{"title":"可扩展的近线性动力学伊辛机","authors":"Aditya Shukla, Mikhail Erementchouk, Pinaki Mazumder","doi":"10.1007/s11047-024-09983-4","DOIUrl":null,"url":null,"abstract":"<p>The past decade has seen the emergence of Ising machines targeting hard combinatorial optimization problems by minimizing the Ising Hamiltonian with spins represented by continuous dynamical variables. However, capabilities of these machines at larger scales are yet to be fully explored. We introduce and investigate an almost-linear Ising machine, a machine based on a network of analog spins with piece-wise linear coupling. We show that such networks leverage the computational resource similar to that of the semidefinite positive relaxation of the Ising model. We estimate the expected performance of the almost-linear machine and benchmark it on a set of <span>\\(\\left\\{ 0, 1\\right\\}\\)</span>-weighted graphs. We show that the running time of the investigated machine scales polynomially (linearly with the number of edges in the connectivity graph). As an example of the physical realization of the machine, we present a CMOS-compatible implementation comprising an array of vertices efficiently storing the continuous spins on charged capacitors and communicating externally via analog current.</p>","PeriodicalId":49783,"journal":{"name":"Natural Computing","volume":"48 1","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Scalable almost-linear dynamical Ising machines\",\"authors\":\"Aditya Shukla, Mikhail Erementchouk, Pinaki Mazumder\",\"doi\":\"10.1007/s11047-024-09983-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The past decade has seen the emergence of Ising machines targeting hard combinatorial optimization problems by minimizing the Ising Hamiltonian with spins represented by continuous dynamical variables. However, capabilities of these machines at larger scales are yet to be fully explored. We introduce and investigate an almost-linear Ising machine, a machine based on a network of analog spins with piece-wise linear coupling. We show that such networks leverage the computational resource similar to that of the semidefinite positive relaxation of the Ising model. We estimate the expected performance of the almost-linear machine and benchmark it on a set of <span>\\\\(\\\\left\\\\{ 0, 1\\\\right\\\\}\\\\)</span>-weighted graphs. We show that the running time of the investigated machine scales polynomially (linearly with the number of edges in the connectivity graph). As an example of the physical realization of the machine, we present a CMOS-compatible implementation comprising an array of vertices efficiently storing the continuous spins on charged capacitors and communicating externally via analog current.</p>\",\"PeriodicalId\":49783,\"journal\":{\"name\":\"Natural Computing\",\"volume\":\"48 1\",\"pages\":\"\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-04-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Natural Computing\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1007/s11047-024-09983-4\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Natural Computing","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1007/s11047-024-09983-4","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
The past decade has seen the emergence of Ising machines targeting hard combinatorial optimization problems by minimizing the Ising Hamiltonian with spins represented by continuous dynamical variables. However, capabilities of these machines at larger scales are yet to be fully explored. We introduce and investigate an almost-linear Ising machine, a machine based on a network of analog spins with piece-wise linear coupling. We show that such networks leverage the computational resource similar to that of the semidefinite positive relaxation of the Ising model. We estimate the expected performance of the almost-linear machine and benchmark it on a set of \(\left\{ 0, 1\right\}\)-weighted graphs. We show that the running time of the investigated machine scales polynomially (linearly with the number of edges in the connectivity graph). As an example of the physical realization of the machine, we present a CMOS-compatible implementation comprising an array of vertices efficiently storing the continuous spins on charged capacitors and communicating externally via analog current.
期刊介绍:
The journal is soliciting papers on all aspects of natural computing. Because of the interdisciplinary character of the journal a special effort will be made to solicit survey, review, and tutorial papers which would make research trends in a given subarea more accessible to the broad audience of the journal.