Last Updated: May 24, 2025
The quantum package provides a comprehensive quantum mechanics library implemented in TypeScript, designed specifically for integration with spin network applications and quantum geometric computations. The package serves as the foundational mathematical layer for quantum state manipulation, operator algebra, and quantum information processing.
Key Objectives:
Scope: The package focuses on core quantum mechanics primitives while providing extension points for specialized applications such as quantum circuits, spin networks, and quantum algorithms. It serves as a dependency for higher-level packages including graph-core and spin-network modules.
The quantum package follows a hierarchical architecture with clear dependency layers and separation of concerns. The design emphasizes both functional purity for mathematical operations and stateful patterns where caching and performance optimization are critical.
packages/quantum/
├── src/
│ ├── core/ # Core types and interfaces (Level 0)
│ ├── utils/ # Mathematical utilities (Level 1)
│ ├── states/ # Quantum state implementations (Level 2)
│ ├── operators/ # Quantum operators (Level 3)
│ ├── angularMomentum/ # Angular momentum specialization (Level 4)
│ └── index.ts # Public API exports
├── docs/ # Documentation and implementation guides
├── __tests__/ # Comprehensive test suite
└── examples/ # Usage examples and tutorials
The architecture enforces a strict one-way dependency flow:
Level 0 (Core) → Level 1 (Utils) → Level 2 (States) → Level 3 (Operators) → Level 4 (Angular Momentum)
This ensures:
The following diagram illustrates the complete dependency structure within the quantum package:
graph TD
types[types.ts] --> complex[complex.ts]
complex --> matrixOperations[matrixOperations.ts]
matrixOperations --> matrixFunctions[matrixFunctions.ts]
types --> stateVector[stateVector.ts]
complex --> stateVector
types --> operator[operator.ts]
matrixOperations --> operator
stateVector --> operator
operator --> gates[gates.ts]
operator --> composition[composition.ts]
stateVector --> composition
types --> densityMatrix[densityMatrix.ts]
operator --> densityMatrix
complex --> densityMatrix
matrixOperations --> densityMatrix
densityMatrix --> information[information.ts]
operator --> hamiltonian[hamiltonian.ts]
gates --> hamiltonian
composition --> hamiltonian
matrixOperations --> hamiltonian
complex --> hamiltonian
types --> hilbertSpace[hilbertSpace.ts]
complex --> hilbertSpace
stateVector --> hilbertSpace
operator --> measurement[measurement.ts]
complex --> measurement
operator --> operatorAlgebra[operatorAlgebra.ts]
complex --> operatorAlgebra
matrixOperations --> operatorAlgebra
operator --> oscillator[oscillator.ts]
complex --> oscillator
complex --> states[states.ts]
stateVector --> states
%% Styling
classDef core fill:#f9f,stroke:#333,stroke-width:2px;
classDef dependent fill:#bbf,stroke:#333,stroke-width:1px;
class types,complex,matrixOperations core;
class stateVector,operator dependent;
Components are organized into five dependency levels:
This hierarchy ensures that lower levels never depend on higher levels, maintaining clean separation and testability.
Location: src/core/
The foundation layer provides essential type definitions and mathematical interfaces used throughout the package.
Key Components: ✅ Implemented
IStateVector, IOperator, IMeasurementOutcome, IDensityMatrix)Core Interfaces:
interface IStateVector {
dimension: number;
amplitudes: Complex[];
norm(): number;
normalize(): IStateVector;
innerProduct(other: IStateVector): Complex;
}
interface IOperator {
dimension: number;
type: OperatorType;
apply(state: IStateVector): IStateVector;
compose(other: IOperator): IOperator;
adjoint(): IOperator;
}
These interfaces establish the mathematical contracts that all higher-level components must satisfy.
Location: src/utils/
This layer provides mathematical utilities and basic operations that support all quantum computations.
Key Modules: ✅ Implemented
validation.ts: Input validation for quantum operations
matrixOperations.ts: Core matrix algebra
matrixFunctions.ts: Advanced matrix functions
information.ts: Quantum information measures
oscillator.ts: Harmonic oscillator utilities
Mathematical Foundation: The utilities layer implements numerically stable algorithms for quantum-specific matrix operations, with particular attention to maintaining unitarity and hermiticity where required.
Location: src/states/
This layer implements quantum state representations and their manipulations.
Key Components: ✅ Implemented
stateVector.ts: Pure quantum state implementation
class StateVector implements IStateVector {
// Core state vector with complex amplitudes
// Maintains normalization invariants
// Supports arbitrary dimensional quantum systems
}
states.ts: Common quantum state preparation
densityMatrix.ts: Mixed quantum state support
composite.ts: Multi-particle system operations
State Space Mathematics: States live in complex Hilbert spaces $\mathcal{H}$ with inner product $\langle\psi|\phi\rangle$. The implementation maintains the normalization condition $\langle\psi|\psi\rangle = 1$ and supports both pure states $|\psi\rangle$ and mixed states $\rho = \sum_i p_i |\psi_i\rangle\langle\psi_i|$.
