Tabu-Driven Quantum Neighborhood Samplers

Abstract

Combinatorial optimization is an important application targeted by quantum computing. However, near-term hardware constraints make quantum algorithms unlikely to be competitive when compared to high-performing classical heuristics on large practical problems. One option to achieve advantages with near-term devices is to use them in combination with classical heuristics. In particular, we propose using quantum methods to sample from classically intractable distributionswhich is the most probable approach to attain a true provable quantum separation in the near-term -which are used to solve optimization problems faster. We numerically study this enhancement by an adaptation of Tabu Search using the Quantum Approximate Optimization Algorithm (QAOA) as a neighborhood sampler. We show that QAOA provides a flexible tool for exploration-exploitation in such hybrid settings and can provide evidence that it can help in solving problems faster by saving many tabu iterations and achieving better solutions.

Unsupervised strategies for identifying optimal parameters in Quantum Approximate Optimization Algorithm

“…From an application perspective, we envision these techniques to be employed in algorithms were QAOA is run on a small part of the problem to solve such as divide-and-conquer [9,10] and iterative algorithms [11,12,13]. Restricting to a few number of circuit calls will help decrease the runtime of quantum-featured or quantum-enhanced algorithms, making them closer to compete with classical heuristics.…”

“…Hence, our approaches allow balancing between circuit calls of small quantum computers and performances. Such settings for instance naturally occur in divide-and-conquer-type schemes to enable smaller quantum computers to improve optimization [9,10,11,12], or in Recursive-QAOA [13] as we demonstrate later.…”

“…In this work, we show two main approaches to encode the instances for clustering. First, we computed a set of features following [25,11]. For Erdős-Rényi graphs, we took the graph density, the logarithm of number of nodes and edges, logarithm of the first and second largest eigenvalues of the laplacian matrix normalized by the average node degree and the logarithm of the ratio of the two largest eigenvalues.…”

“…It exhibits a few properties that makes it interesting for combinatorial optimization [5,6,7,8]. These can be useful when using it as a subroutine [9,10,11,12,13], especially the concentration of parameters [6]. This concentration property suggests that optimal parameters found for one instance can be reused on another.…”

“…On the one hand, the «reasonable» aspect may not be straightforward to characterize [18]. On the other hand, in many QAOAfeatured algorithms [9,10,11,12,13], many instances are generated and could give rise to many distributions. Finally, within a distribution, several areas of concentration may rise.…”