Tensor Network Module Implementation Plan

Created: 2025-06-03 | Updated: 2025-06-03

Overview

This document outlines the implementation plan for the tensor network module (T75) within packages/quantum. The module provides memory-efficient representation and computation of quantum states using tensor network algorithms while leveraging all existing quantum and graph-core infrastructure.

Architecture - Leveraging Existing Infrastructure

Integration with Existing Modules

Quantum Module Dependencies:

• StateVector (IQuantumState interface)
• Operator (IOperator interface)
• QuantumGraph class
• QuantumObject union type
• Matrix operations utilities
• Measurement system
• Gates and quantum channels

Graph-Core Module Dependencies:

• Graph builders (lattice2DPeriodic, etc.)
• GraphologyAdapter
• IGraph interfaces
• Graph algorithms and utilities

File Structure

packages/quantum/src/tensorNetwork/
├── core/
│   ├── tensorIndex.ts        # Index system built on existing graph indices
│   ├── graphTensor.ts        # Tensor class using IGraph topology
│   └── contraction.ts        # Uses existing matrix operations utilities
├── states/
│   ├── tensorNetworkState.ts # Implements IQuantumState interface
│   ├── graphStateDecomposer.ts # Converts QuantumGraph → TensorNetwork
│   └── stateVectorBridge.ts  # Uses existing StateVector conversion
├── operators/
│   ├── tensorOperator.ts     # Implements IOperator interface
│   ├── gateDecomposer.ts     # Converts existing gates to tensor form
│   └── measurementTensor.ts  # Uses existing measurement system
├── networks/
│   ├── latticeNetwork.ts     # Uses graph-core lattice builders
│   ├── toricCodeNetwork.ts   # Builds on existing toric code example
│   └── customNetwork.ts      # Uses QuantumGraph as topology
└── index.ts                  # Exports as QuantumObject variants

MVP Implementation Plan

Phase 1: Core Tensor Infrastructure

Goal: Basic tensor operations leveraging existing matrix utilities

Files: core/graphTensor.ts, core/tensorIndex.ts

Implementation:

class GraphTensor {
  constructor(
    private data: Complex[], 
    private shape: number[], 
    private topology: IGraph,  // Use existing IGraph interface
    private indices: string[]
  ) {}
  
  // Leverage existing matrix operations utilities
  contract(other: GraphTensor): GraphTensor
  reshape(newIndices: string[]): GraphTensor
}

Key Integration Points:

• Use existing Complex type from Math.js integration
• Leverage existing matrix operation utilities
• Build on IGraph interface from graph-core
• Use existing validation utilities

Estimated effort: 2-3 days

Phase 2: Quantum State Integration

Goal: TensorNetworkState implementing IQuantumState interface

Files: states/tensorNetworkState.ts, states/stateVectorBridge.ts

Implementation:

class TensorNetworkState implements IQuantumState {
  objectType = 'tensorNetworkState' as const
  
  constructor(private network: TensorNetwork) {}
  
  // Implement all IQuantumState methods
  dimension: number
  norm(): number
  normalize(): TensorNetworkState
  
  // Bridge to existing StateVector system
  toStateVector(): StateVector
  static fromStateVector(state: StateVector): TensorNetworkState
}

Key Integration Points:

• Implement IQuantumState interface completely
• Use existing StateVector conversion patterns
• Integrate with QuantumObject union type
• Leverage existing normalization utilities

Estimated effort: 3-4 days

Phase 3: QuantumGraph Integration

Goal: Convert QuantumGraph to tensor network representation

Files: states/graphStateDecomposer.ts, networks/customNetwork.ts

Implementation:

class GraphStateDecomposer {
  static decompose(qGraph: QuantumGraph): TensorNetworkState {
    // Extract quantum objects from graph vertices/edges
    // Build tensor network matching graph topology
    // Leverage existing QuantumGraph methods
  }
}

function createTensorNetwork(graph: IGraph): TensorNetwork {
  // Use existing graph builders from graph-core
  // Integrate with existing lattice generators
}