Location: src/operators/
This layer implements quantum operators that act on quantum states, including measurements, gates, and time evolution.
Key Components: ✅ Implemented
operator.ts: Base operator implementation
class MatrixOperator implements IOperator {
// Matrix representation of quantum operators
// Supports composition, adjoint, tensor products
// Validates unitarity and hermiticity properties
}
gates.ts: Fundamental quantum gates
measurement.ts: Quantum measurement framework
hamiltonian.ts: Time evolution and dynamics
algebra.ts: Advanced operator algebra
Operator Mathematics: Operators are linear maps $\hat{A}: \mathcal{H} \rightarrow \mathcal{H}$ with matrix representations. Physical operators are Hermitian ($\hat{A}^\dagger = \hat{A}$) for real eigenvalues, while time evolution operators are unitary ($\hat{U}^\dagger\hat{U} = \mathbb{I}$) for probability conservation.
Location: src/angularMomentum/
This specialized layer implements angular momentum algebra, crucial for spin network applications and quantum mechanical systems with rotational symmetry.
Key Components: ✅ Implemented
Mathematical Framework:
Angular momentum operators satisfy the fundamental commutation relations: $[\hat{J}_i, \hat{J}j] = i\hbar\epsilon{ijk}\hat{J}_k$
Clebsch-Gordan Coefficients: For coupling two angular momenta $j_1$ and $j_2$: $|j_1, j_2; j, m\rangle = \sum_{m_1,m_2} \langle j_1, m_1; j_2, m_2 | j, m \rangle |j_1, m_1\rangle |j_2, m_2\rangle$
Implementation Features:
Applications: Essential for spin network calculations where edges carry SU(2) representations (spins) and vertices represent intertwiner spaces that couple multiple angular momenta according to quantum mechanical selection rules.
The quantum package is built on rigorous mathematical foundations that ensure numerical stability and quantum mechanical consistency.
Integration with math.js: The package migrated from custom complex number operations to math.js for improved numerical stability and performance. Key operations include:
// Complex number creation and manipulation
const z = math.complex({re: a, im: b});
const result = math.add(z1, z2);
const conjugate = math.conj(z);
const magnitude = math.abs(z);
Benefits:
Core Matrix Algebra: All quantum operations are implemented using numerically stable matrix algorithms:
Numerical Considerations:
Hilbert Space Structure: Quantum states live in complex Hilbert spaces with inner product: $\langle\psi|\phi\rangle = \sum_i \psi_i^* \phi_i$
Normalization Invariants: All state operations preserve the normalization condition: $\langle\psi|\psi\rangle = \sum_i |\psi_i|^2 = 1$
Composite Systems: Multi-particle states use tensor product spaces: $\mathcal{H}_{total} = \mathcal{H}_1 \otimes \mathcal{H}_2 \otimes \cdots \otimes \mathcal{H}_n$
Linear Operators: Quantum operators are represented as matrices acting on state vectors: $\hat{A}|\psi\rangle = \sum_{ij} A_{ij}|i\rangle\langle j|\psi\rangle$
Special Operator Classes:
Spectral Decomposition: Hermitian operators decompose as: $\hat{A} = \sum_i \lambda_i |a_i\rangle\langle a_i|$ where $\lambda_i$ are real eigenvalues and $|a_i\rangle$ are orthonormal eigenvectors.
The quantum package is designed for seamless integration with graph-based quantum systems and tensor networks.
Spin Network Architecture: 📋 Planned The package will support spin networks where:
Mathematical Integration: 📋 Planned
// Edge states with quantum numbers - NOT YET IMPLEMENTED
class EdgeState {
spin: number; // j quantum number
state: StateVector; // quantum state |j,m⟩
}
// Node intertwiners - NOT YET IMPLEMENTED
class NodeIntertwiner {
inputSpins: number[]; // incident edge spins
intertwinerIndex: number; // coupling scheme index
tensor: ComplexMatrix; // intertwiner tensor
}
Diffusion on Quantum Networks: 📋 Planned For diffusion processes on spin networks, operators must account for both graph connectivity and quantum properties:
$\hat{\mathcal{L}}|\Gamma, {j_e}, {i_v}\rangle = \sum_{\text{edges}} f(j_e) \hat{\Delta}e + \sum{\text{vertices}} g(i_v) \hat{\Delta}_v$
where $f(j_e)$ and $g(i_v)$ are functions of edge spins and vertex intertwiners.
