Quantum-Inspired Query Optimization

Executive Summary

This enables real-time analytics on complex queries that previously took minutes or hours.

Problem Being Solved

Core Problem: Complex queries with many JOINs become exponentially slow because traditional optimizers cannot find good execution plans in reasonable time.

Root Cause: Query optimization is an NP-hard combinatorial problem:

• Join Order Explosion: n tables have n! possible join orders (10 tables = 3.6 million combinations)
• Greedy Algorithms Fail: Traditional optimizers use heuristics that get stuck in local minima
• Cost Model Limitations: Cardinality estimation errors compound across joins
• Time Constraints: Optimizers must choose quickly, often picking suboptimal plans

HeliosDB Solution: Quantum-Inspired Optimization

Technical Architecture

HeliosDB Quantum-Inspired Query Optimizer:
┌─────────────────────────────────────────────────────────────┐
│                    SQL Query                                 │
└────────────────────────────┬────────────────────────────────┘
                             │
                             ▼
┌─────────────────────────────────────────────────────────────┐
│              Query Analysis & Encoding                       │
│  - Extract join graph structure                              │
│  - Encode as QUBO (Quadratic Unconstrained Binary Opt)      │
│  - Map to quantum circuit representation                     │
└────────────────────────────┬────────────────────────────────┘
                             │
        ┌────────────────────┼────────────────────┐
        │                    │                    │
        ▼                    ▼                    ▼
┌───────────────┐   ┌───────────────┐   ┌───────────────┐
│     QAOA      │   │    Grover     │   │     VQE       │
│ Join Order    │   │  Predicate    │   │    Cost       │
│ Optimization  │   │  Evaluation   │   │ Minimization  │
└───────┬───────┘   └───────┬───────┘   └───────┬───────┘
        │                    │                    │
        └────────────────────┼────────────────────┘
                             │
                             ▼
┌─────────────────────────────────────────────────────────────┐
│              Classical Post-Processing                       │
│  - Decode quantum results to execution plan                 │
│  - Apply local refinements                                  │
│  - Generate optimized physical plan                         │
└────────────────────────────┬────────────────────────────────┘
                             │
                             ▼
┌─────────────────────────────────────────────────────────────┐
│              Vectorized Execution Engine                     │
└─────────────────────────────────────────────────────────────┘

Algorithm Details

QAOA (Quantum Approximate Optimization Algorithm)

-- Enable quantum-inspired optimization
SET quantum_optimizer = 'qaoa';
SET qaoa_layers = 3;  -- Depth of quantum circuit

-- Complex multi-table join
SELECT c.name, o.total, p.description
FROM customers c
JOIN orders o ON c.id = o.customer_id
JOIN order_items oi ON o.id = oi.order_id
JOIN products p ON oi.product_id = p.id
JOIN suppliers s ON p.supplier_id = s.id
JOIN categories cat ON p.category_id = cat.id
JOIN regions r ON s.region_id = r.id
JOIN promotions pr ON o.promo_id = pr.id
WHERE o.date >= '2025-01-01'
  AND c.status = 'active';

-- QAOA finds near-optimal join order in O(poly(n)) instead of O(n!)

Grover-Inspired Search

-- Enable Grover-inspired predicate evaluation
SET grover_search = true;

-- Complex predicate with many constraints
SELECT * FROM transactions
WHERE amount > 1000
  AND merchant_category IN ('electronics', 'jewelry', 'travel')
  AND time_of_day BETWEEN '22:00' AND '04:00'
  AND location_risk_score > 0.7
  AND customer_age < 25
  AND is_first_purchase = true;

-- Grover provides quadratic speedup for constraint satisfaction
-- O(√N) instead of O(N) for finding matching rows

