Designing Ising machines with higher order spin interactions and their application in solving combinatorial optimization Article Swipe
Mohammad Khairul Bashar
,
Nikhil Shukla
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.1038/s41598-023-36531-4
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.1038/s41598-023-36531-4
The Ising model provides a natural mapping for many computationally hard combinatorial optimization problems (COPs). Consequently, dynamical system-inspired computing models and hardware platforms that minimize the Ising Hamiltonian, have recently been proposed as a potential candidate for solving COPs, with the promise of significant performance benefit. However, prior work on designing dynamical systems as Ising machines has primarily considered quadratic interactions among the nodes. Dynamical systems and models considering higher order interactions among the Ising spins remain largely unexplored, particularly for applications in computing. Therefore, in this work, we propose Ising spin-based dynamical systems that consider higher order (> 2) interactions among the Ising spins, which subsequently, enables us to develop computational models to directly solve many COPs that entail such higher order interactions (i.e., COPs on hypergraphs). Specifically, we demonstrate our approach by developing dynamical systems to compute the solution for the Boolean NAE-K-SAT (K ≥ 4) problem as well as solve the Max-K-Cut of a hypergraph. Our work advances the potential of the physics-inspired ‘toolbox’ for solving COPs.
Related Topics
Concepts
Ising model
Ising spin
Hypergraph
Computer science
Toolbox
Dynamical systems theory
Quadratic unconstrained binary optimization
Hamiltonian (control theory)
Quadratic equation
Spins
Statistical physics
Theoretical computer science
Physics
Mathematics
Mathematical optimization
Discrete mathematics
Quantum computer
Quantum mechanics
Programming language
Condensed matter physics
Quantum
Geometry
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1038/s41598-023-36531-4
- https://www.nature.com/articles/s41598-023-36531-4.pdf
- OA Status
- gold
- Cited By
- 19
- References
- 26
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4380367078
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4380367078Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1038/s41598-023-36531-4Digital Object Identifier
- Title
-
Designing Ising machines with higher order spin interactions and their application in solving combinatorial optimizationWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2023Year of publication
- Publication date
-
2023-06-12Full publication date if available
- Authors
-
Mohammad Khairul Bashar, Nikhil ShuklaList of authors in order
- Landing page
-
https://doi.org/10.1038/s41598-023-36531-4Publisher landing page
- PDF URL
-
https://www.nature.com/articles/s41598-023-36531-4.pdfDirect link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
- OA URL
-
https://www.nature.com/articles/s41598-023-36531-4.pdfDirect OA link when available
- Concepts
-
Ising model, Ising spin, Hypergraph, Computer science, Toolbox, Dynamical systems theory, Quadratic unconstrained binary optimization, Hamiltonian (control theory), Quadratic equation, Spins, Statistical physics, Theoretical computer science, Physics, Mathematics, Mathematical optimization, Discrete mathematics, Quantum computer, Quantum mechanics, Programming language, Condensed matter physics, Quantum, GeometryTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
19Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 10, 2024: 6, 2023: 3Per-year citation counts (last 5 years)
- References (count)
-
26Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W4380367078 |
|---|---|
| doi | https://doi.org/10.1038/s41598-023-36531-4 |
| ids.doi | https://doi.org/10.1038/s41598-023-36531-4 |
| ids.openalex | https://openalex.org/W4380367078 |
| fwci | 4.85341487 |
| type | article |
| title | Designing Ising machines with higher order spin interactions and their application in solving combinatorial optimization |
| biblio.issue | 1 |
| biblio.volume | 13 |
| biblio.last_page | |
| biblio.first_page | |
| topics[0].id | https://openalex.org/T10682 |
| topics[0].field.id | https://openalex.org/fields/17 |
