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Architecture Overview

The Topological Quantum Compiler (TQC) is designed with a modular architecture that separates concerns while maintaining tight integration between quantum circuit compilation, anyonic simulation, and topological optimization.

System Architecture

flowchart TB
    subgraph "Input Layer"
        QC[Quantum Circuit<br/>QASM/Qiskit]
        ALG[Quantum Algorithm<br/>VQE/QAOA]
        CUSTOM[Custom Gates]
    end

    subgraph "Compilation Engine"
        PARSER[Circuit Parser]
        ANALYZER[Gate Analyzer]
        MAPPER[Anyon Mapper]
        OPTIMIZER[Braid Optimizer]
    end

    subgraph "Topological Layer"
        ANYON[Anyon Types<br/>Fibonacci/Ising]
        BRAID[Braid Operations]
        FUSION[Fusion Rules]
        FMATRIX[F/R Matrices]
    end

    subgraph "Simulation Engine"
        TENSOR[Tensor Networks]
        JAX[JAX Backend]
        CLASSICAL[Classical Simulation]
        NOISE[Noise Models]
    end

    subgraph "Output Layer"
        RESULT[Simulation Results]
        VIS[Visualizations]
        METRICS[Performance Metrics]
        EXPORT[Export Formats]
    end

    QC --> PARSER
    ALG --> PARSER
    CUSTOM --> PARSER

    PARSER --> ANALYZER
    ANALYZER --> MAPPER
    MAPPER --> OPTIMIZER

    OPTIMIZER --> ANYON
    ANYON --> BRAID
    BRAID --> FUSION
    FUSION --> FMATRIX

    FMATRIX --> TENSOR
    TENSOR --> JAX
    JAX --> CLASSICAL
    CLASSICAL --> NOISE

    NOISE --> RESULT
    RESULT --> VIS
    RESULT --> METRICS
    RESULT --> EXPORT

    classDef inputClass fill:#4caf50,stroke:#2e7d32,color:#fff
    classDef compileClass fill:#ff9800,stroke:#ef6c00,color:#fff
    classDef topoClass fill:#673ab7,stroke:#4527a0,color:#fff
    classDef simClass fill:#2196f3,stroke:#0d47a1,color:#fff
    classDef outputClass fill:#9c27b0,stroke:#6a1b9a,color:#fff

    class QC,ALG,CUSTOM inputClass
    class PARSER,ANALYZER,MAPPER,OPTIMIZER compileClass
    class ANYON,BRAID,FUSION,FMATRIX topoClass
    class TENSOR,JAX,CLASSICAL,NOISE simClass
    class RESULT,VIS,METRICS,EXPORT outputClass

Component Interaction

sequenceDiagram
    participant User
    participant CLI
    participant Compiler
    participant AnyonSystem
    participant BraidEngine
    participant Simulator
    participant Visualizer

    User->>CLI: Submit quantum circuit
    CLI->>Compiler: Parse and validate
    Compiler->>AnyonSystem: Request anyon type
    AnyonSystem-->>Compiler: Return fusion rules

    Compiler->>BraidEngine: Generate braid sequence
    BraidEngine->>BraidEngine: Optimize braids
    BraidEngine-->>Compiler: Optimized sequence

    Compiler->>Simulator: Execute braided circuit
    Simulator->>AnyonSystem: Apply fusion operations
    AnyonSystem-->>Simulator: Update quantum state
    Simulator-->>Compiler: Simulation results

    Compiler->>Visualizer: Generate diagrams
    Visualizer-->>CLI: Braid visualizations
    CLI-->>User: Complete results

Data Flow Architecture

graph LR
    subgraph "Data Input"
        QASM[QASM Files]
        QISKIT[Qiskit Circuits]
        CUSTOM[Custom Formats]
    end

    subgraph "Intermediate Representation"
        AST[Abstract Syntax Tree]
        DAG[Directed Acyclic Graph]
        BRAID_SEQ[Braid Sequences]
    end

    subgraph "Execution Context"
        ANYON_STATE[Anyonic State]
        TENSOR_NET[Tensor Network]
        MEASUREMENT[Measurement Results]
    end

    subgraph "Output Formats"
        JSON[JSON Results]
        SVG[SVG Diagrams]
        PNG[PNG Images]
        CSV[CSV Data]
    end

    QASM --> AST
    QISKIT --> AST
    CUSTOM --> AST

    AST --> DAG
    DAG --> BRAID_SEQ

    BRAID_SEQ --> ANYON_STATE
    ANYON_STATE --> TENSOR_NET
    TENSOR_NET --> MEASUREMENT

    MEASUREMENT --> JSON
    MEASUREMENT --> SVG
    MEASUREMENT --> PNG
    MEASUREMENT --> CSV

    classDef dataClass fill:#4caf50,stroke:#2e7d32,color:#fff
    classDef irClass fill:#ff9800,stroke:#ef6c00,color:#fff
    classDef execClass fill:#673ab7,stroke:#4527a0,color:#fff
    classDef outputClass fill:#2196f3,stroke:#0d47a1,color:#fff

    class QASM,QISKIT,CUSTOM dataClass
    class AST,DAG,BRAID_SEQ irClass
    class ANYON_STATE,TENSOR_NET,MEASUREMENT execClass
    class JSON,SVG,PNG,CSV outputClass

