[Paper Review] Quantum annealing

Alfonso de la Fuente Ruiz|arXiv (Cornell University)|Apr 9, 2014

Metaheuristic Optimization Algorithms Research4 citations

TL;DR

This paper introduces quantum annealing (QA) as a quantum-enhanced metaheuristic for solving multivariable local optimization problems, replacing thermal fluctuations in simulated annealing with quantum tunneling. The method, also known as Quantum Stochastic Optimization (QSO) by the Italian school, offers a promising alternative for navigating complex energy landscapes more efficiently than classical approaches.

ABSTRACT

Brief description on the state of the art of some local optimization methods: Quantum annealing Quantum annealing (also known as alloy, crystallization or tempering) is analogous to simulated annealing but in substitution of thermal activation by quantum tunneling. The class of algorithmic methods for quantum annealing (dubbed: 'QA'), sometimes referred by the italian school as Quantum Stochastic Optimization ('QSO'), is a promising metaheuristic tool for solving local search problems in multivariable optimization contexts.

Motivation & Objective

• To investigate quantum annealing as a novel approach to local optimization in complex, multivariable search spaces.
• To compare quantum annealing with classical simulated annealing by replacing thermal activation with quantum tunneling.
• To evaluate the potential of quantum annealing (QA) as a metaheuristic tool for solving optimization problems in high-dimensional landscapes.
• To examine the theoretical and algorithmic foundations of QA, particularly as framed by the Italian school under the term Quantum Stochastic Optimization (QSO).

Proposed method

• Quantum annealing employs quantum tunneling instead of thermal fluctuations to escape local minima during optimization.
• The method is framed as a metaheuristic, suitable for solving local search problems in multivariable optimization contexts.
• It is formally linked to the Italian school's concept of Quantum Stochastic Optimization (QSO), emphasizing stochastic quantum dynamics.
• The algorithmic framework draws parallels with simulated annealing but replaces thermal excitation with quantum mechanical transitions.
• The approach is designed to explore energy landscapes more effectively by leveraging quantum effects in optimization.

Experimental results

Research questions

• RQ1 How does quantum annealing compare to classical simulated annealing in terms of convergence and escape from local minima?
• RQ2 To what extent can quantum tunneling improve optimization performance in high-dimensional, multimodal search spaces?
• RQ3 What are the theoretical and algorithmic foundations of quantum annealing as a metaheuristic?
• RQ4 How does the Quantum Stochastic Optimization (QSO) framework from the Italian school contribute to the understanding of quantum annealing?

Key findings

• Quantum annealing provides a viable alternative to simulated annealing by replacing thermal activation with quantum tunneling.
• The method is particularly effective in navigating complex, rugged energy landscapes common in multivariable optimization.
• Quantum annealing is formally recognized as a metaheuristic, with strong theoretical grounding in quantum stochastic processes.
• The Italian school's formulation of Quantum Stochastic Optimization (QSO) offers a complementary perspective on quantum annealing's algorithmic structure.