Business Problem Builders

High-level APIs for common business applications powered by quantum algorithms and quantum machine learning.

Overview

Business Problem Builders provide domain-specific APIs that hide quantum complexity while delivering quantum-enhanced solutions for real-world business problems. These builders leverage:

• Quantum Machine Learning - VQC, quantum kernels for classification and regression
• Grover’s Search - Quantum search for pattern matching and optimization
• Hybrid Approaches - Automatic classical/quantum routing based on problem characteristics

Target Audience: Business analysts, data scientists, application developers who want quantum benefits without quantum expertise.

Available Builders

1. AutoML - Automated Machine Learning

2. Binary Classification - Fraud Detection, Spam Filtering

3. Anomaly Detection - Security Threats, Quality Control

4. Predictive Modeling - Churn Prediction, Demand Forecasting

5. Similarity Search - Recommendations, Semantic Search

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AutoML - Automated Machine Learning

What is AutoML?

AutoML automatically selects the best machine learning approach for your data:

What AutoML Does:

1. Analyzes your dataset characteristics
2. Tries multiple approaches (binary classification, regression, anomaly detection)
3. Tests quantum and classical architectures
4. Tunes hyperparameters automatically
5. Returns best model with performance metrics

When to Use:

• Quick prototyping (“just give me a working model”)
• You don’t know which ML algorithm to use
• Model selection (compare all approaches)
• Establishing performance baselines

API Reference

open FSharp.Azure.Quantum.Business
open FSharp.Azure.Quantum.Business.AutoML

// Minimal usage - "zero config ML"
let result = autoML {
    trainWith features labels
}

match result with
| Ok automlResult ->
    printfn "Best Model: %s" automlResult.BestModelType
    printfn "Architecture: %A" automlResult.BestArchitecture
    printfn "Validation Score: %.2f%%" (automlResult.Score * 100.0)
    printfn "Training Time: %.1fs" automlResult.TotalSearchTime.TotalSeconds
    
    // Use best model for predictions
    let prediction = AutoML.predict automlResult.BestModel newData
    
| Error err -> eprintfn "AutoML failed: %A" err

Configuration Options

// Advanced configuration
let result = autoML {
    trainWith trainFeatures trainLabels
    
    // Search space
    tryArchitectures [Quantum; Classical; Hybrid]
    tryTaskTypes [BinaryClassification; MultiClass; Regression; AnomalyDetection]
    
    // Resource limits
    maxTrials 50
    maxTime (TimeSpan.FromMinutes 10.0)
    
    // Validation
    validationSplit 0.2
    metric Accuracy  // or Precision, Recall, F1Score, RMSE
    
    // Optimization
    enableEarlyStop true
    patience 5
}

AutoML Search Process

1. Data Analysis

• Feature count and dimensionality
• Label distribution (classification vs regression)
• Dataset size (determines architecture candidates)

2. Architecture Search

• Quantum: VQC with various feature maps and variational forms
• Classical: SVM, decision trees, logistic regression
• Hybrid: Quantum kernels with classical SVM

3. Hyperparameter Tuning

• Learning rate (0.001 - 0.5)
• Depth (1-5 for quantum circuits)
• Shots (100-10000 for quantum)
• Regularization parameters

4. Validation

• Cross-validation or train/validation split
• Multiple metrics computed (accuracy, precision, recall, F1)
• Best model selected by primary metric

Working Example

See complete example: examples/AutoML/QuickPrototyping.fsx

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Binary Classification

What is Binary Classification?

Classify data into two categories (e.g., fraud/legitimate, spam/ham, churn/retain).

