examples

FSharp.Azure.Quantum Examples

Comprehensive examples organized by business value and technical complexity

This directory contains 60+ examples demonstrating the FSharp.Azure.Quantum library, organized from business-focused (Level 1) to research/educational (Level 4).

Example Categorization

Examples are categorized into 4 levels based on business utility and technical complexity:

• Level 1 - Business-Ready Solutions (Start Here!)
• Level 2 - Practical Optimization Problems
• Level 3 - Advanced Quantum Algorithms
• Level 4 - Research & Educational (Quantum Physics)

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Level 1: Business-Ready Solutions

For: Business analysts, product managers, enterprise developers
Goal: Solve real-world problems without quantum knowledge
Quantum Expertise Required: None (abstracted away)

Machine Learning & AI

Fraud Detection & Security

• BinaryClassification/FraudDetection.fsx START HERE
  Detect fraudulent transactions using quantum ML
  Use Case: Banking, e-commerce, insurance fraud detection
  ROI: Reduce fraud losses by 20-40%, improve detection accuracy
  Ready for: Production (with LocalBackend for <1000 transactions/sec)

• AnomalyDetection/SecurityThreatDetection.fsx
  Identify network intrusions and security threats
  Use Case: SIEM integration, real-time threat monitoring
  ROI: Detect zero-day attacks, reduce false positives by 30%

Customer Intelligence

• PredictiveModeling/CustomerChurnPrediction.fsx
  Predict which customers will cancel service
  Use Case: SaaS, telecom, subscription services
  ROI: Reduce churn by 15%, targeted retention campaigns

• SimilaritySearch/ProductRecommendations.fsx
  Find similar products for recommendations
  Use Case: E-commerce, content platforms
  ROI: Increase cross-sell/upsell by 25%, improve user engagement

AutoML

• AutoML/QuickPrototyping.fsx EASIEST START
  Zero-config machine learning - just provide data
  Use Case: Rapid prototyping, non-ML experts
  ROI: 10x faster model development, no ML expertise needed

• AutoML/CancellationAndProgressExample.fsx
  Production AutoML with progress tracking and cancellation
  Use Case: Long-running model searches, production ML pipelines

Workforce & Operations

Scheduling & Resource Allocation

• JobScheduling/ConstraintScheduler_Example.fsx RECOMMENDED
  Schedule employees/resources with hard and soft constraints
  Use Case: Workforce management, cloud VM allocation, manufacturing
  ROI: $25,000/hour savings (validated in powerplant optimization)

• JobScheduling/JobScheduling.fsx
  Task scheduling with dependencies and resource constraints
  Use Case: Project management, manufacturing workflows
  ROI: Minimize makespan, optimize resource utilization

Supply Chain & Logistics

• DeliveryRouting/DeliveryRouting.fsx
  Optimize delivery routes to minimize distance/time
  Use Case: Last-mile delivery, logistics planning
  ROI: 10-15% reduction in fuel costs, faster deliveries

• SupplyChain/SupplyChain.fsx
  Multi-echelon supply chain optimization
  Use Case: Warehouse allocation, distribution planning
  ROI: Reduce inventory costs by 20%, improve fill rates

• SupplyChain/SupplyChain-Small.fsx
  Small-scale supply chain example (faster execution)

Coverage & Set Cover

• CoverageOptimizer/CoverageOptimizer_Example.fsx NEW
  Minimum-cost set cover (facility placement, sensor deployment, test selection)
  Use Case: Facility placement, sensor networks, test suite minimization
  ROI: Minimize coverage costs while guaranteeing complete coverage

Pairing & Matching

• ResourcePairing/ResourcePairing_Example.fsx NEW
  Optimal pairing/matching maximizing compatibility scores
  Use Case: Mentor-mentee matching, team formation, interview scheduling
  ROI: Better team productivity through optimal skill alignment

Bin Packing & Loading

• PackingOptimizer/PackingOptimizer_Example.fsx NEW
  Minimize bins/containers needed to pack items
  Use Case: Container shipping, server allocation, storage optimization
  ROI: Reduce container/VM costs by minimizing wasted capacity

