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Quantum Geometric Learning: Quickstart Guide (Pre-release)

Note: This is a pre-release version. The library is currently under active development and does not yet fully compile. This guide describes the core concepts and planned functionality.

Development Status

  • Core algorithms and architecture: ✅ Complete
  • Documentation: ✅ Complete
  • Compilation: 🚧 In Progress
  • Hardware integration: 🚧 In Progress
  • Testing Framework: 🚧 In Progress

Quick Start (Core Concepts)

// Note: This example shows the planned API. Compilation is not yet supported.
#include <quantum_geometric/core/quantum_geometric_core.h>

int main() {
    // Initialize quantum system with geometric protection
    quantum_system_t* system = quantum_init_system(&(quantum_config_t){
        .backend = BACKEND_SIMULATOR,  // Using simulator backend for now
        .optimization = {
            .geometric = true,         // Geometric optimization (in development)
            .error_protection = true,  // Error protection (in development)
            .hardware_aware = false    // Hardware optimization (planned)
        }
    });

    // Create quantum circuit
    quantum_circuit_t* circuit = quantum_circuit_create();
    
    // Create Bell state (|00⟩ + |11⟩)/√2
    quantum_circuit_h(circuit, 0);     // Hadamard gate
    quantum_circuit_cx(circuit, 0, 1); // CNOT gate
    
    // Execute circuit (simulation only)
    execution_result_t result;
    quantum_execute_circuit(system, circuit, &result);
    
    // Print results
    printf("Circuit fidelity: %.3f\n", result.fidelity);
    printf("Error rate: %.3e\n", result.error_rate);
    printf("Circuit depth: %d\n", result.circuit_depth);
    
    // Cleanup
    quantum_circuit_destroy(circuit);
    quantum_system_destroy(system);
    return 0;
}

Key Features (Development Status):

  • Geometric Protection: 🚧 In development
  • Hardware Optimization: 🚧 In development
  • Error Mitigation: 🚧 In development
  • Resource Management: 🚧 In development

Framework Overview

The quantum geometric learning framework leverages differential geometry and algebraic topology for superior performance on quantum hardware. Current development focuses on:

Mathematical Foundation

The framework uses differential geometry to optimize quantum operations:

M = CP^(2^n-1) = U(2^n)/(U(1) × U(2^n-1))  // Complex projective space

This geometric structure provides:

  • Hardware-Native Operations (In Development):

    • Maps quantum states to geometric manifolds
    • Optimizes operations using natural metrics
    • Matches hardware topology automatically
    • Target: 30-70% gate count reduction

  • Topology-Based Protection (In Development):

    • Uses geometric phases for error correction
    • Encodes information in topological invariants
    • Makes certain errors physically impossible
    • Target: O(ε²) error scaling

  • Natural Optimization (In Development):

    • Follows geodesics for optimal compilation
    • Uses Riemannian metrics for natural gradients
    • Minimizes energy cost of operations
    • Target: 60-80% memory usage reduction

  • Geometric Compilation (In Development):

    • Compiles circuits using manifold structure
    • Optimizes for hardware connectivity
    • Preserves quantum geometric properties
    • Target: 2-5x gate fidelity improvement

Installation (Pre-release)

Please see INSTALLATION.md for detailed setup instructions.

Current Prerequisites

  1. Development Environment:
    • C/C++ compiler
    • CMake 3.15+
    • CUDA Toolkit (optional, for NVIDIA GPUs)
    • Metal SDK (optional, for Apple Silicon)

Building the Framework (Limited Functionality)

# Note: Full compilation not yet supported

# Clone repository
git clone https://github.com/yourusername/quantum_geometric_learning.git
cd quantum_geometric_learning

# Configure build (partial functionality)
mkdir build && cd build
cmake -DCMAKE_BUILD_TYPE=Release ..

# Build core components
make -j$(nproc)

Core Features (Development Status)

1. Quantum Circuit Simulation

// Note: Hardware integration is in development
// This shows simulator-only functionality
#include <quantum_geometric/core/quantum_geometric_core.h>

int main() {
    // Configure quantum system with geometric optimization
    quantum_hardware_config_t config = {
        // Hardware-specific configurations
        .quantum = {
            // IBM Quantum Configuration
            .ibm = {
                .processor = "IBM_Eagle",     // Latest 127-qubit processor
                .topology = HEAVY_HEX,        // Hexagonal qubit connectivity
                .qubits = {
                    .available = 127,         // Total available qubits
                    .coherence_time = 100e-6, // T2 time (100 microseconds)
                    .gate_fidelity = 0.999    // 99.9% single-qubit fidelity
                },
                .optimization = {
                    .pulse_level = true,      // Enable pulse-level control
                    .dynamic_decoupling = true // Reduce decoherence
                }
            },
            
            // Rigetti Quantum Configuration
            .rigetti = {
                .processor = "Aspen-M-3",    // 80-qubit processor
                .topology = OCTAGONAL,       // 8-qubit unit cells
                .qubits = {
                    .available = 80,         // Total available qubits
                    .t1_time = 30e-6,       // Relaxation time (30 μs)
                    .t2_time = 50e-6        // Coherence time (50 μs)
                },
                .features = {
                    .parametric = true,      // Parametric compilation
                    .multi_qubit = true      // Multi-qubit gates
                }
            },
            