Key Integration Points:

• Use existing QuantumGraph class and methods
• Leverage graph-core builders (lattice2DPeriodic, etc.)
• Integrate with existing quantum object storage
• Use existing graph traversal algorithms

Estimated effort: 2-3 days

Phase 4: Operator Integration

Goal: Tensor network operators implementing IOperator interface

Files: operators/tensorOperator.ts, operators/gateDecomposer.ts

Implementation:

class TensorNetworkOperator implements IOperator {
  objectType = 'tensorNetworkOperator' as const
  
  // Implement all IOperator methods
  apply(state: TensorNetworkState): TensorNetworkState
  tensorProduct(other: IOperator): TensorNetworkOperator
  
  // Convert existing gates to tensor form
  static fromGate(gate: IOperator): TensorNetworkOperator
}

Key Integration Points:

• Implement IOperator interface completely
• Use existing gate implementations (Pauli, Hadamard, CNOT)
• Leverage existing operator algebra utilities
• Integrate with existing measurement system

Estimated effort: 2-3 days

Phase 5: Specialized Networks

Goal: Domain-specific tensor networks using existing infrastructure

Files: networks/latticeNetwork.ts, networks/toricCodeNetwork.ts

Implementation:

// Leverage existing toric code example
function createToricCodeTensorNetwork(width: number, height: number): TensorNetworkState {
  const lattice = lattice2DPeriodic(width, height)  // Existing builder
  const qGraph = new QuantumGraph(lattice)          // Existing QuantumGraph
  return GraphStateDecomposer.decompose(qGraph)     // Convert to tensor network
}

// Use existing lattice builders
function createLatticeNetwork(builder: () => IGraph): TensorNetworkState {
  // Leverage all existing graph builders
}

Key Integration Points:

• Use all existing graph builders from graph-core
• Build on existing toric code implementation
• Leverage existing QuantumGraph initialization patterns
• Integrate with existing stabilizer operator examples

Estimated effort: 1-2 days

Phase 6: Testing and Integration

Goal: Comprehensive testing using existing test infrastructure

Files: Test files in existing __tests__/ structure

Key Integration Points:

• Use existing test utilities and patterns
• Validate against existing StateVector implementations
• Test conversion between existing formats
• Benchmark against existing toric code examples

Estimated effort: 2-3 days

Testing Strategy

Unit Tests

• tensor.test.ts: Core tensor operations
• contraction.test.ts: Einstein summation correctness
• tensorState.test.ts: Quantum state operations
• conversion.test.ts: StateVector compatibility

Integration Tests

• Toric code tensor network representation
• Memory usage validation
• Performance benchmarks vs StateVector

Test Coverage Goals

• 90%+ line coverage
• All public APIs tested
• Edge cases and error conditions

Usage Examples - Leveraging Existing Infrastructure

Example 1: Converting Existing QuantumGraph to Tensor Network

// Use existing graph builder and QuantumGraph
const lattice = lattice2DPeriodic(3, 3)  // Existing graph-core builder
const qGraph = new QuantumGraph(lattice)  // Existing QuantumGraph class

// Initialize with existing state creation
for (const node of qGraph.getNodes()) {
  const plusState = createBasisState(2, 0).add(createBasisState(2, 1)).normalize()
  qGraph.setVertexQuantumObject(node.id, plusState)
}

// Convert to tensor network
const tensorNetwork = GraphStateDecomposer.decompose(qGraph)
console.log('Memory reduction:', qGraph.memorySize / tensorNetwork.memorySize)

Example 2: Toric Code with Tensor Networks

// Build on existing toric code example
const config = { width: 2, height: 2 }
const qGraph = setupToricCode(config)  // Existing function from T73a

// Convert to tensor network for memory efficiency
const tensorNetwork = createToricCodeTensorNetwork(config.width, config.height)

// Use existing measurement system
const result = tensorNetwork.measureSubsystem(['0,0', '0,1', '1,0', '1,1'])
console.log('Measurement result:', result)