Network & Social Analysis

• GraphAnalytics/SocialNetworkAnalyzer_Example.fsx
  Detect communities and fraud rings in social networks
  Use Case: Marketing (influencer groups), fraud detection (collusion)
  ROI: Targeted campaigns, detect coordinated fraud schemes

Drug Discovery & Pharmaceutical

• DrugDiscovery/BindingAffinity.fsx 🧬 NEW
  VQE for protein-ligand binding energy calculation
  Quantum Advantage: ✅ Exponential (electron correlation)
  Use Case: Lead optimization, selectivity calculations

• DrugDiscovery/ReactionPathway.fsx 🧬 NEW
  VQE for drug metabolism (CYP450 activation barriers)
  Quantum Advantage: ✅ Exponential (transition state multiconfigurational)
  Use Case: Half-life prediction, metabolite identification

• DrugDiscovery/CaffeineEnergy.fsx 🧬 NEW
  Fragment Molecular Orbital VQE for caffeine (drug-like molecule)
  Quantum Advantage: ✅ Exponential (electron correlation)
  Use Case: Lead optimization, fragment-based drug design

• DrugDiscovery/DrugDiscoverySolvers_Example.fsx NEW
  QAOA-based drug discovery: independent set (toxicity), influence maximization (target ID), diverse selection (library design)
  Use Case: Hit-to-lead filtering, target pathway analysis, compound library diversification
  ROI: Accelerate early-stage pipeline with quantum-classical hybrid screening

• DrugDiscovery/MolecularSimilarity.fsx
  Quantum kernel similarity for virtual screening
  Quantum Advantage: ⚠️ Unproven on NISQ
  Recommendation: Use classical Tanimoto for production

Financial Risk Management

• FinancialRisk/QuantumVaR.fsx 📊
  Value-at-Risk with quantum amplitude estimation
  Quantum Advantage: ✅ Quadratic O(1/ε) vs O(1/ε²)
  Use Case: Regulatory capital (Basel III)

• FinancialRisk/StressTesting.fsx 📊 NEW
  Multi-scenario stress testing (9 crisis scenarios)
  Quantum Advantage: ✅ Quadratic (amplitude estimation)
  Use Case: CCAR/DFAST regulatory compliance

• FinancialRisk/ExoticOptions.fsx 📊 NEW
  Barrier and lookback options with Greeks
  Quantum Advantage: ✅ Quadratic (path-dependent MC)
  Use Case: Exotic derivatives pricing

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Level 2: Practical Optimization Problems

For: Developers, data scientists, operations research professionals
Goal: Solve combinatorial optimization with quantum acceleration
Quantum Expertise Required: Minimal (basic QAOA understanding helpful)

Classic NP-Hard Problems

Graph Problems

• GraphColoring/GraphColoring.fsx WELL-DOCUMENTED
  Register allocation, frequency assignment, exam scheduling
  Use Case: Compiler optimization, wireless networks, university timetabling
  Algorithm: QAOA (Quantum Approximate Optimization Algorithm)

• MaxCut/MaxCut.fsx
  Graph partitioning for load balancing and circuit design
  Use Case: Circuit partitioning, community detection
  Algorithm: QAOA with D-Wave quantum annealer support

• MaxCut/DWaveMaxCutExample.fsx
  MaxCut using D-Wave quantum annealer (2000+ qubits!)
  Hardware: D-Wave Advantage (5640 qubits)
  Note: Real quantum hardware example

Routing & Assignment

• Knapsack/Knapsack.fsx
  0/1 Knapsack - resource allocation, cargo loading
  Use Case: Portfolio selection, capacity planning

• InvestmentPortfolio/InvestmentPortfolio.fsx
  Financial portfolio optimization with risk/return tradeoff
  Use Case: Asset allocation, investment management

• InvestmentPortfolio/InvestmentPortfolio-Small.fsx
  Smaller portfolio example (faster prototyping)

