ts-quantum

A TypeScript library for quantum mechanics calculations and utilities.

Features

• Quantum state vector operations
• Standard quantum gates (Pauli, Hadamard, CNOT)
• Density matrix operations
• Quantum measurements
• Hilbert space operations
• Hamiltonian evolution
• Quantum information tools
• Angular momentum algebra (J₊, J₋, Jz, J²)
• Wigner symbols (3j, 6j, 9j)
• Angular momentum composition
• Geometric quantum distance calculations

Core Components

State Vectors

import { StateVector } from 'ts-quantum';

// Create a 2-dimensional quantum state
const state = new StateVector(2);

// Create standard basis states
const zeroState = StateVector.computationalBasis(2, 0); // |0⟩
const oneState = StateVector.computationalBasis(2, 1);  // |1⟩
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Quantum Gates

import { PauliX, Hadamard } from 'ts-quantum';

// Apply X gate (NOT gate)
const flippedState = PauliX.apply(zeroState);

// Create superposition with Hadamard
const superposition = Hadamard.apply(zeroState);
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Measurements

import { measure } from 'ts-quantum';

// Measure a state in computational basis
const outcome = measure(state);
console.log(`Measured: ${outcome.value} with probability ${outcome.probability}`);
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Installation

npm install ts-quantum
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Requirements

• Node.js >= 14.0.0
• TypeScript >= 4.5.0
• mathjs >= 10.0.0

Basic Usage

import { 
  StateVector,
  PauliX,
  Hadamard,
  measure
} from 'ts-quantum';

// Create a qubit in |0⟩ state
const qubit = StateVector.computationalBasis(2, 0);

// Apply Hadamard gate to create superposition
const superposition = Hadamard.apply(qubit);

// Measure the state
const result = measure(superposition);
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API Documentation

The quantum module consists of several key components:

StateVector

Core class for quantum state manipulation:

• StateVector(dimension: number)
• setState(index: number, value: Complex)
• getState(index: number): Complex
• innerProduct(other: StateVector): Complex
• normalize(): StateVector

Quantum Gates

Standard quantum gates:

• PauliX - NOT gate
• PauliY - Y rotation
• PauliZ - Phase flip
• Hadamard - Creates superposition
• CNOT - Controlled-NOT gate

Measurement

Quantum measurement operations:

• measure(state: StateVector)
• projectiveMeasurement(state: StateVector, operator: Operator)

DensityMatrix

Mixed state operations:

• DensityMatrix(dimension: number)
• trace(): Complex
• purity(): number
• vonNeumannEntropy(): number

Angular Momentum

Comprehensive angular momentum algebra:

• createJplus(j: number) - Creates raising operator J₊
• createJminus(j: number) - Creates lowering operator J₋
• createJz(j: number) - Creates z-component operator Jz
• createJ2(j: number) - Creates total angular momentum operator J²
• createAngularState(j: number, m: number) - Creates |j,m⟩ eigenstate
• wignerD(j: number, α: number, β: number, γ: number) - Wigner D-matrix
• clebschGordan(j1: number, m1: number, j2: number, m2: number, J: number, M: number) - CG coefficients
• wigner3j(j1: number, j2: number, j3: number, m1: number, m2: number, m3: number) - 3j symbols
• wigner6j(j1: number, j2: number, j3: number, l1: number, l2: number, l3: number) - 6j symbols
• wigner9j(...) - 9j symbols

Geometry

Quantum geometric operations:

• quantumDistance(state1, state2) - Fubini-Study distance between quantum states
• Geometric measures for quantum state spaces

import { quantumDistance } from 'ts-quantum';

const distance = quantumDistance(state1, state2);
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Examples

See the /examples directory for more detailed usage examples.

Contributing

Please see CONTRIBUTING.md for guidelines.

License

MIT License