QuantRS2-Core: Advanced Quantum Computing Foundation

QuantRS2-Core is the foundational library of the QuantRS2 quantum computing framework, providing a comprehensive suite of quantum computing primitives, algorithms, and optimizations that power the entire ecosystem.

Core Features

Basic Quantum Primitives

• Type-Safe Qubit Identifiers: Zero-cost abstractions with compile-time validation
• Comprehensive Gate Library: All standard quantum gates with optimized matrix representations
• Quantum Registers: Fixed-size register types using const generics
• Robust Error Handling: Comprehensive error types with detailed diagnostics

Advanced Decomposition Algorithms

• Solovay-Kitaev: Universal gate set approximation with configurable precision
• Clifford+T Decomposition: T-count optimization for fault-tolerant computing
• KAK Decomposition: Multi-qubit gate decomposition with recursive algorithms
• Shannon Decomposition: Optimal gate count decomposition for arbitrary unitaries
• Cartan Decomposition: Two-qubit gate decomposition using Lie algebra

Quantum Machine Learning

• QML Layers: Rotation, entangling, and hardware-efficient layers
• Data Encoding: Feature maps and data re-uploading strategies
• Training Framework: Optimizers, loss functions, and hyperparameter optimization
• Variational Algorithms: VQE, QAOA with automatic differentiation

Error Correction & Fault Tolerance

• Quantum Error Correction: Surface, color, and Steane codes
• Stabilizer Formalism: Pauli strings and syndrome decoding
• Noise Models: Comprehensive quantum channel representations
• Topological QC: Anyonic models, braiding operations, and fusion trees

Advanced Computing Paradigms

• MBQC: Measurement-based quantum computing with cluster states
• Tensor Networks: Efficient contraction algorithms and optimization
• Fermionic Systems: Jordan-Wigner and Bravyi-Kitaev transformations
• Bosonic Systems: Continuous variable quantum computing

Performance & Optimization

• GPU Acceleration: CUDA and OpenCL backend support
• SIMD Operations: Vectorized quantum state operations
• Batch Processing: Parallel execution of quantum circuits
• ZX-Calculus: Graph-based circuit optimization
• Memory Efficiency: Optimized state vector representations

Usage

Basic Quantum Operations

use quantrs2_core::prelude::*;

fn main() -> QuantRS2Result<()> {
    // Create qubits and apply basic gates
    let q0 = QubitId::new(0);
    let q1 = QubitId::new(1);
    
    // Standard gates
    let x_gate = XGate::new();
    let h_gate = HGate::new();
    let cnot = CXGate::new();
    
    // Parametric gates
    let rz = RZGate::new(std::f64::consts::PI / 4.0);
    
    // Controlled operations
    let controlled_x = make_controlled(XGate::new(), vec![q0]);
    
    Ok(())
}

Gate Decomposition

use quantrs2_core::prelude::*;

fn decomposition_example() -> QuantRS2Result<()> {
    // Solovay-Kitaev decomposition
    let config = SolovayKitaevConfig::default();
    let sk = SolovayKitaev::new(config);
    let target_gate = RYGate::new(0.123);
    let sequence = sk.decompose(&target_gate, 10)?;
    
    // Clifford+T decomposition for fault-tolerant computing
    let decomposer = CliffordTDecomposer::new();
    let ct_sequence = decomposer.decompose_gate(&target_gate)?;
    let t_count = count_t_gates_in_sequence(&ct_sequence);
    
    // KAK decomposition for two-qubit gates
    let cnot = CXGate::new();
    let kak_decomp = decompose_two_qubit_kak(&cnot.matrix())?;
    
    Ok(())
}

Quantum Machine Learning

use quantrs2_core::prelude::*;

fn qml_example() -> QuantRS2Result<()> {
    // Create QML layers
    let rotation_layer = RotationLayer::new(4, vec!['X', 'Y', 'Z']);
    let entangling_layer = EntanglingLayer::circular(4);
    
    // Build a QML circuit
    let mut circuit = QMLCircuit::new(4);
    circuit.add_layer(Box::new(rotation_layer));
    circuit.add_layer(Box::new(entangling_layer));
    
    // Training configuration
    let config = TrainingConfig {
        learning_rate: 0.01,
        epochs: 100,
        batch_size: 32,
        optimizer: Optimizer::Adam,
        loss_function: LossFunction::MeanSquaredError,
    };
    