Constraint Satisfaction

• ConstraintSolver/SudokuSolver.fsx
  SAT solving with Grover's algorithm (Sudoku as example)
  Algorithm: Quantum SAT solver with Grover search

Quantum ML Building Blocks

• QML/VQCExample.fsx
  Variational Quantum Classifier training pipeline
  Use Case: Custom quantum ML models, research

• QML/FeatureMapExample.fsx
  Quantum feature encoding demonstrations

• QML/VariationalFormExample.fsx
  Ansatz circuit design for VQC

Visualization & Debugging

• GraphColoring/GraphColoring-Visualization.fsx
  Visualize graph coloring problems and solutions

• GraphColoring/ProblemAndSolutionVisualization.fsx
  Mermaid diagram generation for problems/solutions

• GraphColoring/QuboVisualization.fsx
  Understand QUBO encoding for graph coloring

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Level 3: Advanced Quantum Algorithms

For: Quantum algorithm researchers, PhD students, quantum enthusiasts
Goal: Explore advanced quantum computing techniques
Quantum Expertise Required: Moderate to High

Quantum Search & Optimization

• Algorithms/Grover_GraphColoring_Example.fsx
  Grover's algorithm applied to graph coloring
  Complexity: O(√N) speedup over classical search

• Algorithms/Grover_SAT_Example.fsx
  Boolean satisfiability with quantum search
  Theory: Amplitude amplification

• TreeSearch/GameAI.fsx
  Quantum tree search for game AI
  Use Case: Chess, Go, decision tree exploration

• PatternMatcher/ConfigurationOptimizer.fsx
  Quantum pattern matching for configuration optimization

Quantum Chemistry & Simulation

• Chemistry/H2Molecule.fsx
  VQE (Variational Quantum Eigensolver) for molecular ground state
  Molecule: Hydrogen (H₂)

• Chemistry/H2GroundState.fsx
  Alternative H₂ ground state calculation

• Chemistry/H2OWater.fsx
  Water molecule (H₂O) quantum simulation
  Complexity: 10 qubits (requires cloud backend)

• Chemistry/ElectronTransportChain.fsx 🧬 NEW
  VQE for cytochrome Fe2+/Fe3+ redox chemistry
  Quantum Advantage: ✅ Exponential (d-orbital correlation, spin states)
  Use Case: Mitochondrial dysfunction targets, antimicrobial respiration
  Biochemistry: Harper's Ch.12-13 (Biologic Oxidation, Respiratory Chain)

• Chemistry/HamiltonianTimeEvolution.fsx
  Time evolution of molecular systems

• Chemistry/H2_UCCSD_VQE_Example.fsx
  UCCSD (Unitary Coupled Cluster) ansatz for H₂

• Chemistry/UCCSDExample.fsx
  Complete UCCSD workflow

• Chemistry/HartreeFockInitialStateExample.fsx
  Hartree-Fock initial state preparation

Quantum Arithmetic & Cryptography

• QuantumArithmetic/RSAEncryption.fsx
  Quantum arithmetic for RSA operations

• CryptographicAnalysis/RSAFactorization.fsx
  Shor's algorithm for RSA factorization
  Security Implication: Breaks RSA-2048 (with 4096+ qubits)

• CryptographicAnalysis/DiscreteLogAttack.fsx
  Quantum discrete logarithm attack using Shor's algorithm
  Security Implication: Breaks Diffie-Hellman and DSA key exchange

• CryptographicAnalysis/GroverAESThreat.fsx
  Grover's algorithm threat to AES symmetric encryption
  Security Implication: Halves AES key strength (AES-128 → 64-bit security)

• CryptographicAnalysis/ECCBitcoinThreat.fsx
  Quantum ECDLP threat to Bitcoin/cryptocurrency elliptic curve cryptography
  Security Implication: Breaks secp256k1 (~2,330 logical qubits needed)
  Uses NBitcoin for real secp256k1 key pairs, addresses, and ECDSA signatures