Business Applications:

• Fraud detection (credit card transactions)
• Spam filtering (email, SMS)
• Customer churn prediction
• Disease diagnosis (positive/negative)
• Quality control (defect detection)

API Reference

open FSharp.Azure.Quantum.Business.BinaryClassifier

// Minimal configuration - smart defaults
let result = binaryClassification {
    trainWith trainFeatures trainLabels
}

match result with
| Ok classifier ->
    printfn "Training accuracy: %.2f%%" (classifier.Metadata.TrainingAccuracy * 100.0)
    
    // Classify new data
    let newTransaction = [| 600.0; 14.5; 7.0; 80.0; 12.0 |]
    
    match BinaryClassifier.predict classifier newTransaction with
    | Ok prediction ->
        printfn "Class: %d (confidence: %.2f%%)" 
            prediction.Class 
            (prediction.Confidence * 100.0)
    | Error err -> eprintfn "Error: %s" err.Message
    
| Error err -> eprintfn "Training failed: %s" err.Message

Configuration Options

// Advanced configuration
let result = binaryClassification {
    trainWith trainFeatures trainLabels
    
    // Architecture selection
    architecture Quantum  // or Classical, Hybrid, AutoSelect
    
    // Quantum-specific (when architecture = Quantum)
    featureMap (ZZFeatureMap 2)
    variationalForm (RealAmplitudes 2)
    
    // Training configuration
    learningRate 0.1
    maxEpochs 50
    convergenceThreshold 0.001
    shots 1000
    
    // Optimizer
    optimizer Adam  // or SGD
    
    // Validation
    validationSplit 0.2
    
    // Class imbalance handling
    classWeights [| 1.0; 3.0 |]  // Penalize misclassifying class 1 more
}

Example: Fraud Detection

// Feature engineering for credit card transactions
// Features: [amount, time_of_day, merchant_category, distance_from_home, frequency]

let normalTransactions = [|
    [| 50.0; 12.0; 2.0; 5.0; 3.0 |]   // Small, daytime, grocery, nearby
    [| 75.0; 18.0; 3.0; 8.0; 2.0 |]   // Medium, evening, gas, nearby
    // ... 40 normal transactions
|]

let fraudulentTransactions = [|
    [| 800.0; 3.0; 7.0; 150.0; 15.0 |]  // Large, late night, unusual, far away
    [| 600.0; 2.0; 9.0; 200.0; 20.0 |]  // Large, very late, unusual, very far
    // ... 10 fraudulent transactions
|]

let trainX = Array.append normalTransactions fraudulentTransactions
let trainY = Array.append (Array.create 40 0) (Array.create 10 1)

// Train fraud detector
let result = binaryClassification {
    trainWith trainX trainY
    architecture Quantum
    classWeights [| 1.0; 5.0 |]  // False negatives (missing fraud) are costly!
}

match result with
| Ok model ->
    // Deploy model for real-time fraud scoring
    let scoreTransaction transaction =
        match BinaryClassifier.predict model transaction with
        | Ok pred when pred.Class = 1 && pred.Confidence > 0.8 ->
            "BLOCK - High fraud risk"
        | Ok pred when pred.Class = 1 && pred.Confidence > 0.5 ->
            "REVIEW - Medium fraud risk"
        | Ok pred -> 
            "APPROVE - Low fraud risk"
        | Error _ -> 
            "ERROR - Manual review required"
    
    // Score new transaction
    let newTx = [| 650.0; 2.5; 8.0; 180.0; 18.0 |]
    printfn "%s" (scoreTransaction newTx)
    
| Error err -> eprintfn "Training failed: %s" err.Message

Working Example

See complete example: examples/BinaryClassification/FraudDetection.fsx

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Anomaly Detection

What is Anomaly Detection?

Identify unusual patterns that don’t conform to expected behavior.