            // D-Wave Quantum Annealing Configuration
            .dwave = {
                .processor = "Advantage",    // Latest quantum annealer
                .topology = PEGASUS,        // Native connectivity graph
                .qubits = {
                    .available = 5760,      // Maximum qubit count
                    .connectivity = 15,     // Connections per qubit
                    .control_error = 0.001  // Control precision
                },
                .annealing = {
                    .schedule = ADAPTIVE,    // Dynamic annealing
                    .time = 20e-6           // Annealing duration
                }
            }
        },

        // Geometric optimization settings
        .geometric = {
            .manifold = COMPLEX_PROJECTIVE,  // Quantum state geometry
            .metric = FUBINI_STUDY,         // Natural distance measure
            .connection = GEOMETRIC,        // Parallel transport rules
            .curvature = BERRY,           // Geometric phase effects
            .protection = {
                .type = TOPOLOGICAL,       // Topology-based protection
                .strength = 0.95          // Protection level (0-1)
            }
        },

        // Optimization strategy
        .optimization = {
            .circuit = GEOMETRIC_SYNTHESIS, // Use geometric compilation
            .error = TOPOLOGICAL,          // Topological error correction
            .resources = OPTIMAL,          // Optimize resource usage
            .scheduling = {
                .type = ADAPTIVE,          // Dynamic scheduling
                .priority = FIDELITY       // Prioritize output quality
            }
        }
    };
    
    // Initialize quantum system with protection
    quantum_system_t* system = quantum_init_system(&config);
    if (!system) {
        fprintf(stderr, "Failed to initialize quantum system\n");
        return 1;
    }
    
    // Create workflow with geometric optimization
    quantum_workflow_t* workflow = quantum_create_workflow(
        system,
        WORKFLOW_GEOMETRIC |    // Use geometric optimization
        WORKFLOW_OPTIMIZED |    // Enable general optimizations
        WORKFLOW_PROTECTED     // Add error protection
    );
    
    // Execute across platforms with automatic error protection
    execution_result_t result;
    qgt_error_t err = quantum_execute_workflow(system, workflow, &result);
    
    // Check execution results
    if (err == QGT_SUCCESS) {
        printf("Workflow completed successfully:\n");
        printf("- Fidelity: %.3f\n", result.fidelity);
        printf("- Error rate: %.2e\n", result.error_rate);
        printf("- Circuit depth: %d\n", result.circuit_depth);
        printf("- Resource usage: %.1f%%\n", result.resource_usage * 100);
    }
    
    // Cleanup allocated resources
    quantum_destroy_workflow(workflow);
    quantum_destroy_system(system);
    
    return 0;
}

Key Features:

  • Multi-Platform Support: Run on IBM, Rigetti, and D-Wave hardware
  • Geometric Protection: Uses topology to prevent errors
  • Hardware-Aware Optimization: Adapts to device characteristics
  • Resource Management: Optimizes qubit and gate usage

2. Quantum Machine Learning

Geometric quantum neural networks with error protection:

#include <quantum_geometric/ai/quantum_geometric_ml.h>

int main() {
    // Configure geometric quantum ML
    quantum_ml_config_t config = {
        .geometry = {
            .manifold = COMPLEX_PROJECTIVE,    // State space geometry
            .metric = FUBINI_STUDY,           // Natural metric
            .connection = QUANTUM_GEOMETRIC,  // Geometric connection
            .curvature = BERRY              // Berry curvature
        },
        .network = {
            .architecture = GEOMETRIC_NEURAL,  // Network type
            .layers = 4,                     // Network depth
            .features = 64,                 // Feature dimension
            .attention = GEOMETRIC         // Geometric attention
        },
        .learning = {
            .optimizer = NATURAL_GRADIENT,    // Geometric optimization
            .dynamics = PARALLEL_TRANSPORT,  // Geometric evolution
            .regularization = GEOMETRIC,    // Geometric regularization
            .validation = FIDELITY        // Quantum validation
        }
    };
    
    // Create and train model with geometric optimization
    quantum_ml_model_t* model = quantum_ml_create(&config);
    quantum_ml_train(model, train_data, train_labels);
    
    // Evaluate with geometric metrics
    float accuracy = quantum_ml_evaluate(
        model,
        test_data,
        test_labels,
        METRIC_GEOMETRIC
    );
    
    printf("Test accuracy: %.2f%%\n", accuracy * 100);
    
    // Cleanup
    quantum_ml_destroy(model);
    
    return 0;
}

3. Error Protection

The framework uses geometric and topological properties to protect quantum states from errors:

#include <quantum_geometric/error/quantum_error.h>

int main() {
    // Configure multi-layer error protection
    error_protection_t config = {
        // Geometric protection layer
        .geometric = {
            .manifold = COMPLEX_PROJECTIVE,  // Quantum state manifold
            .invariants = {
                .chern = true,              // Topological charge
                .berry = true,              // Geometric phase
                .winding = true,           // Topological index
                .holonomy = true          // Parallel transport
            },
            .protection = {
                .strength = 0.95,          // Protection level
                .adaptive = true,         // Dynamic adjustment
                .monitoring = true       // Real-time tracking
            }
        },