• CryptographicAnalysis/QuantumMining.fsx
  Quantum Proof-of-Work mining using Grover's algorithm to break simplified Bitcoin-like puzzles
  Security Implication: Quadratic speedup for mining (2^70 → 2^35), but not near-term feasible
  Uses SHA-256 hashing with NBitcoin for real Bitcoin block structure comparison

Quantum Phase Estimation

• PhaseEstimation/MolecularEnergy.fsx
  QPE (Quantum Phase Estimation) for molecular energies

Linear Algebra & Systems

• LinearSystemSolver/HHLAlgorithm.fsx
  HHL algorithm for solving linear systems
  Speedup: Exponential over classical (for specific systems)

• LinearSystemSolver/HHL_Extensions_Rigetti_Example.fsx
  HHL with Rigetti backend extensions

Quantum Communication & Security

• Protocols/BB84_Complete_Pipeline_Example.fsx Complete BB84 quantum key distribution protocol
  Use Case: Secure communication, quantum cryptography

• Protocols/BB84_Issue_Fix_Verification.fsx
  Verification tests for BB84 implementation

• Protocols/QuantumTeleportationExample.fsx
  Quantum teleportation protocol

Finance & Risk

• FinancialRisk/OptionPricing.fsx
  Monte Carlo option pricing with quantum acceleration

• QuantumDistributions/QuantumDistributions.fsx
  Load probability distributions into quantum states

Parameter Optimization

• Optimization/QaoaParameterOptimizationExample.fsx
  QAOA parameter tuning strategies

• IntegerVariables/IntegerVariablesExample.fsx
  Encoding integer variables in QUBO

• IntegerVariables/test-encoding.fsx
  Test integer encoding strategies

• IntegerVariables/verify-fix.fsx
  Verification for integer variable encoding

Sparse QUBO & Problem Decomposition

• SparseQubo/SparseQubo_Example.fsx NEW
  Sparse QUBO encoding pipeline: coordinate-list (COO) representation, density analysis, and conversion to standard QUBO
  Use Case: Large-scale optimization where QUBO matrices are >95% sparse
  Algorithm: COO-based storage with O(nnz) operations instead of O(n²)

• ProblemDecomposition/ProblemDecomposition_Example.fsx NEW
  Automatic problem decomposition: splits large QUBOs into sub-problems that fit backend qubit limits, solves independently, and merges results
  Use Case: Run 50+ variable problems on 16-qubit LocalBackend via divide-and-conquer
  Algorithm: Graph-based partitioning with budget-aware execution orchestration

Quantum Circuit Building

• CircuitBuilder/QuantumCircuits.fsx
  Low-level quantum circuit construction

• CircuitBuilder/CircuitVisualization.fsx
  Visualize quantum circuits (Mermaid, ASCII)

Azure Quantum Integration

• AzureQuantumWorkspace/WorkspaceExample.fsx
  Cloud quantum hardware (IonQ, Rigetti, Quantinuum, Atom Computing)
  Features: Quota management, job submission, circuit conversion

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Level 4: Research & Educational (Quantum Physics)

For: Quantum physics students, topological quantum computing researchers
Goal: Understand fundamental quantum mechanics and exotic quantum models
Quantum Expertise Required: Advanced (graduate-level physics)

Topological Quantum Computing

• Topological/TopologicalExample.fsx
  Introduction to anyon braiding and topological qubits

• Topological/ToricCodeExample.fsx ⭐ EDUCATIONAL
  Toric code error correction
  Theory: Surface codes, topological protection

• Topological/ModularDataExample.fsx
  Modular S and T matrices (topological invariants)
  Theory: Modular tensor categories, fusion rules

• Topological/TopologicalVisualization.fsx
  Visualize anyon braiding operations

Topological Backend Examples

• Topological/BellState.fsx
  Bell state using topological qubits

• Topological/BasicFusion.fsx
  Anyon fusion demonstrations

• Topological/BackendComparison.fsx
  Compare gate-based vs topological backends

• Topological/FormatDemo.fsx
  Topological circuit file format (.tqp)

Educational Quantum Algorithms

• Algorithms/BellStatesExample.fsx
  Bell states and quantum entanglement

• Algorithms/DeutschJozsaExample.fsx
  Deutsch-Jozsa algorithm (first quantum advantage proof)

Game Examples (Educational)

• Kasino/Kasino.fsx
  Card game with quantum decision-making

• Gomoku/ (F# project)
  Board game AI with quantum tree search

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Quick Start Guides

For Business Users (Start Here!)

