Year: 2023
Type: article
Abstract: An algorithm for a particular problem may find some instances of the problem easier and others harder to solve, even for a fixed input size. We numerically analyze the relative hardness of MAX 2-SAT problem instances for various continuous-time quantum algorithms and a comparable classical algorithm. This has two motivations: To investigate whether small-sized problem instances, which are commonly used in numerical simulations of quantum algorithms for benchmarking purposes, are a good representation of larger instances in terms of their hardness to solve, and to determine the applicability of continuous-time quantum algorithms in a portfolio approach, where we take advantage of the variation in the hardness of instances between different algorithms by running them in parallel. We find that, while there are correlations in instance hardness between all of the algorithms considered, they appear weak enough that a portfolio approach would likely be desirable in practice. Our results also show a widening range of hardness of randomly generated instances as the problem size is increased, which demonstrates both the difference in the distribution of hardness at small sizes and the value of a portfolio approach that can reduce the number of extremely hard instances. We identify specific weaknesses of these quantum algorithms that can be overcome with a portfolio approach, such their inability to efficiently solve satisfiable instances (which is easy classically).
Source: Physical Review Research
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,625
Awards: G1590245666, G2503488389, G2560450154, G3283010597, DTP 2020-2021 Durham University, G5025975358, G5617769834, EPSRC Hub in Quantum Computing and Simulation, EPSRC Centre for Doctoral Training in Controlled Quantum Dynamics, G719273988, Hybrid quantum and classical computation: exploiting the best of both paradigms, G7478130978, Hybrid Quantum Energy Landscape Computing, G8377342588
OpenAlex ID: W4379382944