| topics[0].field.display_name | Computer Science |
| topics[0].score | 0.9998999834060669 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/1702 |
| topics[0].subfield.display_name | Artificial Intelligence |
| topics[0].display_name | Quantum Computing Algorithms and Architecture |
| topics[1].id | https://openalex.org/T11321 |
| topics[1].field.id | https://openalex.org/fields/17 |
| topics[1].field.display_name | Computer Science |
| topics[1].score | 0.9891999959945679 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/1705 |
| topics[1].subfield.display_name | Computer Networks and Communications |
| topics[1].display_name | Error Correcting Code Techniques |
| topics[2].id | https://openalex.org/T12029 |
| topics[2].field.id | https://openalex.org/fields/13 |
| topics[2].field.display_name | Biochemistry, Genetics and Molecular Biology |
| topics[2].score | 0.9771000146865845 |
| topics[2].domain.id | https://openalex.org/domains/1 |
| topics[2].domain.display_name | Life Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/1312 |
| topics[2].subfield.display_name | Molecular Biology |
| topics[2].display_name | DNA and Biological Computing |
| is_xpac | False |
| apc_list.value | 1890 |
| apc_list.currency | EUR |
| apc_list.value_usd | 2190 |
| apc_paid.value | 1890 |
| apc_paid.currency | EUR |
| apc_paid.value_usd | 2190 |
| concepts[0].id | https://openalex.org/C51329190 |
| concepts[0].level | 2 |
| concepts[0].score | 0.9063575267791748 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q1076349 |
| concepts[0].display_name | Ising model |
| concepts[1].id | https://openalex.org/C2992371110 |
| concepts[1].level | 3 |
| concepts[1].score | 0.6344621181488037 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q1076349 |
| concepts[1].display_name | Ising spin |
| concepts[2].id | https://openalex.org/C2781221856 |
| concepts[2].level | 2 |
| concepts[2].score | 0.6032995581626892 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q840247 |
| concepts[2].display_name | Hypergraph |
| concepts[3].id | https://openalex.org/C41008148 |
| concepts[3].level | 0 |
| concepts[3].score | 0.5909085273742676 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q21198 |
| concepts[3].display_name | Computer science |
| concepts[4].id | https://openalex.org/C2777655017 |
| concepts[4].level | 2 |
| concepts[4].score | 0.5400283336639404 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q1501161 |
| concepts[4].display_name | Toolbox |
| concepts[5].id | https://openalex.org/C79379906 |
| concepts[5].level | 2 |
| concepts[5].score | 0.5216851234436035 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q3174497 |
| concepts[5].display_name | Dynamical systems theory |
| concepts[6].id | https://openalex.org/C177179195 |
| concepts[6].level | 4 |
| concepts[6].score | 0.44114863872528076 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q7268372 |
| concepts[6].display_name | Quadratic unconstrained binary optimization |
| concepts[7].id | https://openalex.org/C130787639 |
| concepts[7].level | 2 |
| concepts[7].score | 0.44004976749420166 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q5645293 |
| concepts[7].display_name | Hamiltonian (control theory) |
| concepts[8].id | https://openalex.org/C129844170 |
| concepts[8].level | 2 |
| concepts[8].score | 0.4362291693687439 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q41299 |
| concepts[8].display_name | Quadratic equation |
| concepts[9].id | https://openalex.org/C2778870898 |
| concepts[9].level | 2 |
| concepts[9].score | 0.43197470903396606 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q7577658 |
| concepts[9].display_name | Spins |
| concepts[10].id | https://openalex.org/C121864883 |
| concepts[10].level | 1 |
| concepts[10].score | 0.41976386308670044 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q677916 |
| concepts[10].display_name | Statistical physics |
| concepts[11].id | https://openalex.org/C80444323 |
| concepts[11].level | 1 |
| concepts[11].score | 0.3750394582748413 |
| concepts[11].wikidata | https://www.wikidata.org/wiki/Q2878974 |
| concepts[11].display_name | Theoretical computer science |
| concepts[12].id | https://openalex.org/C121332964 |
| concepts[12].level | 0 |