Step 1: Install the library

dotnet add package FSharp.Azure.Quantum

Step 2: Run the easiest example (AutoML)

cd examples/AutoML
dotnet fsi QuickPrototyping.fsx

Step 3: Try a business problem

cd examples/BinaryClassification
dotnet fsi FraudDetection.fsx

For Developers

Step 1: Explore optimization problems

cd examples/GraphColoring
dotnet fsi GraphColoring.fsx

Step 2: Compare quantum vs classical

cd examples/MaxCut
dotnet fsi MaxCut.fsx

Step 3: Try cloud quantum hardware

cd examples/AzureQuantumWorkspace
# Edit WorkspaceExample.fsx with your Azure credentials
dotnet fsi WorkspaceExample.fsx

For Researchers

Step 1: Quantum chemistry

cd examples/Chemistry
dotnet fsi H2Molecule.fsx

Step 2: Advanced algorithms

cd examples/LinearSystemSolver
dotnet fsi HHLAlgorithm.fsx

Step 3: Topological quantum computing

dotnet fsi ToricCodeExample.fsx

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Running Examples

Prerequisites

# Install .NET 8.0+
dotnet --version

# Install FSharp.Azure.Quantum
dotnet add package FSharp.Azure.Quantum

Running Individual Examples

# Navigate to example directory
cd examples/BinaryClassification

# Run with F# Interactive
dotnet fsi FraudDetection.fsx

Running All Examples (Validation)

# From examples/ directory
dotnet fsi test-all-examples.fsx

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🎓 Learning Path Recommendations

Beginner Path (Business Focus)

1. AutoML/QuickPrototyping.fsx - Easiest start
2. BinaryClassification/FraudDetection.fsx - Real use case
3. JobScheduling/ConstraintScheduler_Example.fsx - Optimization intro
4. CoverageOptimizer/CoverageOptimizer_Example.fsx - Set cover problems
5. ResourcePairing/ResourcePairing_Example.fsx - Matching & pairing
6. GraphColoring/GraphColoring.fsx - Classic problem

Developer Path (Quantum Optimization)

1. GraphColoring/GraphColoring.fsx - Best documented
2. MaxCut/MaxCut.fsx - Graph partitioning
3. Knapsack/Knapsack.fsx - Classic NP problem
4. PackingOptimizer/PackingOptimizer_Example.fsx - Bin packing
5. DrugDiscovery/DrugDiscoverySolvers_Example.fsx - QAOA drug discovery
6. MaxCut/DWaveMaxCutExample.fsx - Real quantum hardware

Research Path (Quantum Algorithms)

1. Algorithms/BellStatesExample.fsx - Quantum basics
2. Algorithms/Grover_SAT_Example.fsx - Quantum search
3. SparseQubo/SparseQubo_Example.fsx - Sparse QUBO pipeline
4. ProblemDecomposition/ProblemDecomposition_Example.fsx - Auto-decomposition
5. Chemistry/H2Molecule.fsx - VQE
6. Topological/ToricCodeExample.fsx - Topological qubits

Expert Path (Full Stack)

1. CircuitBuilder/ - Low-level circuits
2. AzureQuantumWorkspace/ - Cloud infrastructure
3. Topological/ - Exotic quantum models
4. CryptographicAnalysis/ - Quantum cryptographic attacks (RSA, ECC, AES, discrete log)

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License

All examples are part of FSharp.Azure.Quantum library.
License: Unlicense (Public Domain)