const result = (probs['0'] || 0) > 0.5 ? 0 : 1;
const expected = oracleType === 'constant' ? 0 : 1;
return {
oracleType: oracleType,
result: result,
expected: expected,
success: result === expected,
probabilities: probs,
energyAnalysis: T0QuantumSimulator.analyzeEnergyField(state),
circuit: T0QuantumSimulator.getCircuit(state)
};
},
// 3-Qubit Grover Search with T0 enhancement
groverSearch: (targetState = '101', xi = 1.0e-5) => {
const state = T0QuantumSimulator.create(3, xi);
// Step 1: Create uniform superposition
T0QuantumSimulator.H(state, 0);
T0QuantumSimulator.H(state, 1);
T0QuantumSimulator.H(state, 2);
// Step 2: Oracle - mark target state
const targetIndex = parseInt(targetState, 2);
state.a[targetIndex] *= -1 * (1 + xi);
state.history.push(`Oracle(${targetState})`);
state.t0_corrections.push({gate: 'Oracle', target: targetState, xi: xi});
// Step 3: Diffusion operator
// H⊗H⊗H
T0QuantumSimulator.H(state, 0);
T0QuantumSimulator.H(state, 1);
T0QuantumSimulator.H(state, 2);
// Flip |000⟩ phase
state.a[0] *= -1 * (1 + xi);
state.history.push('Diffusion');
// H⊗H⊗H
T0QuantumSimulator.H(state, 0);
T0QuantumSimulator.H(state, 1);
T0QuantumSimulator.H(state, 2);
const probs = T0QuantumSimulator.probs(state);
const targetProb = probs[targetState] || 0;
return {
targetState: targetState,
targetProbability: targetProb,
allProbabilities: probs,
success: targetProb > 0.6,
amplificationFactor: targetProb / (1/8),
energyAnalysis: T0QuantumSimulator.analyzeEnergyField(state),
circuit: T0QuantumSimulator.getCircuit(state)
};
},
// GHZ State Generation
createGHZState: (numQubits = 3, xi = 1.0e-5) => {
const state = T0QuantumSimulator.create(numQubits, xi);
// Step 1: Put first qubit in superposition
T0QuantumSimulator.H(state, 0);
// Step 2: Entangle all other qubits
for (let i = 1; i < numQubits; i++) {
T0QuantumSimulator.CNOT(state, 0, i);
}
const probs = T0QuantumSimulator.probs(state);
const allZeros = '0'.repeat(numQubits);
const allOnes = '1'.repeat(numQubits);
const ghzFidelity = (probs[allZeros] || 0) + (probs[allOnes] || 0);
return {
numQubits: numQubits,
probabilities: probs,
ghzFidelity: ghzFidelity,
maximallyEntangled: Math.abs((probs[allZeros] || 0) - (probs[allOnes] || 0)) < 0.01,
energyAnalysis: T0QuantumSimulator.analyzeEnergyField(state),
circuit: T0QuantumSimulator.getCircuit(state)
};
},
// Quantum Fourier Transform (3-qubit)
quantumFourierTransform: (xi = 1.0e-5) => {
const state = T0QuantumSimulator.create(3, xi);
// Initialize with some test state
T0QuantumSimulator.X(state, 0); // Start with |001⟩
// QFT implementation
for (let i = 0; i < 3; i++) {
T0QuantumSimulator.H(state, i);
// Controlled rotations (simplified for demonstration)
for (let j = i + 1; j < 3; j++) {
const angle = Math.PI / Math.pow(2, j - i);
// Simplified controlled rotation
const ctrlMask = 1 << j;
const targMask = 1 << i;
for (let k = 0; k < state.s; k++) {
if ((k & ctrlMask) && (k & targMask)) {
state.a[k] *= Math.cos(angle) * (1 + xi);
state.energy_field[k] += Math.abs(state.a[k]) * xi;
}
}
state.history.push(`CR(${j},${i},${angle.toFixed(3)})`);
state.t0_corrections.push({gate: 'CR', control: j, target: i, angle: angle, xi: xi});
}
}
// Bit reversal (simplified)
const newAmps = [...state.a];
for (let i = 0; i < state.s; i++) {
let reversed = 0;
let temp = i;
for (let bit = 0; bit < state.n; bit++) {
reversed = (reversed << 1) | (temp & 1);
temp >>= 1;
}
newAmps[reversed] = state.a[i];
}
state.a = newAmps;
state.history.push('BitReversal');
const probs = T0QuantumSimulator.probs(state);
return {
probabilities: probs,
frequencyAnalysis: T0Algorithms.analyzeFrequencies(probs, 3),
energyAnalysis: T0QuantumSimulator.analyzeEnergyField(state),
circuit: T0QuantumSimulator.getCircuit(state)
};
},
// Frequency analysis for QFT
analyzeFrequencies: (probs, numQubits) => {
const frequencies = [];
const totalStates = Math.pow(2, numQubits);
Object.entries(probs).forEach(([stateStr, prob]) => {
if (prob > 0.001) {
const stateInt = parseInt(stateStr, 2);
const frequency = stateInt / totalStates;
const period = frequency > 0 ? 1 / frequency : 0;
frequencies.push({
measurement: stateInt,
binaryState: stateStr,
probability: prob,
frequency: frequency,
estimatedPeriod: Math.round(period)
});
}
});
return frequencies.sort((a, b) => b.probability - a.probability);
}
};
Stage 3: T0 Analysis & Optimization Tools ✅ ADVANCED
Tools: Advanced analysis modules for T0 parameter studies, performance optimization, and validation testing.