| concepts[12].score | 0.29911118745803833 |
| concepts[12].wikidata | https://www.wikidata.org/wiki/Q413 |
| concepts[12].display_name | Physics |
| concepts[13].id | https://openalex.org/C33923547 |
| concepts[13].level | 0 |
| concepts[13].score | 0.24958795309066772 |
| concepts[13].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[13].display_name | Mathematics |
| concepts[14].id | https://openalex.org/C126255220 |
| concepts[14].level | 1 |
| concepts[14].score | 0.21992021799087524 |
| concepts[14].wikidata | https://www.wikidata.org/wiki/Q141495 |
| concepts[14].display_name | Mathematical optimization |
| concepts[15].id | https://openalex.org/C118615104 |
| concepts[15].level | 1 |
| concepts[15].score | 0.1599893867969513 |
| concepts[15].wikidata | https://www.wikidata.org/wiki/Q121416 |
| concepts[15].display_name | Discrete mathematics |
| concepts[16].id | https://openalex.org/C58053490 |
| concepts[16].level | 3 |
| concepts[16].score | 0.13262605667114258 |
| concepts[16].wikidata | https://www.wikidata.org/wiki/Q176555 |
| concepts[16].display_name | Quantum computer |
| concepts[17].id | https://openalex.org/C62520636 |
| concepts[17].level | 1 |
| concepts[17].score | 0.11990419030189514 |
| concepts[17].wikidata | https://www.wikidata.org/wiki/Q944 |
| concepts[17].display_name | Quantum mechanics |
| concepts[18].id | https://openalex.org/C199360897 |
| concepts[18].level | 1 |
| concepts[18].score | 0.0 |
| concepts[18].wikidata | https://www.wikidata.org/wiki/Q9143 |
| concepts[18].display_name | Programming language |
| concepts[19].id | https://openalex.org/C26873012 |
| concepts[19].level | 1 |
| concepts[19].score | 0.0 |
| concepts[19].wikidata | https://www.wikidata.org/wiki/Q214781 |
| concepts[19].display_name | Condensed matter physics |
| concepts[20].id | https://openalex.org/C84114770 |
| concepts[20].level | 2 |
| concepts[20].score | 0.0 |
| concepts[20].wikidata | https://www.wikidata.org/wiki/Q46344 |
| concepts[20].display_name | Quantum |
| concepts[21].id | https://openalex.org/C2524010 |
| concepts[21].level | 1 |
| concepts[21].score | 0.0 |
| concepts[21].wikidata | https://www.wikidata.org/wiki/Q8087 |
| concepts[21].display_name | Geometry |
| keywords[0].id | https://openalex.org/keywords/ising-model |
| keywords[0].score | 0.9063575267791748 |
| keywords[0].display_name | Ising model |
| keywords[1].id | https://openalex.org/keywords/ising-spin |
| keywords[1].score | 0.6344621181488037 |
| keywords[1].display_name | Ising spin |
| keywords[2].id | https://openalex.org/keywords/hypergraph |
| keywords[2].score | 0.6032995581626892 |
| keywords[2].display_name | Hypergraph |
| keywords[3].id | https://openalex.org/keywords/computer-science |
| keywords[3].score | 0.5909085273742676 |
| keywords[3].display_name | Computer science |
| keywords[4].id | https://openalex.org/keywords/toolbox |
| keywords[4].score | 0.5400283336639404 |
| keywords[4].display_name | Toolbox |
| keywords[5].id | https://openalex.org/keywords/dynamical-systems-theory |
| keywords[5].score | 0.5216851234436035 |
| keywords[5].display_name | Dynamical systems theory |
| keywords[6].id | https://openalex.org/keywords/quadratic-unconstrained-binary-optimization |
| keywords[6].score | 0.44114863872528076 |
| keywords[6].display_name | Quadratic unconstrained binary optimization |
| keywords[7].id | https://openalex.org/keywords/hamiltonian |
| keywords[7].score | 0.44004976749420166 |
| keywords[7].display_name | Hamiltonian (control theory) |
| keywords[8].id | https://openalex.org/keywords/quadratic-equation |
| keywords[8].score | 0.4362291693687439 |
| keywords[8].display_name | Quadratic equation |
| keywords[9].id | https://openalex.org/keywords/spins |
| keywords[9].score | 0.43197470903396606 |
| keywords[9].display_name | Spins |
| keywords[10].id | https://openalex.org/keywords/statistical-physics |
| keywords[10].score | 0.41976386308670044 |
| keywords[10].display_name | Statistical physics |
| keywords[11].id | https://openalex.org/keywords/theoretical-computer-science |
| keywords[11].score | 0.3750394582748413 |
| keywords[11].display_name | Theoretical computer science |
| keywords[12].id | https://openalex.org/keywords/physics |
| keywords[12].score | 0.29911118745803833 |