Tensor Structure: Quantum states can be represented as tensor networks:
Integration Points:
Functional Core with Stateful Shell: ✅ Implemented
Composition Patterns: 📋 Planned
// Operator composition - PLANNED FLUENT API
const evolved = timeEvolution(hamiltonian, time)
.compose(measurement(observable))
.apply(initialState);
// State preparation pipeline - PLANNED FLUENT API
const entangledState = bellState()
.tensorProduct(groundState())
.normalize();
Custom Operator Support: 📋 Planned
// NOT YET IMPLEMENTED
interface CustomOperator extends IOperator {
// Implementation-specific properties
quantumProperty: QuantumNumber;
// Required methods
apply(state: IStateVector): IStateVector;
compose(other: IOperator): IOperator;
}
Algorithm Integration: 📋 Planned The package will provide foundation classes for quantum algorithms:
Math.js Integration:
Caching Strategies: 📋 Planned
// NOT YET IMPLEMENTED
class CachedOperator implements IOperator {
private cachedMatrix: ComplexMatrix | null = null;
private cachedEigendecomposition: EigenResult | null = null;
// Lazy evaluation for expensive operations
getMatrix(): ComplexMatrix {
if (!this.cachedMatrix) {
this.cachedMatrix = this.computeMatrix();
}
return this.cachedMatrix;
}
}
Memory Management:
Precision Considerations:
Error Propagation:
Immutable State Management:
// States are immutable - operations return new states
const evolvedState = operator.apply(initialState); // Creates new state
const originalState = initialState; // Unchanged
Type Safety:
Functional Programming:
Large Quantum Systems:
Memory Footprint:
The quantum package provides multiple extension points for specialized quantum applications and algorithms.
Circuit Framework: 📋 Planned
// NOT YET IMPLEMENTED
interface IQuantumCircuit {
readonly numQubits: number;
readonly depth: number;
addGate(gate: IOperator, targets: number[]): this;
addMeasurement(qubit: number): this;
execute(initialState?: IStateVector): CircuitResult;
}
Gate Extensions: 📋 Planned
Quantum Walk Framework: 📋 Planned
// NOT YET IMPLEMENTED
interface IQuantumWalk {
graph: IGraph;
coinOperator: IOperator;
step(): IStateVector;
evolve(steps: number): IStateVector;
}
Optimization Algorithms: 📋 Planned
Operator Extension Pattern: 📋 Planned
// NOT YET IMPLEMENTED
class CustomQuantumOperator extends MatrixOperator {
constructor(
private parameters: QuantumParameters,
dimension: number
) {
super(dimension, OperatorType.CUSTOM);
}
protected computeMatrix(): ComplexMatrix {
// Custom implementation using quantum parameters
return this.buildCustomMatrix();
}
}
Test Infrastructure: 📋 Planned
Validation Utilities: 📋 Planned
// NOT YET IMPLEMENTED
interface QuantumValidator {
validateUnitarity(operator: IOperator, tolerance?: number): boolean;
validateNormalization(state: IStateVector, tolerance?: number): boolean;
validateHermiticity(operator: IOperator, tolerance?: number): boolean;
}
Custom Test Patterns: 📋 Planned
From lib/quantum to packages/quantum:
The quantum package represents a migration from the original lib/quantum structure to a proper monorepo package architecture.
Migration Benefits:
Backward Compatibility:
Package Configuration:
{
"name": "@spin-network/quantum",
"version": "0.1.0",
"main": "dist/index.js",
"module": "dist/index.mjs",
"types": "dist/index.d.ts",
"dependencies": {
"mathjs": "^12.4.3"
}
}
Build System:
Integration Points:
API Stability:
Dependency Management:
This architecture provides a solid foundation for quantum mechanical computations while maintaining flexibility for specialized applications in spin networks and quantum geometry.
Priority: HIGH 🔄
The following components exist in lib/quantum and need migration to packages/quantum:
circuit.ts - Currently empty file, needs complete implementation
IQuantumCircuit interfaceQuantumCircuit class with gate compositionCircuitResult and measurement distribution handlingEnhanced Testing Framework - Basic tests exist but need expansion
Example Documentation - Examples exist in lib/quantum/examples
Priority: MEDIUM 📋
CachedOperator Implementation
Advanced Numerical Stability
Fluent API Design
Custom Operator Framework
CustomOperator interface implementationPriority: LOW 📋
EdgeState Class
NodeIntertwiner Class
Diffusion Operators
Quantum Walk Framework
IQuantumWalk interfaceOptimization Algorithm Support
This roadmap provides a structured approach to completing the quantum package implementation while maintaining backwards compatibility and preparing for future enhancements.