Finding a Hadamard Matrix by Simulated Quantum Annealing
Hard problems have recently become an important issue in computing. Various methods, including a heuristic approach that is inspired by physical phenomena, are being explored. In this paper, we propose the use of simulated quantum annealing (SQA) to find a Hadamard matrix, which is itself a hard pro...
Gespeichert in:
| Veröffentlicht in: | Entropy (Basel, Switzerland) Switzerland), 2018-02, Vol.20 (2), p.141 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | 2 |
| container_start_page | 141 |
| container_title | Entropy (Basel, Switzerland) |
| container_volume | 20 |
| creator | Suksmono, Andriyan |
| description | Hard problems have recently become an important issue in computing. Various methods, including a heuristic approach that is inspired by physical phenomena, are being explored. In this paper, we propose the use of simulated quantum annealing (SQA) to find a Hadamard matrix, which is itself a hard problem. We reformulate the problem as an energy minimization of spin vectors connected by a complete graph. The computation is conducted based on a path-integral Monte-Carlo (PIMC) SQA of the spin vector system, with an applied transverse magnetic field whose strength is decreased over time. In the numerical experiments, the proposed method is employed to find low-order Hadamard matrices, including the ones that cannot be constructed trivially by the Sylvester method. The scaling property of the method and the measurement of residual energy after a sufficiently large number of iterations show that SQA outperforms simulated annealing (SA) in solving this hard problem. |
| doi_str_mv | 10.3390/e20020141 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_pubme</sourceid><recordid>TN_cdi_pubmedcentral_primary_oai_pubmedcentral_nih_gov_7512635</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2466767198</sourcerecordid><originalsourceid>FETCH-LOGICAL-c380t-4f930a2c707dcaa52b60ff856e8332b8d8ae4d6b52f052a607b980e291fafb333</originalsourceid><addsrcrecordid>eNpdkVFLwzAQx4Mobk4f_AYFX_RheknaNH0RxnBOUETU53BtktnRprNpxX17MzaG-nR33O_-_O-OkHMK15xncGMYAAMa0wMypJBl45gDHP7KB-TE-2WAOKPimAw4ZyIJxZDIWel06RYRRnPUWGOroyfs2vI7ytfRa1n3FXZGRy89uq6vo4lzBqswcEqOLFbenO3iiLzP7t6m8_Hj8_3DdPI4LriEbhzbjAOyIoVUF4gJywVYKxNhZDCRSy3RxFrkCbOQMBSQ5pkEwzJq0eac8xG53equ-rw2ujCua7FSq7YMXteqwVL97bjyQy2aL5UmlAmeBIHLnUDbfPbGd6oufWGqCp1peq9YLEQqUprJgF78Q5dN37qwntqcNwWWso2jqy1VtI33rbF7MxTU5h9q_w_-AwMUefY</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2014702723</pqid></control><display><type>article</type><title>Finding a Hadamard Matrix by Simulated Quantum Annealing</title><source>DOAJ Directory of Open Access Journals</source><source>PubMed Central Open Access</source><source>MDPI - Multidisciplinary Digital Publishing Institute</source><source>PubMed Central</source><source>EZB Electronic Journals Library</source><creator>Suksmono, Andriyan</creator><creatorcontrib>Suksmono, Andriyan</creatorcontrib><description>Hard problems have recently become an important issue in computing. Various methods, including a heuristic approach that is inspired by physical phenomena, are being explored. In this paper, we propose the use of simulated quantum annealing (SQA) to find a Hadamard matrix, which is itself a hard problem. We reformulate the problem as an energy minimization of spin vectors connected by a complete graph. The computation is conducted based on a path-integral Monte-Carlo (PIMC) SQA of the spin vector system, with an applied transverse magnetic field whose strength is decreased over time. In the numerical experiments, the proposed method is employed to find low-order Hadamard matrices, including the ones that cannot be constructed trivially by the Sylvester method. The scaling property of the method and the measurement of residual energy after a sufficiently large number of iterations show that SQA outperforms simulated annealing (SA) in solving this hard problem.</description><identifier>ISSN: 1099-4300</identifier><identifier>EISSN: 1099-4300</identifier><identifier>DOI: 10.3390/e20020141</identifier><identifier>PMID: 33265232</identifier><language>eng</language><publisher>Basel: MDPI AG</publisher><subject>Computer simulation ; Energy conservation ; Energy measurement ; Heuristic methods ; Monte Carlo simulation ; Residual energy ; Simulated annealing</subject><ispartof>Entropy (Basel, Switzerland), 2018-02, Vol.20 (2), p.141</ispartof><rights>Copyright MDPI AG 2018</rights><rights>2018 by the author. 2018</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c380t-4f930a2c707dcaa52b60ff856e8332b8d8ae4d6b52f052a607b980e291fafb333</citedby><cites>FETCH-LOGICAL-c380t-4f930a2c707dcaa52b60ff856e8332b8d8ae4d6b52f052a607b980e291fafb333</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC7512635/pdf/$$EPDF$$P50$$Gpubmedcentral$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC7512635/$$EHTML$$P50$$Gpubmedcentral$$Hfree_for_read</linktohtml><link.rule.ids>230,314,727,780,784,864,885,27924,27925,53791,53793</link.rule.ids></links><search><creatorcontrib>Suksmono, Andriyan</creatorcontrib><title>Finding a Hadamard Matrix by Simulated Quantum Annealing</title><title>Entropy (Basel, Switzerland)</title><description>Hard problems have recently become an important issue in computing. Various methods, including a heuristic approach that is inspired by physical phenomena, are being explored. In this paper, we propose the use of simulated quantum annealing (SQA) to find a Hadamard matrix, which is itself a hard problem. We reformulate the problem as an energy minimization of spin vectors connected by a complete graph. The computation is conducted based on a path-integral Monte-Carlo (PIMC) SQA of the spin vector system, with an applied transverse magnetic field whose strength is decreased over time. In the numerical experiments, the proposed method is employed to find low-order Hadamard matrices, including the ones that cannot be constructed trivially by the Sylvester method. The scaling property of the method and the measurement of residual energy after a sufficiently large number of iterations show that SQA outperforms simulated annealing (SA) in solving this hard problem.