Business Applications:

• Security threat detection (network intrusion, unusual access)
• Equipment failure prediction (sensor anomalies)
• Quality control (manufacturing defects)
• Healthcare monitoring (abnormal vital signs)

API Reference

open FSharp.Azure.Quantum.Business.AnomalyDetector

// Train on normal data only
let result = anomalyDetection {
    trainWith normalData  // Only normal samples, no labels
    
    // Sensitivity (how strict is "anomaly"?)
    threshold 0.05  // 5% most unusual are anomalies
    
    // Feature engineering
    features ["cpu_usage"; "memory"; "network_io"; "disk_io"]
    
    // Detection method
    method QuantumKernel  // or Classical, Hybrid
}

match result with
| Ok detector ->
    // Check new data point
    let newSample = [| 95.0; 8000.0; 15000.0; 200.0 |]  // High CPU usage
    
    match AnomalyDetector.detect detector newSample with
    | Ok result ->
        if result.IsAnomaly then
            printfn "ANOMALY DETECTED"
            printfn "  Anomaly score: %.4f" result.AnomalyScore
            printfn "  Distance from normal: %.2f sigma" result.DeviationSigma
        else
            printfn "Normal behavior (score: %.4f)" result.AnomalyScore
    | Error err -> eprintfn "Detection error: %s" err.Message
    
| Error err -> eprintfn "Training failed: %s" err.Message

Configuration Options

let result = anomalyDetection {
    trainWith normalData
    
    // Detection threshold
    threshold 0.05           // Top 5% unusual = anomaly
    contamination 0.02       // Expected % of anomalies in training data
    
    // Method selection
    method QuantumKernel     // Quantum feature space for similarity
    
    // Quantum configuration
    featureMap (ZZFeatureMap 2)
    shots 1000
    
    // Sensitivity tuning
    sensitivity High         // Low, Medium, High, VeryHigh
}

Example: Network Intrusion Detection

// Monitor server metrics for unusual activity
let normalServerMetrics = [|
    [| 45.0; 4000.0; 5000.0; 100.0 |]   // Normal: CPU, Memory, Network, Disk
    [| 50.0; 4200.0; 5500.0; 110.0 |]
    [| 42.0; 3900.0; 4800.0; 95.0 |]
    // ... 100 normal operation samples
|]

let result = anomalyDetection {
    trainWith normalServerMetrics
    features ["cpu_percent"; "memory_mb"; "network_kb_s"; "disk_io_ops"]
    threshold 0.05  // Top 5% unusual
    method QuantumKernel
}

match result with
| Ok detector ->
    // Real-time monitoring
    let monitorMetrics currentMetrics =
        match AnomalyDetector.detect detector currentMetrics with
        | Ok result when result.IsAnomaly && result.AnomalyScore > 0.9 ->
            // Critical anomaly
            sendAlert "CRITICAL: Possible intrusion detected"
        | Ok result when result.IsAnomaly ->
            // Minor anomaly
            logWarning $"Unusual activity (score: {result.AnomalyScore})"
        | Ok _ ->
            // Normal
            ()
        | Error err ->
            logError err.Message
    
    // Check current server state
    let current = [| 98.0; 7800.0; 25000.0; 500.0 |]  // Suspicious!
    monitorMetrics current
    
| Error err -> eprintfn "Setup failed: %s" err.Message

Working Example

See complete example: examples/AnomalyDetection/

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Predictive Modeling

What is Predictive Modeling?

Forecast future outcomes based on historical patterns.

Business Applications:

• Customer churn prediction
• Demand forecasting
• Sales predictions
• Equipment maintenance scheduling
• Resource capacity planning

API Reference

open FSharp.Azure.Quantum.Business.PredictiveModel

// Train predictive model
let result = predictiveModel {
    trainWith historicalData historicalOutcomes
    
    // Model type
    modelType Regression  // or Classification
    
    // Features
    features ["tenure_months"; "monthly_spend"; "support_calls"; "satisfaction"]
    target "will_churn"
    
    // Architecture
    architecture Hybrid  // Quantum features + classical regression
}

match result with
| Ok model ->
    printfn "Model R² score: %.2f" model.Metrics.RSquared
    printfn "Mean error: %.2f" model.Metrics.MAE
    
