| name | adiabatic-quantum-optimization-tunneling |
| description | Adiabatic Quantum Optimization methodology analyzing quantum tunneling gains for convex functions with spikes. Extends Hamming Weight with a Spike analysis to general log-concave potentials. Use when analyzing AQO tunneling speedups, designing adiabatic optimization schedules, or studying log-concave optimization landscapes. |
Adiabatic Quantum Optimization with Tunneling Analysis
Core Methodology
Extends analysis of the Hamming Weight with a Spike (HWS) problem to more general log-concave potentials, exploring algorithmic gains from quantum tunneling in AQO.
Key Insight
Quantum tunneling provides computational speedup for convex functions with non-convex perturbations (spikes). The tunneling rate depends on the potential shape.
Analysis Framework
- Characterize potential landscape (log-concavity + spike parameters)
- Analyze tunneling rate through energy barriers
- Compare AQO performance to classical optimization baselines
- Identify regimes where tunneling provides algorithmic advantage
Application Domains
- Convex optimization with local minima
- Combinatorial optimization on structured instances
- Adiabatic schedule design for quantum annealers