Error Handling Strategy

stateDiagram-v2
    [*] --> Parsing
    Parsing --> ValidationError : Invalid syntax
    Parsing --> GateAnalysis : Valid circuit

    GateAnalysis --> UnsupportedGate : Gate not supported
    GateAnalysis --> BraidCompilation : All gates supported

    BraidCompilation --> OptimizationError : Optimization failed
    BraidCompilation --> Simulation : Compilation successful

    Simulation --> RuntimeError : Simulation failed
    Simulation --> Results : Simulation successful

    ValidationError --> ErrorReport
    UnsupportedGate --> ErrorReport
    OptimizationError --> Fallback
    RuntimeError --> ErrorReport

    Fallback --> Simulation : Retry with basic optimization
    ErrorReport --> [*]
    Results --> [*]

    state ValidationError {
        [*] --> CircuitSyntaxError
        [*] --> GateParameterError
        [*] --> QubitIndexError
    }

    state UnsupportedGate {
        [*] --> CustomGateError
        [*] --> ParameterizedGateError
        [*] --> ControlledGateError
    }

    state RuntimeError {
        [*] --> MemoryError
        [*] --> NumericalInstability
        [*] --> TimeoutError
    }

Performance Characteristics

gantt
    title TQC Performance Timeline
    dateFormat X
    axisFormat %s

    section Circuit Analysis
    Parsing           :0, 1
    Gate Decomposition:1, 3
    Dependency Analysis:2, 4

    section Braid Compilation
    Anyon Mapping     :4, 7
    Braid Generation  :7, 12
    Optimization      :12, 18

    section Simulation
    State Preparation :18, 20
    Tensor Operations :20, 35
    Measurement       :35, 37

    section Post-Processing
    Data Analysis     :37, 39
    Visualization     :39, 42
    Export            :42, 43

Scalability Model

graph TD
    subgraph "Small Scale (1-10 qubits)"
        S1[Classical Simulation]
        S2[Full State Vector]
        S3[Exact Results]
    end

    subgraph "Medium Scale (10-50 qubits)"
        M1[Tensor Network]
        M2[Matrix Product States]
        M3[Approximate Results]
    end

    subgraph "Large Scale (50+ qubits)"
        L1[Distributed Computing]
        L2[Compressed Tensors]
        L3[Statistical Sampling]
    end

    QUBITS{Number of Qubits} --> S1
    QUBITS --> M1
    QUBITS --> L1

    S1 --> S2 --> S3
    M1 --> M2 --> M3
    L1 --> L2 --> L3

    classDef smallClass fill:#4caf50,stroke:#2e7d32,color:#fff
    classDef medClass fill:#ff9800,stroke:#ef6c00,color:#fff
    classDef largeClass fill:#f44336,stroke:#c62828,color:#fff

    class S1,S2,S3 smallClass
    class M1,M2,M3 medClass
    class L1,L2,L3 largeClass

Module Dependencies

classDiagram
    class TopologicalCompiler {
        +compile(circuit)
        +optimize()
        +simulate()
        -_analyze_gates()
        -_generate_braids()
    }

    class AnyonSystem {
        <<abstract>>
        +fusion_rules()
        +f_matrix()
        +r_matrix()
        +braiding_statistics()
    }

    class FibonacciAnyons {
        +fusion_rules()
        +f_matrix()
        +r_matrix()
        +golden_ratio: float
    }

    class IsingAnyons {
        +fusion_rules()
        +f_matrix()
        +r_matrix()
        +sigma_matrices()
    }

    class BraidWord {
        +generators: List
        +compose(other)
        +inverse()
        +visualize()
    }

    class AnyonicSimulator {
        +simulate(braid_program)
        +measure(observables)
        -_tensor_contraction()
    }

    class BraidOptimizer {
        +optimize(braid_word)
        +strategies: List
        -_solovay_kitaev()
        -_greedy_simplify()
    }

    TopologicalCompiler --> AnyonSystem
    TopologicalCompiler --> BraidWord
    TopologicalCompiler --> AnyonicSimulator
    TopologicalCompiler --> BraidOptimizer

    AnyonSystem <|-- FibonacciAnyons
    AnyonSystem <|-- IsingAnyons

    AnyonicSimulator --> AnyonSystem
    BraidOptimizer --> BraidWord

This architecture ensures:

  • Modularity: Each component has a well-defined responsibility
  • Extensibility: New anyon types and optimization strategies can be easily added
  • Performance: Efficient data flow and minimal copying
  • Reliability: Comprehensive error handling and fallback mechanisms
  • Scalability: Architecture adapts to different problem sizes