adiabatic-quantum-optimization-tunneling

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

1. Characterize potential landscape (log-concavity + spike parameters)
2. Analyze tunneling rate through energy barriers
3. Compare AQO performance to classical optimization baselines
4. 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