# Efficiency of quantum versus classical annealing in non-convex learning problems

## TL;DR

This paper compares quantum and classical annealing methods for non-convex learning problems, showing quantum annealing's efficiency in escaping local minima where classical methods struggle, especially in machine learning contexts.

## Contribution

It identifies classes of non-convex problems where quantum annealing outperforms classical thermal annealing, highlighting its potential in machine learning optimization tasks.

## Key findings

- Quantum annealing efficiently finds solutions in complex landscapes.
- Classical thermal annealing experiences exponential slowdowns.
- Quantum tunneling enables escape from local minima.

## Abstract

Quantum annealers aim at solving non-convex optimization problems by exploiting cooperative tunneling effects to escape local minima. The underlying idea consists in designing a classical energy function whose ground states are the sought optimal solutions of the original optimization problem and add a controllable quantum transverse field to generate tunneling processes. A key challenge is to identify classes of non-convex optimization problems for which quantum annealing remains efficient while thermal annealing fails. We show that this happens for a wide class of problems which are central to machine learning. Their energy landscapes is dominated by local minima that cause exponential slow down of classical thermal annealers while simulated quantum annealing converges efficiently to rare dense regions of optimal solutions.