</description><subject>Computer simulation</subject><subject>Energy conservation</subject><subject>Energy measurement</subject><subject>Heuristic methods</subject><subject>Monte Carlo simulation</subject><subject>Residual energy</subject><subject>Simulated annealing</subject><issn>1099-4300</issn><issn>1099-4300</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNpdkVFLwzAQx4Mobk4f_AYFX_RheknaNH0RxnBOUETU53BtktnRprNpxX17MzaG-nR33O_-_O-OkHMK15xncGMYAAMa0wMypJBl45gDHP7KB-TE-2WAOKPimAw4ZyIJxZDIWel06RYRRnPUWGOroyfs2vI7ytfRa1n3FXZGRy89uq6vo4lzBqswcEqOLFbenO3iiLzP7t6m8_Hj8_3DdPI4LriEbhzbjAOyIoVUF4gJywVYKxNhZDCRSy3RxFrkCbOQMBSQ5pkEwzJq0eac8xG53equ-rw2ujCua7FSq7YMXteqwVL97bjyQy2aL5UmlAmeBIHLnUDbfPbGd6oufWGqCp1peq9YLEQqUprJgF78Q5dN37qwntqcNwWWso2jqy1VtI33rbF7MxTU5h9q_w_-AwMUefY</recordid><startdate>20180222</startdate><enddate>20180222</enddate><creator>Suksmono, Andriyan</creator><general>MDPI AG</general><general>MDPI</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>HCIFZ</scope><scope>KR7</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>7X8</scope><scope>5PM</scope></search><sort><creationdate>20180222</creationdate><title>Finding a Hadamard Matrix by Simulated Quantum Annealing</title><author>Suksmono, Andriyan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c380t-4f930a2c707dcaa52b60ff856e8332b8d8ae4d6b52f052a607b980e291fafb333</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Computer simulation</topic><topic>Energy conservation</topic><topic>Energy measurement</topic><topic>Heuristic methods</topic><topic>Monte Carlo simulation</topic><topic>Residual energy</topic><topic>Simulated annealing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Suksmono, Andriyan</creatorcontrib><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>ProQuest Central Essentials</collection><collection>AUTh Library subscriptions: ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>Engineering Research Database</collection><collection>SciTech Premium Collection (Proquest) (PQ_SDU_P3)</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>ProQuest Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>MEDLINE - Academic</collection><collection>PubMed Central (Full Participant titles)</collection><jtitle>Entropy (Basel, Switzerland)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Suksmono, Andriyan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Finding a Hadamard Matrix by Simulated Quantum Annealing</atitle><jtitle>Entropy (Basel, Switzerland)</jtitle><date>2018-02-22</date><risdate>2018</risdate><volume>20</volume><issue>2</issue><spage>141</spage><pages>141-</pages><issn>1099-4300</issn><eissn>1099-4300</eissn><abstract>Hard problems have recently become an important issue in computing. Various methods, including a heuristic approach that is inspired by physical phenomena, are being explored. In this paper, we propose the use of simulated quantum annealing (SQA) to find a Hadamard matrix, which is itself a hard problem. We reformulate the problem as an energy minimization of spin vectors connected by a complete graph. The computation is conducted based on a path-integral Monte-Carlo (PIMC) SQA of the spin vector system, with an applied transverse magnetic field whose strength is decreased over time. In the numerical experiments, the proposed method is employed to find low-order Hadamard matrices, including the ones that cannot be constructed trivially by the Sylvester method. The scaling property of the method and the measurement of residual energy after a sufficiently large number of iterations show that SQA outperforms simulated annealing (SA) in solving this hard problem.</abstract><cop>Basel</cop><pub>MDPI AG</pub><pmid>33265232</pmid><doi>10.3390/e20020141</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1099-4300 |
| ispartof | Entropy (Basel, Switzerland), 2018-02, Vol.20 (2), p.141 |
| issn | 1099-4300 1099-4300 |
| language | eng |
| recordid | cdi_pubmedcentral_primary_oai_pubmedcentral_nih_gov_7512635 |
| source | DOAJ Directory of Open Access Journals; PubMed Central Open Access; MDPI - Multidisciplinary Digital Publishing Institute; PubMed Central; EZB Electronic Journals Library |
| subjects | Computer simulation Energy conservation Energy measurement Heuristic methods Monte Carlo simulation Residual energy Simulated annealing |
| title | Finding a Hadamard Matrix by Simulated Quantum Annealing |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-07T18%3A54%3A19IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_pubme&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Finding%20a%20Hadamard%20Matrix%20by%20Simulated%20Quantum%20Annealing&rft.jtitle=Entropy%20(Basel,%20Switzerland)&rft.au=Suksmono,%20Andriyan&rft.date=2018-02-22&rft.volume=20&rft.issue=2&rft.spage=141&rft.pages=141-&rft.issn=1099-4300&rft.eissn=1099-4300&rft_id=info:doi/10.3390/e20020141&rft_dat=%3Cproquest_pubme%3E2466767198%3C/proquest_pubme%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2014702723&rft_id=info:pmid/33265232&rfr_iscdi=true |