Stability of oscillator Ising machines: Not all solutions are created equal Article Swipe
Mohammad Khairul Bashar
,
Zongli Lin
,
Nikhil Shukla
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.1063/5.0157107
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.1063/5.0157107
Nonlinear dynamical systems such as coupled oscillators are being actively investigated as Ising machines for solving computationally hard problems in combinatorial optimization. Prior works have established the equivalence between the global minima of the cost function describing the coupled oscillator system and the ground state of the Ising Hamiltonian. However, the properties of the oscillator Ising machine (OIM) from a nonlinear control viewpoint, such as the stability of the OIM solutions, remain unexplored. Therefore, in this work, using nonlinear control-theoretic analysis, we (i) identify the conditions required to ensure the functionality of the coupled oscillators as an Ising machine, (ii) show that all globally optimal phase configurations may not always be stable, resulting in some configurations being more favored over others and, thus, creating a biased OIM, and (iii) elucidate the impact of the stability of locally optimal phase configurations on the quality of the solution computed by the system. Our work, fostered through the unique convergence between nonlinear control theory and analog systems for computing, provides a new toolbox for the design and implementation of dynamical system-based computing platforms.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1063/5.0157107
- https://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/5.0157107/18161910/144901_1_5.0157107.pdf
- OA Status
- bronze
- Cited By
- 12
- References
- 26
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4387458800
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- OpenAlex ID
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https://openalex.org/W4387458800Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1063/5.0157107Digital Object Identifier
- Title
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Stability of oscillator Ising machines: Not all solutions are created equalWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2023Year of publication
- Publication date
-
2023-10-09Full publication date if available
- Authors
-
Mohammad Khairul Bashar, Zongli Lin, Nikhil ShuklaList of authors in order
- Landing page
-
https://doi.org/10.1063/5.0157107Publisher landing page
- PDF URL
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https://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/5.0157107/18161910/144901_1_5.0157107.pdfDirect link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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bronzeOpen access status per OpenAlex
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https://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/5.0157107/18161910/144901_1_5.0157107.pdfDirect OA link when available
- Concepts
-
Ising model, Nonlinear system, Maxima and minima, Stability (learning theory), Computer science, Toolbox, Statistical physics, Dynamical systems theory, Hamiltonian (control theory), Physics, Mathematics, Mathematical optimization, Quantum mechanics, Mathematical analysis, Machine learning, Programming languageTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
12Total citation count in OpenAlex
- Citations by year (recent)
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2025: 8, 2024: 2, 2023: 2Per-year citation counts (last 5 years)
- References (count)
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26Number of works referenced by this work
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.of | 32, 45, 52, 67, 91, 132, 135, 143, 175 |
| abstract_inverted_index.on | 140 |
| abstract_inverted_index.to | 87 |
| abstract_inverted_index.we | 81 |
| abstract_inverted_index.(i) | 82 |
| abstract_inverted_index.OIM | 69 |
| abstract_inverted_index.Our | 150 |
| abstract_inverted_index.all | 102 |
| abstract_inverted_index.and | 41, 127, 161, 173 |
| abstract_inverted_index.are | 7 |
| abstract_inverted_index.for | 14, 164, 170 |
| abstract_inverted_index.may | 107 |
| abstract_inverted_index.new | 168 |
| abstract_inverted_index.not | 108 |
| abstract_inverted_index.the | 26, 29, 33, 37, 42, 46, 50, 53, 65, 68, 84, 89, 92, 130, 133, 141, 144, 148, 154, 171 |