    Ok(())
}

Error Correction

use quantrs2_core::prelude::*;

fn error_correction_example() -> QuantRS2Result<()> {
    // Surface code for error correction
    let surface_code = SurfaceCode::new(3, 3)?;
    let stabilizers = surface_code.stabilizers();
    
    // Syndrome measurement and decoding
    let syndrome = vec![0, 1, 0, 1]; // Example syndrome
    let decoder = LookupDecoder::new(&surface_code);
    let correction = decoder.decode(&syndrome)?;
    
    // Quantum channels for noise modeling
    let depolarizing = QuantumChannels::depolarizing(0.01);
    let amplitude_damping = QuantumChannels::amplitude_damping(0.05);
    
    Ok(())
}

Batch Operations & GPU Acceleration

use quantrs2_core::prelude::*;

fn batch_and_gpu_example() -> QuantRS2Result<()> {
    // Create batch state vectors for parallel processing
    let batch_config = BatchConfig::new(1000, 4); // 1000 states, 4 qubits each
    let mut batch = create_batch(&batch_config)?;
    
    // Apply gates to entire batch
    apply_single_qubit_gate_batch(&mut batch, 0, &HGate::new())?;
    apply_two_qubit_gate_batch(&mut batch, 0, 1, &CXGate::new())?;
    
    // GPU acceleration (if available)
    let gpu_config = GpuConfig::default();
    let gpu_backend = GpuBackendFactory::create(&gpu_config)?;
    let gpu_state = gpu_backend.create_state_vector(10)?;
    
    Ok(())
}

Module Structure

Core Foundations

• error.rs: Comprehensive error types and result wrappers
• gate.rs: Gate trait definitions and standard quantum gates
• qubit.rs: Type-safe qubit identifier with zero-cost abstractions
• register.rs: Quantum register types with const generics
• complex_ext.rs: Extended complex number operations for quantum states
• matrix_ops.rs: Efficient quantum matrix operations with SciRS2 integration
• operations.rs: Non-unitary quantum operations (measurements, reset, POVM)

Decomposition & Synthesis

• decomposition.rs: Universal gate decomposition algorithms
• decomposition/solovay_kitaev.rs: Universal gate set approximation
• decomposition/clifford_t.rs: Fault-tolerant gate decomposition
• synthesis.rs: Unitary matrix synthesis into gate sequences
• shannon.rs: Quantum Shannon decomposition with optimal gate counts
• cartan.rs: Cartan (KAK) decomposition using Lie algebra
• kak_multiqubit.rs: Multi-qubit KAK decomposition with recursive algorithms

Advanced Quantum Systems

• fermionic.rs: Fermionic operators with Jordan-Wigner transformations
• bosonic.rs: Bosonic operators for continuous variable quantum computing
• topological.rs: Anyonic models, braiding operations, and fusion trees
• mbqc.rs: Measurement-based quantum computing with cluster states
• tensor_network.rs: Tensor network representations and contraction algorithms

Error Correction & Fault Tolerance

• error_correction.rs: Quantum error correction codes (surface, color, Steane)
• quantum_channels.rs: Quantum channel representations (Kraus, Choi, Stinespring)
• characterization.rs: Gate characterization and eigenstructure analysis

Optimization & Performance

• optimization/: Circuit optimization passes and algorithms
  • compression.rs: Gate sequence compression with configurable strategies
  • fusion.rs: Gate fusion for reducing circuit depth
  • peephole.rs: Local optimization patterns and T-count reduction
  • zx_optimizer.rs: ZX-calculus based optimization passes
• zx_calculus.rs: ZX-diagram representation and manipulation
• zx_extraction.rs: Circuit extraction from ZX-diagrams
• simd_ops.rs: SIMD-accelerated quantum operations
• memory_efficient.rs: Memory-optimized state vector representations

Variational & Machine Learning

• variational.rs: Variational quantum circuits with automatic differentiation
• variational_optimization.rs: Optimization algorithms for variational methods
• qml/: Quantum machine learning components
  • layers.rs: Parameterized quantum layers (rotation, entangling, pooling)
  • encoding.rs: Data encoding strategies and feature maps
  • training.rs: Training algorithms and hyperparameter optimization
• parametric.rs: Parametric gates with symbolic computation
• qaoa.rs: Quantum Approximate Optimization Algorithm
• qpca.rs: Quantum Principal Component Analysis

Specialized Algorithms

• hhl.rs: HHL algorithm for linear systems
• eigensolve.rs: Quantum eigenvalue algorithms
• quantum_counting.rs: Quantum counting and amplitude estimation
• quantum_walk.rs: Discrete and continuous quantum walks