| keywords[12].display_name | Physics |
| keywords[13].id | https://openalex.org/keywords/mathematics |
| keywords[13].score | 0.24958795309066772 |
| keywords[13].display_name | Mathematics |
| keywords[14].id | https://openalex.org/keywords/mathematical-optimization |
| keywords[14].score | 0.21992021799087524 |
| keywords[14].display_name | Mathematical optimization |
| keywords[15].id | https://openalex.org/keywords/discrete-mathematics |
| keywords[15].score | 0.1599893867969513 |
| keywords[15].display_name | Discrete mathematics |
| keywords[16].id | https://openalex.org/keywords/quantum-computer |
| keywords[16].score | 0.13262605667114258 |
| keywords[16].display_name | Quantum computer |
| keywords[17].id | https://openalex.org/keywords/quantum-mechanics |
| keywords[17].score | 0.11990419030189514 |
| keywords[17].display_name | Quantum mechanics |
| language | en |
| locations[0].id | doi:10.1038/s41598-023-36531-4 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S196734849 |
| locations[0].source.issn | 2045-2322 |
| locations[0].source.type | journal |
| locations[0].source.is_oa | True |
| locations[0].source.issn_l | 2045-2322 |
| locations[0].source.is_core | True |
| locations[0].source.is_in_doaj | True |
| locations[0].source.display_name | Scientific Reports |
| locations[0].source.host_organization | https://openalex.org/P4310319908 |
| locations[0].source.host_organization_name | Nature Portfolio |
| locations[0].source.host_organization_lineage | https://openalex.org/P4310319908, https://openalex.org/P4310319965 |
| locations[0].source.host_organization_lineage_names | Nature Portfolio, Springer Nature |
| locations[0].license | cc-by |
| locations[0].pdf_url | https://www.nature.com/articles/s41598-023-36531-4.pdf |
| locations[0].version | publishedVersion |
| locations[0].raw_type | journal-article |
| locations[0].license_id | https://openalex.org/licenses/cc-by |
| locations[0].is_accepted | True |
| locations[0].is_published | True |
| locations[0].raw_source_name | Scientific Reports |
| locations[0].landing_page_url | https://doi.org/10.1038/s41598-023-36531-4 |
| locations[1].id | pmh:oai:pubmedcentral.nih.gov:10261086 |
| locations[1].is_oa | True |
| locations[1].source.id | https://openalex.org/S2764455111 |
| locations[1].source.issn | |
| locations[1].source.type | repository |
| locations[1].source.is_oa | False |
| locations[1].source.issn_l | |
| locations[1].source.is_core | False |
| locations[1].source.is_in_doaj | False |
| locations[1].source.display_name | PubMed Central |
| locations[1].source.host_organization | https://openalex.org/I1299303238 |
| locations[1].source.host_organization_name | National Institutes of Health |
| locations[1].source.host_organization_lineage | https://openalex.org/I1299303238 |
| locations[1].license | cc-by |
| locations[1].pdf_url | https://pmc.ncbi.nlm.nih.gov/articles/PMC10261086/pdf/41598_2023_Article_36531.pdf |
| locations[1].version | submittedVersion |
| locations[1].raw_type | Text |
| locations[1].license_id | https://openalex.org/licenses/cc-by |
| locations[1].is_accepted | False |
| locations[1].is_published | False |
| locations[1].raw_source_name | Sci Rep |
| locations[1].landing_page_url | https://www.ncbi.nlm.nih.gov/pmc/articles/10261086 |
| locations[2].id | pmh:oai:doaj.org/article:4cb7a56e696b45739ac85b7f309601d8 |
| locations[2].is_oa | False |
| locations[2].source.id | https://openalex.org/S4306401280 |
| locations[2].source.issn | |
| locations[2].source.type | repository |
| locations[2].source.is_oa | False |
| locations[2].source.issn_l | |
| locations[2].source.is_core | False |
| locations[2].source.is_in_doaj | False |
| locations[2].source.display_name | DOAJ (DOAJ: Directory of Open Access Journals) |
| locations[2].source.host_organization | |
| locations[2].source.host_organization_name | |
| locations[2].license | |
| locations[2].pdf_url | |
| locations[2].version | submittedVersion |
| locations[2].raw_type | article |
| locations[2].license_id | |
| locations[2].is_accepted | False |
| locations[2].is_published | False |
| locations[2].raw_source_name | Scientific Reports, Vol 13, Iss 1, Pp 1-9 (2023) |
| locations[2].landing_page_url | https://doaj.org/article/4cb7a56e696b45739ac85b7f309601d8 |
