3.0 KiB
Quantum-Hybrid HNSW (Theoretical) - Results
Simulation ID: quantum-hybrid
Iterations: 3 | Time: 6,142 ms
⚠️ DISCLAIMER: Theoretical analysis for research purposes. Requires fault-tolerant quantum computers.
Executive Summary
Grover search offers √16 = 4x theoretical speedup for neighbor selection. Quantum walks provide limited benefit (√log N speedup) for small-world graphs. Full quantum advantage NOT viable with 2025 hardware. Projected practical in 2040-2045 timeframe.
Viability Assessment
- 2025 (Current): 12.4% viable (qubits, coherence, error rate bottlenecks)
- 2030 (Near-term): 38.2% viable (NISQ era, hybrid workflows)
- 2040 (Long-term): 84.7% viable (fault-tolerant quantum)
Theoretical Speedup Analysis
| Algorithm | Theoretical Speedup | Qubits Required | Gate Depth | Coherence (ms) |
|---|---|---|---|---|
| Classical (baseline) | 1.0x | 0 | 0 | - |
| Grover (M=16) | 4.0x | 4 | 3 | 0.003 |
| Quantum Walk | 1.2x | 17 | 316 | 0.316 |
| Amplitude Encoding | 384x (theoretical) | 9 | 384 | 0.384 |
| Hybrid | 2.4x | 50 | 158 | 0.158 |
Hardware Requirement Analysis
2025 Hardware (Current NISQ)
- Qubits Available: 100
- Coherence Time: 0.1ms
- Error Rate: 0.1%
- Viability: 12.4% ⚠️
Bottleneck: Coherence time (need 1ms+)
2030 Hardware (Improved NISQ)
- Qubits Available: 1,000
- Coherence Time: 1.0ms
- Error Rate: 0.01%
- Viability: 38.2% ⚠️
Bottleneck: Error rate (need <0.001%)
2040 Hardware (Fault-Tolerant)
- Qubits Available: 10,000
- Coherence Time: 10ms
- Error Rate: 0.001%
- Viability: 84.7% ✅
Practical Quantum Advantage Achieved
Recommended Approach by Timeline
2025-2030: Hybrid Classical-Quantum
- Use Grover for neighbor selection (4x speedup)
- Classical for graph traversal
- Hybrid efficiency: 1.6x realistic speedup
2030-2040: Expanding Quantum Components
- Quantum walk integration
- Partial amplitude encoding
- Hybrid efficiency: 2.8x projected
2040+: Full Quantum HNSW
- Fault-tolerant quantum circuits
- Full amplitude encoding
- Theoretical: 50-100x speedup potential
Practical Recommendations
Current (2025)
- ⚠️ Do NOT deploy quantum (not viable)
- Continue classical optimization (8x speedup already achieved)
- Invest in theoretical research
Near-Term (2025-2030)
- Prototype hybrid workflows on NISQ devices
- Focus on Grover search (most practical)
- Prepare for expanded quantum access
Long-Term (2030+)
- Develop fault-tolerant quantum implementations
- Full amplitude encoding for embeddings
- Distributed quantum-classical hybrid systems
Conclusion
Quantum-enhanced HNSW shows theoretical promise (4-100x speedup) but NOT viable with current hardware. Focus on classical optimizations (already achieving 8x speedup) while preparing for 2040-2045 quantum advantage era.
Report Generated: 2025-11-30