| abstract_inverted_index.(ii) | 99 |
| abstract_inverted_index.OIM, | 126 |
| abstract_inverted_index.and, | 121 |
| abstract_inverted_index.cost | 34 |
| abstract_inverted_index.from | 58 |
| abstract_inverted_index.hard | 17 |
| abstract_inverted_index.have | 24 |
| abstract_inverted_index.more | 117 |
| abstract_inverted_index.over | 119 |
| abstract_inverted_index.show | 100 |
| abstract_inverted_index.some | 114 |
| abstract_inverted_index.such | 3, 63 |
| abstract_inverted_index.that | 101 |
| abstract_inverted_index.this | 75 |
| abstract_inverted_index.(OIM) | 57 |
| abstract_inverted_index.(iii) | 128 |
| abstract_inverted_index.Ising | 12, 47, 55, 97 |
| abstract_inverted_index.Prior | 22 |
| abstract_inverted_index.being | 8, 116 |
| abstract_inverted_index.phase | 105, 138 |
| abstract_inverted_index.state | 44 |
| abstract_inverted_index.thus, | 122 |
| abstract_inverted_index.using | 77 |
| abstract_inverted_index.work, | 76, 151 |
| abstract_inverted_index.works | 23 |
| abstract_inverted_index.always | 109 |
| abstract_inverted_index.analog | 162 |
| abstract_inverted_index.biased | 125 |
| abstract_inverted_index.design | 172 |
| abstract_inverted_index.ensure | 88 |
| abstract_inverted_index.global | 30 |
| abstract_inverted_index.ground | 43 |
| abstract_inverted_index.impact | 131 |
| abstract_inverted_index.minima | 31 |
| abstract_inverted_index.others | 120 |
| abstract_inverted_index.remain | 71 |
| abstract_inverted_index.system | 40 |
| abstract_inverted_index.theory | 160 |
| abstract_inverted_index.unique | 155 |
| abstract_inverted_index.between | 28, 157 |
| abstract_inverted_index.control | 61, 159 |
| abstract_inverted_index.coupled | 5, 38, 93 |
| abstract_inverted_index.favored | 118 |
| abstract_inverted_index.locally | 136 |
| abstract_inverted_index.machine | 56 |
| abstract_inverted_index.optimal | 104, 137 |
| abstract_inverted_index.quality | 142 |
| abstract_inverted_index.solving | 15 |
| abstract_inverted_index.stable, | 111 |
| abstract_inverted_index.system. | 149 |
| abstract_inverted_index.systems | 2, 163 |
| abstract_inverted_index.through | 153 |
| abstract_inverted_index.toolbox | 169 |
| abstract_inverted_index.However, | 49 |
| abstract_inverted_index.actively | 9 |
| abstract_inverted_index.computed | 146 |
| abstract_inverted_index.creating | 123 |
| abstract_inverted_index.fostered | 152 |
| abstract_inverted_index.function | 35 |
| abstract_inverted_index.globally | 103 |
| abstract_inverted_index.identify | 83 |
| abstract_inverted_index.machine, | 98 |
| abstract_inverted_index.machines | 13 |
| abstract_inverted_index.problems | 18 |
| abstract_inverted_index.provides | 166 |
| abstract_inverted_index.required | 86 |
| abstract_inverted_index.solution | 145 |
| abstract_inverted_index.Nonlinear | 0 |
| abstract_inverted_index.analysis, | 80 |
| abstract_inverted_index.computing | 178 |
| abstract_inverted_index.dynamical | 1, 176 |
| abstract_inverted_index.elucidate | 129 |
| abstract_inverted_index.nonlinear | 60, 78, 158 |
| abstract_inverted_index.resulting | 112 |
| abstract_inverted_index.stability | 66, 134 |
| abstract_inverted_index.Therefore, | 73 |
| abstract_inverted_index.computing, | 165 |
| abstract_inverted_index.conditions | 85 |
| abstract_inverted_index.describing | 36 |
| abstract_inverted_index.oscillator | 39, 54 |
| abstract_inverted_index.platforms. | 179 |
| abstract_inverted_index.properties | 51 |
| abstract_inverted_index.solutions, | 70 |
| abstract_inverted_index.viewpoint, | 62 |
| abstract_inverted_index.convergence | 156 |
| abstract_inverted_index.equivalence | 27 |
| abstract_inverted_index.established | 25 |
| abstract_inverted_index.oscillators | 6, 94 |
| abstract_inverted_index.unexplored. | 72 |
| abstract_inverted_index.Hamiltonian. | 48 |
| abstract_inverted_index.investigated | 10 |
| abstract_inverted_index.system-based | 177 |
| abstract_inverted_index.combinatorial | 20 |
| abstract_inverted_index.functionality | 90 |
| abstract_inverted_index.optimization. | 21 |
| abstract_inverted_index.configurations | 106, 115, 139 |
| abstract_inverted_index.implementation | 174 |
| abstract_inverted_index.computationally | 16 |
| abstract_inverted_index.control-theoretic | 79 |
| cited_by_percentile_year.max | 99 |
| cited_by_percentile_year.min | 94 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile.value | 0.91271153 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |