Adiabatic Quantum Optimization Tunneling

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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