Experimental Analysis of Quantum Annealers and Hybrid Solvers Using Benchmark Optimization Problems
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 Hamiltonian...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/8/1294 |
| _version_ | 1797434455640506368 |
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| author | Evangelos Stogiannos Christos Papalitsas Theodore Andronikos |
| author_facet | Evangelos Stogiannos Christos Papalitsas Theodore Andronikos |
| author_sort | Evangelos Stogiannos |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T10:32:29Z |
| format | Article |
| id | doaj.art-d70b9fddc8e24307bcca6e7806bc25dc |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T10:32:29Z |
| publishDate | 2022-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-d70b9fddc8e24307bcca6e7806bc25dc2023-12-01T21:12:08ZengMDPI AGMathematics2227-73902022-04-01108129410.3390/math10081294Experimental Analysis of Quantum Annealers and Hybrid Solvers Using Benchmark Optimization ProblemsEvangelos Stogiannos0Christos Papalitsas1Theodore Andronikos2Department of Informatics, Ionian University, 7 Tsirigoti Square, 49100 Corfu, GreeceDepartment of Informatics, Ionian University, 7 Tsirigoti Square, 49100 Corfu, GreeceDepartment of Informatics, Ionian University, 7 Tsirigoti Square, 49100 Corfu, GreeceThis 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.https://www.mdpi.com/2227-7390/10/8/1294optimizationmetaheuristicsHamiltonian cycleTSPquantum annealingQUBO |
| spellingShingle | Evangelos Stogiannos Christos Papalitsas Theodore Andronikos Experimental Analysis of Quantum Annealers and Hybrid Solvers Using Benchmark Optimization Problems Mathematics optimization metaheuristics Hamiltonian cycle TSP quantum annealing QUBO |
| title | Experimental Analysis of Quantum Annealers and Hybrid Solvers Using Benchmark Optimization Problems |
| title_full | Experimental Analysis of Quantum Annealers and Hybrid Solvers Using Benchmark Optimization Problems |
| title_fullStr | Experimental Analysis of Quantum Annealers and Hybrid Solvers Using Benchmark Optimization Problems |
| title_full_unstemmed | Experimental Analysis of Quantum Annealers and Hybrid Solvers Using Benchmark Optimization Problems |
| title_short | Experimental Analysis of Quantum Annealers and Hybrid Solvers Using Benchmark Optimization Problems |
| title_sort | experimental analysis of quantum annealers and hybrid solvers using benchmark optimization problems |
| topic | optimization metaheuristics Hamiltonian cycle TSP quantum annealing QUBO |
| url | https://www.mdpi.com/2227-7390/10/8/1294 |
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