Hardware & Acceleration

• gpu/: GPU acceleration support
  • mod.rs: GPU backend abstractions
  • cpu_backend.rs: CPU fallback support
• controlled.rs: Efficient controlled gate operations
• batch/: Batch processing for parallel quantum computations
  • operations.rs: Batch gate operations
  • execution.rs: Batch circuit execution
  • measurement.rs: Batch measurement and tomography
  • optimization.rs: Batch parameter optimization

Testing & Validation

• testing.rs: Quantum-specific testing utilities and assertions

API Overview

Core Types

• QubitId: Type-safe qubit identifier with zero-cost abstractions
• Register<N>: Fixed-size quantum register using const generics
• QuantRS2Error: Comprehensive error enumeration with detailed diagnostics
• QuantRS2Result<T>: Convenient result type alias for error handling

Gate System

• GateOp: Core trait for quantum gates with matrix representations
• Standard gates: XGate, YGate, ZGate, HGate, SGate, TGate, CXGate, CZGate
• Parametric gates: RXGate, RYGate, RZGate, U1Gate, U2Gate, U3Gate
• Controlled operations: ControlledGate, MultiControlledGate, ToffoliGate, FredkinGate

Decomposition & Synthesis

• SolovayKitaev: Universal gate set approximation with configurable precision
• CliffordTDecomposer: T-count optimization for fault-tolerant computing
• KAKDecomposition: Multi-qubit gate decomposition structures
• ShannonDecomposer: Optimal gate count decomposition algorithms
• CartanDecomposer: Two-qubit gate decomposition using Lie algebra

Machine Learning

• QMLLayer: Base trait for quantum machine learning layers
• QMLCircuit: Parameterized quantum circuits for ML applications
• TrainingConfig: Configuration for quantum ML training
• VariationalGate: Gates with trainable parameters and autodiff support

Error Correction

• StabilizerCode: Base trait for quantum error correction codes
• SurfaceCode, ColorCode: Specific error correction codes
• QuantumChannel: Noise models with Kraus, Choi, and Stinespring representations
• SyndromeDecoder: Syndrome decoding algorithms (lookup, MWPM)

Advanced Computing

• TensorNetwork: Tensor network representations with contraction optimization
• FermionOperator: Fermionic system representations with transformations
• BosonOperator: Bosonic operators for continuous variable systems
• AnyonType: Topological quantum computing with anyonic models

Performance & Optimization

• BatchStateVector: Parallel processing of multiple quantum states
• GpuBackend: GPU acceleration for quantum computations
• ZXDiagram: ZX-calculus based circuit optimization
• OptimizationPass: Circuit optimization pass framework

Performance Features

SIMD Acceleration

• Vectorized quantum state operations using platform-specific SIMD instructions
• Optimized inner products, normalizations, and phase applications
• Batch processing of expectation values

Memory Optimization

• Efficient state vector representations with configurable precision
• Sparse matrix support through SciRS2 integration
• Memory-mapped storage for large gate databases

GPU Computing

• CUDA and OpenCL backend support for large-scale simulations
• Optimized kernels for common quantum operations
• Automatic fallback to CPU processing

SciRS2 Integration

• Advanced linear algebra operations using SciRS2's optimized BLAS/LAPACK bindings
• Sparse matrix solvers for large quantum systems
• Parallel algorithms for batch quantum computations

Technical Details

• Zero-cost abstractions: QubitId uses #[repr(transparent)] for no runtime overhead
• Column-major storage: Gate matrices stored for optimal BLAS compatibility
• Const generics: Compile-time validation of quantum register sizes
• Trait specialization: Optimized handling for common gate patterns
• Error propagation: Comprehensive error handling with detailed context

Integration with QuantRS2 Ecosystem

Circuit Module Integration

• Provides foundational gate types for circuit construction
• Supplies optimization passes for circuit compilation
• Offers decomposition algorithms for gate translation

Simulation Module Integration

• Supplies optimized matrix representations for quantum simulation
• Provides batch processing capabilities for parallel simulations
• Offers GPU acceleration for large-scale quantum computations

Device Module Integration

• Provides gate calibration data structures for hardware backends
• Supplies noise models for realistic quantum device simulation
• Offers translation algorithms for device-specific gate sets

ML Module Integration

• Provides QML layers and training frameworks
• Supplies variational optimization algorithms
• Offers automatic differentiation for quantum gradients

License

This project is licensed under either:

• Apache License, Version 2.0
• MIT License

at your option.