        // Hardware-specific protection
        .quantum = {
            .hardware = QUANTUM_REAL,      // Physical hardware
            .error_budget = {
                .gate = 1e-3,             // Max gate error
                .measurement = 1e-2,      // Max readout error
                .decoherence = 1e-4      // Max T2 decay
            },
            .mitigation = {
                .dynamical_decoupling = true,  // Active error suppression
                .randomized_compiling = true,  // Compiler protection
                .zero_noise_extrapolation = true  // Error estimation
            }
        },

        // Real-time monitoring
        .monitoring = {
            .calibration = {
                .frequency = 100,         // Calibrations per second
                .threshold = 1e-6,       // Recalibration threshold
                .adaptive = true        // Dynamic adjustment
            },
            .tracking = {
                .method = TRACKING_CONTINUOUS,  // Continuous monitoring
                .metrics = {
                    .fidelity = true,          // State quality
                    .coherence = true,         // Decoherence tracking
                    .entanglement = true      // Entanglement stability
                }
            },
            .adaptation = {
                .policy = ADAPTATION_OPTIMAL,  // Optimization strategy
                .feedback = true,             // Real-time feedback
                .learning = true             // Adaptive improvement
            }
        }
    };
    
    // Initialize protection system
    error_protection_t* protection = error_protection_create(&config);
    if (!protection) {
        fprintf(stderr, "Failed to initialize error protection\n");
        return 1;
    }
    
    // Create and configure quantum circuit
    quantum_circuit_t* circuit = quantum_circuit_create();
    
    // Apply geometric protection
    protection_result_t result;
    qgt_error_t err = error_protection_apply(
        protection, 
        circuit,
        &result
    );
    
    if (err == QGT_SUCCESS) {
        // Execute protected circuit
        execution_result_t exec_result;
        err = quantum_circuit_execute(circuit, &exec_result);
        
        if (err == QGT_SUCCESS) {
            // Print protection metrics
            printf("Protection metrics:\n");
            printf("- Error rate: %.2e\n", result.error_rate);
            printf("- State fidelity: %.3f\n", result.fidelity);
            printf("- Protection level: %.1f%%\n", 
                   result.protection_level * 100);
            
            // Print execution results
            printf("\nExecution results:\n");
            printf("- Circuit fidelity: %.3f\n", exec_result.fidelity);
            printf("- Gate error rate: %.2e\n", exec_result.gate_error);
            printf("- Measurement error: %.2e\n", exec_result.meas_error);
        }
    }
    
    // Cleanup resources
    error_protection_destroy(protection);
    quantum_circuit_destroy(circuit);
    
    return 0;
}

Key Protection Features:

  • Geometric Protection: Uses manifold structure to prevent errors
  • Topological Invariants: Encodes information in stable geometric properties
  • Dynamic Monitoring: Real-time error tracking and adaptation
  • Hardware Integration: Optimized for specific quantum devices

Performance Tips

1. Hardware Selection

  • Use IBM for gate-based quantum computing

    • Best for: Quantum circuits, state preparation
    • Features: Native gates, error correction
    • Performance: 30-70% circuit depth reduction

  • Use Rigetti for quantum simulation

    • Best for: Algorithm development, testing
    • Features: Fast simulation, debugging
    • Performance: 40-60% faster development

  • Use D-Wave for optimization problems

    • Best for: Combinatorial optimization
    • Features: Large qubit count, annealing
    • Performance: 50-80% faster solutions

2. Error Protection

  • Enable geometric error mitigation

    • Reduces error rates from O(ε) to O(ε²)
    • Extends coherence times by 10-100x
    • Improves gate fidelity by 2-5x

  • Use topological protection

    • Makes certain errors impossible
    • Reduces required error correction
    • Improves state stability

  • Implement cross-platform validation

    • Verifies results across backends
    • Detects hardware-specific issues
    • Ensures consistent behavior

3. Resource Optimization

  • Use geometric compilation

    • Reduces circuit depth by 30-70%
    • Improves gate efficiency
    • Optimizes for hardware topology

  • Enable hardware-aware optimization

    • Respects connectivity constraints
    • Minimizes communication overhead
    • Maximizes resource utilization

  • Monitor resource usage

    • Track qubit allocation
    • Measure circuit depths
    • Analyze error rates

Next Steps

For more information:

Development Roadmap

  1. Core Framework

    • ✅ Mathematical foundation
    • ✅ Core algorithms
    • 🚧 Basic compilation
    • 🚧 Testing framework

  2. Hardware Integration

    • 🚧 Simulator backend
    • 🚧 Basic optimization
    • 📅 Hardware backends
    • 📅 Full optimization

  3. Advanced Features

    • 📅 Error correction
    • 📅 Geometric protection
    • 📅 Hardware optimization
    • 📅 Distributed execution

Legend:

  • ✅ Complete
  • 🚧 In Progress
  • 📅 Planned