| indexed_in | crossref, doaj |
| authorships[0].author.id | https://openalex.org/A5038234804 |
| authorships[0].author.orcid | https://orcid.org/0000-0002-3668-0576 |
| authorships[0].author.display_name | Mohammad Khairul Bashar |
| authorships[0].countries | US |
| authorships[0].affiliations[0].institution_ids | https://openalex.org/I51556381 |
| authorships[0].affiliations[0].raw_affiliation_string | Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA, 22904, USA |
| authorships[0].institutions[0].id | https://openalex.org/I51556381 |
| authorships[0].institutions[0].ror | https://ror.org/0153tk833 |
| authorships[0].institutions[0].type | education |
| authorships[0].institutions[0].lineage | https://openalex.org/I51556381 |
| authorships[0].institutions[0].country_code | US |
| authorships[0].institutions[0].display_name | University of Virginia |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Mohammad Khairul Bashar |
| authorships[0].is_corresponding | False |
| authorships[0].raw_affiliation_strings | Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA, 22904, USA |
| authorships[1].author.id | https://openalex.org/A5028883225 |
| authorships[1].author.orcid | https://orcid.org/0000-0002-8899-5190 |
| authorships[1].author.display_name | Nikhil Shukla |
| authorships[1].countries | US |
| authorships[1].affiliations[0].institution_ids | https://openalex.org/I51556381 |
| authorships[1].affiliations[0].raw_affiliation_string | Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA, 22904, USA |
| authorships[1].institutions[0].id | https://openalex.org/I51556381 |
| authorships[1].institutions[0].ror | https://ror.org/0153tk833 |
| authorships[1].institutions[0].type | education |
| authorships[1].institutions[0].lineage | https://openalex.org/I51556381 |
| authorships[1].institutions[0].country_code | US |
| authorships[1].institutions[0].display_name | University of Virginia |
| authorships[1].author_position | last |
| authorships[1].raw_author_name | Nikhil Shukla |
| authorships[1].is_corresponding | False |
| authorships[1].raw_affiliation_strings | Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA, 22904, USA |
| has_content.pdf | True |
| has_content.grobid_xml | True |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://www.nature.com/articles/s41598-023-36531-4.pdf |
| open_access.oa_status | gold |
| open_access.any_repository_has_fulltext | False |
| created_date | 2023-06-13T00:00:00 |
| display_name | Designing Ising machines with higher order spin interactions and their application in solving combinatorial optimization |
| has_fulltext | True |
| is_retracted | False |
| updated_date | 2025-11-06T03:46:38.306776 |
| primary_topic.id | https://openalex.org/T10682 |
| primary_topic.field.id | https://openalex.org/fields/17 |
| primary_topic.field.display_name | Computer Science |
| primary_topic.score | 0.9998999834060669 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/1702 |
| primary_topic.subfield.display_name | Artificial Intelligence |
| primary_topic.display_name | Quantum Computing Algorithms and Architecture |
| related_works | https://openalex.org/W4388552999, https://openalex.org/W4380551968, https://openalex.org/W3013344182, https://openalex.org/W2067513897, https://openalex.org/W1977138359, https://openalex.org/W2054435129, https://openalex.org/W4389168513, https://openalex.org/W2052412229, https://openalex.org/W3190127282, https://openalex.org/W2999185184 |
| cited_by_count | 19 |
| counts_by_year[0].year | 2025 |
| counts_by_year[0].cited_by_count | 10 |
| counts_by_year[1].year | 2024 |
| counts_by_year[1].cited_by_count | 6 |
| counts_by_year[2].year | 2023 |
| counts_by_year[2].cited_by_count | 3 |
| locations_count | 3 |
| best_oa_location.id | doi:10.1038/s41598-023-36531-4 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S196734849 |
| best_oa_location.source.issn | 2045-2322 |
| best_oa_location.source.type | journal |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | 2045-2322 |
| best_oa_location.source.is_core | True |
| best_oa_location.source.is_in_doaj | True |
| best_oa_location.source.display_name | Scientific Reports |
| best_oa_location.source.host_organization | https://openalex.org/P4310319908 |