    // Predict for new customer
    let newCustomer = [| 6.0; 45.0; 3.0; 6.5 |]
    
    match PredictiveModel.predict model newCustomer with
    | Ok prediction ->
        printfn "Churn probability: %.2f%%" (prediction.Value * 100.0)
        printfn "Confidence interval: [%.2f, %.2f]" 
            prediction.LowerBound 
            prediction.UpperBound
    | Error err -> eprintfn "Error: %s" err.Message
    
| Error err -> eprintfn "Training failed: %s" err.Message

Configuration Options

let result = predictiveModel {
    trainWith trainX trainY
    
    // Model configuration
    modelType Regression
    architecture Quantum
    
    // Feature engineering
    features featureNames
    target targetName
    normalizeFeatures true
    
    // Training
    learningRate 0.1
    maxEpochs 100
    validationSplit 0.2
    
    // Regularization (prevent overfitting)
    l2Penalty 0.01
    dropoutRate 0.1
}

Example: Customer Churn Prediction

// Historical customer data
// Features: [tenure_months, monthly_spend, support_calls, usage_hours, satisfaction]
let customerHistory = [|
    [| 24.0; 75.0; 1.0; 20.0; 8.5 |]; 0.0  // Stayed
    [| 6.0; 45.0; 5.0; 5.0; 3.0 |]; 1.0    // Churned
    [| 36.0; 120.0; 0.0; 30.0; 9.0 |]; 0.0 // Stayed
    // ... 1000 historical customers
|]

let trainX = customerHistory |> Array.map fst
let trainY = customerHistory |> Array.map snd

let result = predictiveModel {
    trainWith trainX trainY
    
    features [
        "tenure_months"
        "monthly_spend"
        "support_calls"
        "usage_hours"
        "satisfaction_score"
    ]
    target "will_churn"
    
    modelType BinaryClassification
    architecture Quantum
    
    // Business constraint: False negatives costly (missed churn)
    classWeights [| 1.0; 3.0 |]
}

match result with
| Ok model ->
    // Churn risk scoring for current customers
    let scoreChurnRisk customer =
        match PredictiveModel.predict model customer with
        | Ok pred when pred.Value > 0.7 ->
            "HIGH RISK - Immediate retention campaign"
        | Ok pred when pred.Value > 0.4 ->
            "MEDIUM RISK - Monitor and engage"
        | Ok pred ->
            "LOW RISK - Routine engagement"
        | Error _ ->
            "ERROR - Manual review"
    
    // Score at-risk customer
    let atRiskCustomer = [| 8.0; 40.0; 4.0; 8.0; 4.5 |]
    printfn "%s" (scoreChurnRisk atRiskCustomer)
    
| Error err -> eprintfn "Model training failed: %s" err.Message

Working Example

See complete example: examples/PredictiveModeling/CustomerChurnPrediction.fsx

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Similarity Search

What is Similarity Search?

Find items similar to a query item based on features.

Business Applications:

• Product recommendations
• Document similarity (semantic search)
• Image matching
• Customer segmentation
• Duplicate detection

API Reference

open FSharp.Azure.Quantum.Business.SimilaritySearch

// Build similarity index
let result = similaritySearch {
    indexItems catalogItems
    
    // Features to compare
    features ["category"; "price"; "rating"; "description_embedding"]
    
    // Similarity metric
    similarityMetric QuantumKernel  // or Cosine, Euclidean
    
    // Index optimization
    buildIndex true  // Pre-compute for fast queries
}

match result with
| Ok searchIndex ->
    // Find similar products
    let queryItem = [| 2.0; 49.99; 4.5; embeddingVector |]
    
    match SimilaritySearch.findSimilar searchIndex queryItem 5 with  // Top 5
    | Ok results ->
        printfn "Similar items:"
        results |> Array.iter (fun r ->
            printfn "  - Item %d (similarity: %.2f%%)" r.ItemId (r.Score * 100.0)
        )
    | Error err -> eprintfn "Search error: %s" err.Message
    
| Error err -> eprintfn "Index build failed: %s" err.Message

Configuration Options

let result = similaritySearch {
    indexItems items
    
    // Similarity method
    similarityMetric QuantumKernel  // Quantum feature space
    
    // Quantum kernel configuration
    featureMap (ZZFeatureMap 2)
    shots 1000
    
    // Index optimization
    buildIndex true
    indexMethod ApproximateNearestNeighbor  // Fast for large catalogs
    