Concrete Examples

Example 1: Financial Fraud Detection

Query: Real-time fraud pattern detection across 12 tables

-- Fraud detection query (12-table join)
SELECT
    t.transaction_id,
    c.customer_name,
    fraud_score(t.*, c.*, m.*, d.*, l.*, h.*) AS risk_score
FROM transactions t
JOIN customers c ON t.customer_id = c.id
JOIN merchants m ON t.merchant_id = m.id
JOIN devices d ON t.device_id = d.id
JOIN locations l ON t.location_id = l.id
JOIN customer_history h ON c.id = h.customer_id
JOIN merchant_history mh ON m.id = mh.merchant_id
JOIN device_fingerprints df ON d.id = df.device_id
JOIN geo_risk gr ON l.geo_hash = gr.geo_hash
JOIN time_patterns tp ON t.hour = tp.hour
JOIN velocity_rules vr ON c.segment = vr.segment
JOIN fraud_models fm ON c.risk_tier = fm.tier
WHERE t.timestamp >= NOW() - INTERVAL '5 minutes'
  AND t.amount > 500;

-- Now possible to run per-transaction in batch

Example 2: Supply Chain Optimization

Company Profile: Global manufacturer with 50,000 SKUs

Query: Multi-echelon inventory optimization

-- Supply chain optimization query
WITH RECURSIVE supply_chain AS (
    -- Base: raw materials
    SELECT
        sku_id, supplier_id, lead_time, cost,
        1 AS level
    FROM raw_materials
    WHERE supplier_region = 'APAC'

    UNION ALL

    -- Recursive: assembly chain
    SELECT
        a.output_sku_id,
        sc.supplier_id,
        sc.lead_time + a.assembly_time,
        sc.cost + a.assembly_cost,
        sc.level + 1
    FROM supply_chain sc
    JOIN assemblies a ON sc.sku_id = a.input_sku_id
    WHERE sc.level < 10
)
SELECT
    sc.*,
    i.current_stock,
    f.forecast_demand,
    CASE
        WHEN i.current_stock < f.forecast_demand * sc.lead_time
        THEN 'REORDER'
        ELSE 'OK'
    END AS status
FROM supply_chain sc
JOIN inventory i ON sc.sku_id = i.sku_id
JOIN forecasts f ON sc.sku_id = f.sku_id
JOIN warehouses w ON i.warehouse_id = w.id
JOIN shipping_routes sr ON w.region = sr.origin
WHERE f.period = 'Q1-2025';

Example 3: Healthcare Analytics

Company Profile: Hospital network analyzing patient outcomes

-- Patient outcome correlation analysis
SELECT
    d.diagnosis_category,
    t.treatment_protocol,
    p.demographic_group,
    COUNT(DISTINCT o.patient_id) AS patient_count,
    AVG(o.recovery_days) AS avg_recovery,
    PERCENTILE_CONT(0.5) WITHIN GROUP (ORDER BY o.recovery_days) AS median_recovery,
    CORR(t.dosage, o.recovery_days) AS dosage_correlation
FROM outcomes o
JOIN patients p ON o.patient_id = p.id
JOIN diagnoses d ON o.diagnosis_id = d.id
JOIN treatments t ON o.treatment_id = t.id
JOIN providers pr ON o.provider_id = pr.id
JOIN facilities f ON pr.facility_id = f.id
JOIN insurance i ON p.insurance_id = i.id
JOIN comorbidities c ON p.id = c.patient_id
JOIN lab_results lr ON o.id = lr.outcome_id
JOIN imaging img ON o.id = img.outcome_id
WHERE o.discharge_date >= '2024-01-01'
GROUP BY d.diagnosis_category, t.treatment_protocol, p.demographic_group
HAVING COUNT(*) > 100
ORDER BY avg_recovery;

Conclusion

HeliosDB's quantum-inspired query optimization enables complex analytical queries that were previously impractical.

• Enable Real-Time Analytics: Complex queries in seconds, not minutes
• Improve Decision Quality: Faster insights, better decisions
• Reduce Infrastructure Costs: Same hardware, much faster results