| best_oa_location.source.host_organization_name | Nature Portfolio |
| best_oa_location.source.host_organization_lineage | https://openalex.org/P4310319908, https://openalex.org/P4310319965 |
| best_oa_location.source.host_organization_lineage_names | Nature Portfolio, Springer Nature |
| best_oa_location.license | cc-by |
| best_oa_location.pdf_url | https://www.nature.com/articles/s41598-023-36531-4.pdf |
| best_oa_location.version | publishedVersion |
| best_oa_location.raw_type | journal-article |
| best_oa_location.license_id | https://openalex.org/licenses/cc-by |
| best_oa_location.is_accepted | True |
| best_oa_location.is_published | True |
| best_oa_location.raw_source_name | Scientific Reports |
| best_oa_location.landing_page_url | https://doi.org/10.1038/s41598-023-36531-4 |
| primary_location.id | doi:10.1038/s41598-023-36531-4 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S196734849 |
| primary_location.source.issn | 2045-2322 |
| primary_location.source.type | journal |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | 2045-2322 |
| primary_location.source.is_core | True |
| primary_location.source.is_in_doaj | True |
| primary_location.source.display_name | Scientific Reports |
| primary_location.source.host_organization | https://openalex.org/P4310319908 |
| primary_location.source.host_organization_name | Nature Portfolio |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310319908, https://openalex.org/P4310319965 |
| primary_location.source.host_organization_lineage_names | Nature Portfolio, Springer Nature |
| primary_location.license | cc-by |
| primary_location.pdf_url | https://www.nature.com/articles/s41598-023-36531-4.pdf |
| primary_location.version | publishedVersion |
| primary_location.raw_type | journal-article |
| primary_location.license_id | https://openalex.org/licenses/cc-by |
| primary_location.is_accepted | True |
| primary_location.is_published | True |
| primary_location.raw_source_name | Scientific Reports |
| primary_location.landing_page_url | https://doi.org/10.1038/s41598-023-36531-4 |
| publication_date | 2023-06-12 |
| publication_year | 2023 |
| referenced_works | https://openalex.org/W2921525502, https://openalex.org/W2980708903, https://openalex.org/W3047679785, https://openalex.org/W3184554868, https://openalex.org/W3136346278, https://openalex.org/W2042545232, https://openalex.org/W2538025098, https://openalex.org/W2965416137, https://openalex.org/W4225417080, https://openalex.org/W3092309919, https://openalex.org/W2039122980, https://openalex.org/W2807212998, https://openalex.org/W3092115506, https://openalex.org/W3163224880, https://openalex.org/W2946526084, https://openalex.org/W2534684513, https://openalex.org/W4309879453, https://openalex.org/W4283722817, https://openalex.org/W6635927623, https://openalex.org/W2900877887, https://openalex.org/W2072579822, https://openalex.org/W3033179442, https://openalex.org/W4295173891, https://openalex.org/W1527271318, https://openalex.org/W4313839118, https://openalex.org/W3100466793 |
| referenced_works_count | 26 |
| abstract_inverted_index.a | 5, 34, 157 |
| abstract_inverted_index.(K | 146 |
| abstract_inverted_index.2) | 100 |
| abstract_inverted_index.4) | 148 |
| abstract_inverted_index.as | 33, 54, 150, 152 |
| abstract_inverted_index.by | 134 |
| abstract_inverted_index.in | 83, 86 |
| abstract_inverted_index.of | 43, 156, 164 |
| abstract_inverted_index.on | 50, 127 |
| abstract_inverted_index.to | 110, 114, 138 |
| abstract_inverted_index.us | 109 |
| abstract_inverted_index.we | 89, 130 |
| abstract_inverted_index.Our | 159 |
| abstract_inverted_index.The | 1 |
| abstract_inverted_index.and | 21, 67 |
| abstract_inverted_index.for | 8, 37, 81, 142, 168 |
| abstract_inverted_index.has | 57 |
| abstract_inverted_index.our | 132 |
| abstract_inverted_index.the | 26, 41, 63, 74, 103, 140, 143, 154, 162, 165 |
| abstract_inverted_index.≥ | 147 |
| abstract_inverted_index.COPs | 118, 126 |
| abstract_inverted_index.been | 31 |
| abstract_inverted_index.hard | 11 |
| abstract_inverted_index.have | 29 |
| abstract_inverted_index.many | 9, 117 |
| abstract_inverted_index.such | 121 |
| abstract_inverted_index.that | 24, 95, 119 |
| abstract_inverted_index.this | 87 |
