Experimental Analysis of Quantum Annealers and Hybrid Solvers Using Benchmark Optimization Problems

Evangelos Stogiannos, Christos Papalitsas and Theodore Andronikos
Additional contact information
Evangelos Stogiannos: Department of Informatics, Ionian University, 7 Tsirigoti Square, 49100 Corfu, Greece
Christos Papalitsas: Department of Informatics, Ionian University, 7 Tsirigoti Square, 49100 Corfu, Greece
Theodore Andronikos: Department of Informatics, Ionian University, 7 Tsirigoti Square, 49100 Corfu, Greece

Mathematics, 2022, vol. 10, issue 8, 1-24

Abstract: This paper studies the Hamiltonian cycle problem (HCP) and the traveling salesman problem (TSP) on D-Wave quantum systems. Motivated by the fact that most libraries present their benchmark instances in terms of adjacency matrices, we develop a novel matrix formulation for the HCP and TSP Hamiltonians, which enables the seamless and automatic integration of benchmark instances in quantum platforms. We also present a thorough mathematical analysis of the precise number of constraints required to express the HCP and TSP Hamiltonians. This analysis explains quantitatively why, almost always, running incomplete graph instances requires more qubits than complete instances. It turns out that QUBO models for incomplete graphs require more quadratic constraints than complete graphs, a fact that has been corroborated by a series of experiments. Moreover, we introduce a technique for the min-max normalization for the coefficients of the TSP Hamiltonian to address the problem of invalid solutions produced by the quantum annealer, a trend often observed. Our extensive experimental tests have demonstrated that the D-Wave Advantage_system4.1 is more efficient than the Advantage_system1.1, both in terms of qubit utilization and the quality of solutions. Finally, we experimentally establish that the D-Wave hybrid solvers always provide valid solutions, without violating the given constraints, even for arbitrarily big problems up to 120 nodes.

Keywords: optimization; metaheuristics; Hamiltonian cycle; TSP; quantum annealing; QUBO (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/8/1294/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/8/1294/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:8:p:1294-:d:792958

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().