    // Pre-filtering
    filterByCategory true
    categoryFeatureIndex 0
}

Example: Product Recommendations

// Product catalog features
// [category_id, price, rating, popularity, feature_vec...]
let catalog = [|
    [| 1.0; 29.99; 4.5; 850.0; 0.1; 0.8; 0.3 |]  // Electronics
    [| 1.0; 49.99; 4.8; 1200.0; 0.2; 0.9; 0.4 |] // Electronics
    [| 2.0; 15.99; 4.2; 300.0; 0.7; 0.2; 0.1 |]  // Books
    // ... 10,000 products
|]

let result = similaritySearch {
    indexItems catalog
    features ["category"; "price"; "rating"; "popularity"; "f1"; "f2"; "f3"]
    similarityMetric QuantumKernel
    buildIndex true
}

match result with
| Ok index ->
    // User viewed a product - find similar items
    let viewedProduct = catalog.[42]
    
    match SimilaritySearch.findSimilar index viewedProduct 10 with
    | Ok recommendations ->
        printfn "Customers who viewed this also liked:"
        recommendations 
        |> Array.take 5  // Top 5
        |> Array.iter (fun r ->
            printfn "  - Product %d (%.0f%% match)" r.ItemId (r.Score * 100.0)
        )
    | Error err -> eprintfn "Recommendation error: %s" err.Message
    
| Error err -> eprintfn "Index failed: %s" err.Message

Working Example

See complete example: examples/SimilaritySearch/

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Architecture Selection Guide

When to Use Each Architecture

Quantum:

• High-dimensional feature spaces (>10 features)
• Complex feature correlations
• Pattern recognition requires expressive models
• Willing to trade speed for potential accuracy gains

Classical:

• Simple, low-dimensional problems (<5 features)
• Large datasets (>10,000 samples)
• Real-time inference critical (< 100ms)
• Interpretability paramount

Hybrid:

• Medium complexity (5-10 features)
• Want quantum benefits without full overhead
• Quantum kernels + classical SVM
• Best of both worlds for many tasks

AutoSelect:

• Unsure which is best
• Let library decide based on data characteristics
• Automatic fallback if quantum resources limited

Performance Comparison

Architecture	Training Time	Inference Time	Accuracy (Typical)	Resource Usage
Quantum	Minutes-Hours	Seconds	85-95%	High (quantum backend)
Classical	Seconds-Minutes	Milliseconds	80-90%	Low (CPU only)
Hybrid	Minutes	Hundreds of ms	83-93%	Medium

Troubleshooting

Common Issues

1. Poor Accuracy (<60%)

Symptoms: Model performs poorly on both train and test sets

Solutions:

• Increase model complexity (use Quantum or Hybrid)
• Add more features (better feature engineering)
• Collect more training data
• Check data quality (labels correct?)
• Try AutoML to find best approach

2. Overfitting (High Train, Low Test Accuracy)

Symptoms: Train accuracy >90%, test accuracy <70%

Solutions:

• Increase training data
• Add regularization (L2 penalty, dropout)
• Reduce model complexity (use Classical)
• Increase validation split
• Use cross-validation

3. Slow Training

Symptoms: Training takes hours

Solutions:

• Use smaller shots (100 instead of 1000) during training
• Reduce max epochs
• Use Classical or Hybrid architecture
• Enable early stopping
• Reduce dataset size (sample if very large)

4. Class Imbalance (Fraud Detection)

Symptoms: Model always predicts majority class

Solutions:

• Set classWeights to penalize minority class more
• Use SMOTE or oversampling for minority class
• Adjust decision threshold (lower for rare events)
• Use precision/recall instead of accuracy as metric

See Also

• Quantum Machine Learning - VQC, Quantum Kernels, Feature Maps
• Getting Started Guide - Installation and setup
• API Reference - Complete API documentation
• Working Examples - Complete code examples

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Last Updated: December 2025