Example 3: Operator Application Using Existing Gates

// Use existing quantum gates
const cnotGate = CNOT  // Existing gate from quantum module
const tensorCNOT = TensorNetworkOperator.fromGate(cnotGate)

// Apply to tensor network state
const initialState = TensorNetworkState.fromStateVector(someBellState)
const finalState = tensorCNOT.apply(initialState)

// Convert back to StateVector for validation
const stateVector = finalState.toStateVector()

Example 4: Integration with Existing Quantum Graph Operations

// Use existing quantum graph operations
const qGraph = new QuantumGraph(lattice2DPeriodic(2, 2))
qGraph.applyOperation(['0,0', '0,1'], PauliX.tensorProduct(PauliX))

// Convert to tensor network for efficient representation
const tensorNetwork = GraphStateDecomposer.decompose(qGraph)

// Perform tensor network operations
const contracted = tensorNetwork.contract()  // Get full state vector when needed

Performance Targets

Memory Efficiency

• Product states: 10-100x reduction vs StateVector
• Structured states: 2-10x reduction vs StateVector
• Entangled states: Minimal overhead

Computational Performance

• Tensor contractions should be competitive with direct matrix operations
• Conversion overhead should be minimal
• Target: Handle 12+ qubit systems efficiently

Integration Points with Existing Infrastructure

Quantum Module Integration

• IQuantumState: TensorNetworkState implements full interface
• IOperator: TensorNetworkOperator implements full interface
• QuantumObject: Add tensor network types to union
• StateVector: Bidirectional conversion support
• Measurement: Use existing measurement system and utilities
• Gates: Convert existing gates to tensor network representation
• Matrix Operations: Leverage existing utilities for contractions

Graph-Core Module Integration

• IGraph: Use as topology foundation for tensor networks
• Graph Builders: Leverage all existing builders (lattice2D, random, etc.)
• GraphologyAdapter: Use existing graph algorithms and traversals
• Graph Utilities: Use existing path finding and analysis tools

QuantumGraph Integration

• Conversion: Direct QuantumGraph → TensorNetwork conversion
• Operations: Use existing applyOperation infrastructure
• Composite States: Leverage existing composite state management
• Examples: Build on existing toric code and Bell state examples

Implementation Timeline

Week 1: Phase 1 (Core tensor with existing matrix ops) + Phase 2 (IQuantumState integration) Week 2: Phase 3 (QuantumGraph conversion) + Phase 4 (IOperator integration)
Week 3: Phase 5 (Specialized networks using existing builders) + Phase 6 (Testing with existing infrastructure) Week 4: Documentation + Performance benchmarks + Integration examples

Success Criteria

1. Functional: All MVP features implemented and tested using existing infrastructure
2. Performance: 5x+ memory reduction for structured states vs existing StateVector
3. Integration: Seamless integration with existing QuantumGraph and graph-core modules
4. Compatibility: Full IQuantumState and IOperator interface compliance
5. Quality: 90%+ test coverage using existing test patterns
6. Validation: Existing toric code example working with tensor networks
7. Conversion: Lossless bidirectional conversion with existing StateVector

Future Extensions (Post-MVP)

• Bond dimension truncation for approximation algorithms
• Matrix Product State (MPS) canonical forms leveraging existing angular momentum
• Advanced contraction order optimization using existing graph algorithms
• Integration with existing Wigner symbol calculations for spin networks
• Quantum circuit tensor network compilation using existing gate infrastructure

Risk Mitigation

Risk: Breaking existing interfaces Mitigation: Implement all existing interfaces exactly, maintain full compatibility

Risk: Performance overhead in existing workflows
Mitigation: Make tensor networks optional, maintain existing StateVector performance

Risk: Integration complexity with QuantumGraph Mitigation: Use existing patterns from QuantumGraph implementation

Risk: Testing complexity Mitigation: Build on existing test infrastructure and validation patterns

Risk: Memory overhead in conversion Mitigation: Implement lazy evaluation, leverage existing matrix operation optimizations