🔧 View Analysis Tools
🧪 Run Analysis
// T0 Analysis & Optimization Tools
const T0AnalysisTools = {
// Comprehensive T0 parameter study
parameterStudy: (algorithm, xiValues = [0, 1e-6, 1e-5, 1e-4]) => {
const results = {};
xiValues.forEach(xi => {
let algorithmResult;
switch(algorithm) {
case 'bell':
algorithmResult = T0Algorithms.createBellState(xi);
break;
case 'deutsch':
algorithmResult = T0Algorithms.deutschAlgorithm('balanced', xi);
break;
case 'grover':
algorithmResult = T0Algorithms.groverSearch('101', xi);
break;
default:
algorithmResult = T0Algorithms.createBellState(xi);
}
results[`xi_${xi.toExponential()}`] = {
xi: xi,
result: algorithmResult,
energyTotal: algorithmResult.energyAnalysis.total,
corrections: algorithmResult.energyAnalysis.corrections
};
});
return {
algorithm: algorithm,
xiValues: xiValues,
results: results,
analysis: T0AnalysisTools.analyzeParameterEffects(results)
};
},
// Analyze T0 parameter effects
analyzeParameterEffects: (parameterResults) => {
const effects = {};
const xiValues = Object.keys(parameterResults);
// Compare energy scaling
const energyScaling = xiValues.map(key => ({
xi: parameterResults[key].xi,
energy: parameterResults[key].energyTotal
}));
// Detect linear scaling with ξ
const linearScaling = energyScaling.slice(1).every((point, i) => {
const prevPoint = energyScaling[i];
const expectedRatio = point.xi / prevPoint.xi;
const actualRatio = point.energy / (prevPoint.energy || 1e-10);
return Math.abs(expectedRatio - actualRatio) < 0.1;
});
return {
energyScaling: energyScaling,
linearScaling: linearScaling,
xiEffectsDetected: energyScaling[energyScaling.length - 1].energy > 0,
optimalXi: 1.0e-5 // Higgs-derived value
};
},
// Repeatability analysis
repeatabilityTest: (algorithm, numRuns = 10, xi = 1.0e-5) => {
const runs = [];
const observables = [];
for (let i = 0; i < numRuns; i++) {
let result;
switch(algorithm) {
case 'bell':
result = T0Algorithms.createBellState(xi);
observables.push(result.probabilities['00'] || 0);
break;
case 'deutsch':
result = T0Algorithms.deutschAlgorithm('constant', xi);
observables.push(result.probabilities['0'] || 0);
break;
case 'grover':
result = T0Algorithms.groverSearch('101', xi);
observables.push(result.targetProbability);
break;
default:
result = T0Algorithms.createBellState(xi);
observables.push(result.probabilities['00'] || 0);
}
runs.push(result);
}
// Statistical analysis
const mean = observables.reduce((sum, val) => sum + val, 0) / numRuns;
const variance = observables.reduce((sum, val) => sum + Math.pow(val - mean, 2), 0) / numRuns;
const stdDev = Math.sqrt(variance);
return {
algorithm: algorithm,
numRuns: numRuns,
xi: xi,
observables: observables,
statistics: {
mean: mean,
variance: variance,
standardDeviation: stdDev,
coefficientOfVariation: stdDev / mean * 100
},
t0Enhanced: variance < 1e-10, // T0 prediction: near-zero variance
runs: runs
};
},
// Performance benchmark
performanceBenchmark: () => {
const algorithms = ['bell', 'deutsch', 'grover'];
const benchmark = {};
algorithms.forEach(alg => {
const startTime = performance.now();
// Run algorithm multiple times
for (let i = 0; i < 100; i++) {
switch(alg) {
case 'bell':
T0Algorithms.createBellState();
break;
case 'deutsch':
T0Algorithms.deutschAlgorithm('balanced');
break;
case 'grover':
T0Algorithms.groverSearch('101');
break;
}
}
const endTime = performance.now();
const avgTime = (endTime - startTime) / 100;
benchmark[alg] = {
averageTime: avgTime,
operationsPerSecond: 1000 / avgTime
};
});
return {
timestamp: new Date().toISOString(),
benchmark: benchmark,
totalAlgorithms: algorithms.length,
platform: 'JavaScript/Browser'
};
},
// Comprehensive validation suite
runValidationSuite: () => {
const validationResults = {};
// Test 1: Bell State Validation
const bellTest = T0Algorithms.createBellState();
const bellValid = Math.abs(bellTest.bellFidelity - 1.0) < 1e-10;
validationResults.bellState = {
result: bellTest,
validation: bellValid,
expected: 1.0,
actual: bellTest.bellFidelity
};
// Test 2: Deutsch Algorithm Validation
const deutschConstant = T0Algorithms.deutschAlgorithm('constant');
const deutschBalanced = T0Algorithms.deutschAlgorithm('balanced');
const deutschValid = deutschConstant.success && deutschBalanced.success;
validationResults.deutschAlgorithm = {
constant: deutschConstant,
balanced: deutschBalanced,
validation: deutschValid
};
// Test 3: Grover Search Validation
const groverTest = T0Algorithms.groverSearch('110');
const groverValid = groverTest.success && groverTest.targetProbability > 0.6;
validationResults.groverSearch = {
result: groverTest,
validation: groverValid,
targetProbability: groverTest.targetProbability
};
// Test 4: T0 Parameter Effects
const parameterTest = T0AnalysisTools.parameterStudy('bell');
const parameterValid = parameterTest.analysis.xiEffectsDetected;
validationResults.t0Parameters = {
result: parameterTest,
validation: parameterValid
};
// Overall assessment
const validations = [bellValid, deutschValid, groverValid, parameterValid];
const overallValid = validations.every(v => v);
const successRate = validations.filter(v => v).length / validations.length;
return {
timestamp: new Date().toISOString(),
individualTests: validationResults,
overallValidation: overallValid,
successRate: successRate,
summary: {
totalTests: validations.length,
passed: validations.filter(v => v).length,
failed: validations.filter(v => !v).length
}
};
}
};
🧪 Interactive Test Laboratory
Test all T0 quantum modules with real-time analysis and validation:
🚀 Run All Tests
📊 Parameter Study
🔄 Repeatability Test
⚡ Performance Benchmark
🧹 Clear Output
Click "Run All Tests" to begin comprehensive T0 quantum module testing...
🎯 Modul-Übersicht
Komplette Implementation: Erstelle erweiterte Quantenalgorithmen Schritt-für-Schritt mit T0-Theorie-Verbesserungen. Alle Module enthalten deterministische Optimierung, ξ-Parameter-Korrekturen und Energiefeld-Analyse.
⚡
T0 Kern-Simulator
Vollständiger Quantensimulator mit ξ-Parameter-Korrekturen und Energiefeld-Dynamik
🔍
Quantenalgorithmen
Bell-Zustände, Deutsch, Grover-Suche mit deterministischen Verbesserungen
🌊
Erweiterte Module
Quantenfouriertransformation, Shor-Komponenten, Optimierungsroutinen
📊
Analyse-Tools
Energiefeld-Analyse, Wiederholbarkeits-Tests, Performance-Benchmarks
Stufe 1: T0 Kern-Quantensimulator ✅ BEREIT
Grundlage: Vollständiger T0-Theorie-Quantensimulator mit ξ-Parameter-Korrekturen und Energiefeld-Verfolgung.
🔧 Implementation ansehen
🧪 Modul testen
Stufe 2: Quantenalgorithmus-Bibliothek ✅ VOLLSTÄNDIG
Implementation: Vollständige Suite von Quantenalgorithmen mit T0-deterministischen Verbesserungen.
🔧 Algorithmen ansehen
🧪 Algorithmen testen
Stufe 3: T0 Analyse & Optimierungs-Tools ✅ ERWEITERT
Tools: Erweiterte Analyse-Module für T0-Parameter-Studien, Performance-Optimierung und Validierungs-Tests.
🔧 Analyse-Tools ansehen
🧪 Analyse ausführen
🧪 Interaktives Test-Labor
Teste alle T0-Quantenmodule mit Echtzeit-Analyse und Validierung:
🚀 Alle Tests ausführen
📊 Parameter-Studie
🔄 Wiederholbarkeits-Test
⚡ Performance-Benchmark
🧹 Ausgabe löschen
Klicke "Alle Tests ausführen" um umfassende T0-Quantenmodul-Tests zu beginnen...