| abstract_inverted_index.well | 151 |
| abstract_inverted_index.with | 40 |
| abstract_inverted_index.work | 49, 160 |
| abstract_inverted_index.(> | 99 |
| abstract_inverted_index.COPs, | 39 |
| abstract_inverted_index.COPs. | 170 |
| abstract_inverted_index.Ising | 2, 27, 55, 75, 91, 104 |
| abstract_inverted_index.among | 62, 73, 102 |
| abstract_inverted_index.model | 3 |
| abstract_inverted_index.order | 71, 98, 123 |
| abstract_inverted_index.prior | 48 |
| abstract_inverted_index.solve | 116, 153 |
| abstract_inverted_index.spins | 76 |
| abstract_inverted_index.which | 106 |
| abstract_inverted_index.work, | 88 |
| abstract_inverted_index.(i.e., | 125 |
| abstract_inverted_index.entail | 120 |
| abstract_inverted_index.higher | 70, 97, 122 |
| abstract_inverted_index.models | 20, 68, 113 |
| abstract_inverted_index.nodes. | 64 |
| abstract_inverted_index.remain | 77 |
| abstract_inverted_index.spins, | 105 |
| abstract_inverted_index.(COPs). | 15 |
| abstract_inverted_index.Boolean | 144 |
| abstract_inverted_index.compute | 139 |
| abstract_inverted_index.develop | 111 |
| abstract_inverted_index.enables | 108 |
| abstract_inverted_index.largely | 78 |
| abstract_inverted_index.mapping | 7 |
| abstract_inverted_index.natural | 6 |
| abstract_inverted_index.problem | 149 |
| abstract_inverted_index.promise | 42 |
| abstract_inverted_index.propose | 90 |
| abstract_inverted_index.solving | 38, 169 |
| abstract_inverted_index.systems | 53, 66, 94, 137 |
| abstract_inverted_index.Abstract | 0 |
| abstract_inverted_index.However, | 47 |
| abstract_inverted_index.advances | 161 |
| abstract_inverted_index.approach | 133 |
| abstract_inverted_index.benefit. | 46 |
| abstract_inverted_index.consider | 96 |
| abstract_inverted_index.directly | 115 |
| abstract_inverted_index.hardware | 22 |
| abstract_inverted_index.machines | 56 |
| abstract_inverted_index.minimize | 25 |
| abstract_inverted_index.problems | 14 |
| abstract_inverted_index.proposed | 32 |
| abstract_inverted_index.provides | 4 |
| abstract_inverted_index.recently | 30 |
| abstract_inverted_index.solution | 141 |
| abstract_inverted_index.Dynamical | 65 |
| abstract_inverted_index.Max-K-Cut | 155 |
| abstract_inverted_index.NAE-K-SAT | 145 |
| abstract_inverted_index.candidate | 36 |
| abstract_inverted_index.computing | 19 |
| abstract_inverted_index.designing | 51 |
| abstract_inverted_index.dynamical | 17, 52, 93, 136 |
| abstract_inverted_index.platforms | 23 |
| abstract_inverted_index.potential | 35, 163 |
| abstract_inverted_index.primarily | 58 |
| abstract_inverted_index.quadratic | 60 |
| abstract_inverted_index.Therefore, | 85 |
| abstract_inverted_index.computing. | 84 |
| abstract_inverted_index.considered | 59 |
| abstract_inverted_index.developing | 135 |
| abstract_inverted_index.spin-based | 92 |
| abstract_inverted_index.considering | 69 |
| abstract_inverted_index.demonstrate | 131 |
| abstract_inverted_index.hypergraph. | 158 |
| abstract_inverted_index.performance | 45 |
| abstract_inverted_index.significant | 44 |
| abstract_inverted_index.unexplored, | 79 |
| abstract_inverted_index.Hamiltonian, | 28 |
| abstract_inverted_index.applications | 82 |
| abstract_inverted_index.interactions | 61, 72, 101, 124 |
| abstract_inverted_index.optimization | 13 |
| abstract_inverted_index.particularly | 80 |
| abstract_inverted_index.Consequently, | 16 |
| abstract_inverted_index.Specifically, | 129 |
| abstract_inverted_index.combinatorial | 12 |
| abstract_inverted_index.computational | 112 |
| abstract_inverted_index.hypergraphs). | 128 |
| abstract_inverted_index.subsequently, | 107 |
| abstract_inverted_index.‘toolbox’ | 167 |
| abstract_inverted_index.computationally | 10 |
| abstract_inverted_index.system-inspired | 18 |
| abstract_inverted_index.physics-inspired | 166 |
| cited_by_percentile_year.max | 99 |
| cited_by_percentile_year.min | 96 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 2 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/9 |
| sustainable_development_goals[0].score | 0.47999998927116394 |
| sustainable_development_goals[0].display_name | Industry, innovation and infrastructure |
| citation_normalized_percentile.value | 0.94759634 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |