Quantum Computing Algorithms

// Quantum Computing Algorithms Framework class QuantumAlgorithms { constructor() { this.qubits = []; this.gates = []; this.circuits = []; this.measurements = []; } // Shor's Algorithm for Factoring shorsAlgorithm(n) { const algorithm = { input: n, output: null, steps: [], complexity: 'O((log n)³)' }; // Step 1: Choose random integer a const a = this.chooseRandomInteger(n); algorithm.steps.push(`Chose random integer a = ${a}`); // Step 2: Find period using quantum period finding const period = this.quantumPeriodFinding(a, n); algorithm.steps.push(`Found period r = ${period}`); // Step 3: Check if period is even and a^(r/2) ≠ ±1 (mod n) if (this.isValidPeriod(period, a, n)) { const factor1 = this.gcd(a**(period/2) + 1, n); const factor2 = this.gcd(a**(period/2) - 1, n); algorithm.output = { factor1, factor2 }; } else { algorithm.steps.push('Period not suitable, restarting...'); return this.shorsAlgorithm(n); } return algorithm; } // Grover's Algorithm for Search groversAlgorithm(database, target) { const algorithm = { database: database, target: target, iterations: Math.floor(Math.PI/4 * Math.sqrt(database.length)), steps: [], result: null }; // Initialize uniform superposition algorithm.steps.push('Initialize uniform superposition of all states'); // Apply Grover iterations for (let i = 0; i < algorithm.iterations; i++) { // Oracle: Mark target state algorithm.steps.push(`Oracle: Mark target state ${target}`); // Diffusion: Invert about average algorithm.steps.push('Diffusion: Invert about average'); } // Measure the result algorithm.result = this.measureQuantumState(); algorithm.steps.push(`Measured result: ${algorithm.result}`); return algorithm; } // Quantum Fourier Transform quantumFourierTransform(inputState) { const qft = { input: inputState, output: null, gates: [], complexity: 'O(n²)' }; const n = inputState.length; // Apply Hadamard gates for (let i = 0; i < n; i++) { qft.gates.push(`H(${i})`); } // Apply controlled phase gates for (let i = 0; i < n; i++) { for (let j = i + 1; j < n; j++) { const phase = 2 * Math.PI / (2**(j - i)); qft.gates.push(`CP(${i}, ${j}, ${phase})`); } } // Apply final Hadamard gates for (let i = 0; i < n; i++) { qft.gates.push(`H(${i})`); } qft.output = this.applyQuantumGates(inputState, qft.gates); return qft; } // Variational Quantum Eigensolver variationalQuantumEigensolver(hamiltonian, ansatz) { const vqe = { hamiltonian: hamiltonian, ansatz: ansatz, parameters: this.initializeParameters(ansatz), energy: null, iterations: 0 }; // Optimization loop for (let iteration = 0; iteration < 100; iteration++) { vqe.iterations = iteration; // Prepare quantum state const state = this.prepareQuantumState(vqe.parameters, vqe.ansatz); // Measure expectation value const energy = this.measureExpectationValue(state, vqe.hamiltonian); vqe.energy = energy; // Update parameters using classical optimizer vqe.parameters = this.updateParameters(vqe.parameters, energy); // Check convergence if (this.isConverged(energy, iteration)) { break; } } return vqe; } // Quantum Approximate Optimization Algorithm qaoa(problem, p) { const qaoa = { problem: problem, p: p, parameters: this.initializeQAOAParameters(p), expectation: null, iterations: 0 }; // Optimization loop for (let iteration = 0; iteration < 100; iteration++) { qaoa.iterations = iteration; // Prepare QAOA state const state = this.prepareQAOAState(qaoa.parameters, qaoa.problem, p); // Measure expectation value const expectation = this.measureExpectationValue(state, qaoa.problem); qaoa.expectation = expectation; // Update parameters qaoa.parameters = this.updateQAOAParameters(qaoa.parameters, expectation); // Check convergence if (this.isConverged(expectation, iteration)) { break; } } return qaoa; } }