{"title":"Correspondence between the Hamiltonian cycle problem and the quantum lattice gauge theory","authors":"Xiaopeng Cui, Yu Shi","doi":"10.1209/0295-5075/ad130b","DOIUrl":null,"url":null,"abstract":"<jats:title>Abstract</jats:title> We propose the correspondence between the Hamiltonian cycle (HC) problem in graph theory and the quantum <jats:inline-formula> <jats:tex-math><?CDATA $\\mathbb {Z}_{2}$ ?></jats:tex-math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"epl23100758ieqn3.gif\" xlink:type=\"simple\" /> </jats:inline-formula> lattice gauge theory (QZ2LGT) defined on the lattice dual to that graph. For the QZ2LGT, when the coupling parameter <jats:italic>g</jats:italic> is less than the critical value <jats:italic>g</jats:italic> <jats:sub> <jats:italic>c</jats:italic> </jats:sub>, the ground state is a superposition of all configurations with closed strings of same spins, which can be obtained by using an adiabatic quantum algorithm. A subsequent search for a HC among those closed strings solves the original HC problem. The method is demonstrated for random samples of small graphs.","PeriodicalId":11738,"journal":{"name":"EPL","volume":"16 1","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"EPL","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1209/0295-5075/ad130b","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract We propose the correspondence between the Hamiltonian cycle (HC) problem in graph theory and the quantum lattice gauge theory (QZ2LGT) defined on the lattice dual to that graph. For the QZ2LGT, when the coupling parameter g is less than the critical value gc, the ground state is a superposition of all configurations with closed strings of same spins, which can be obtained by using an adiabatic quantum algorithm. A subsequent search for a HC among those closed strings solves the original HC problem. The method is demonstrated for random samples of small graphs.
摘要 我们提出了图论中的哈密顿循环（HC）问题与定义在该图对偶晶格上的量子晶格规理论（QZ2LGT）之间的对应关系。对于 QZ2LGT，当耦合参数 g 小于临界值 g c 时，基态是所有具有相同自旋的闭合弦的构型的叠加，可以通过绝热量子算法获得。随后在这些闭合弦中寻找一个 HC，就解决了最初的 HC 问题。该方法针对小型图的随机样本进行了演示。
期刊介绍：
General physics – physics of elementary particles and fields – nuclear physics – atomic, molecular and optical physics – classical areas of phenomenology – physics of gases, plasmas and electrical discharges – condensed matter – cross-disciplinary physics and related areas of science and technology.
Letters submitted to EPL should contain new results, ideas, concepts, experimental methods, theoretical treatments, including those with application potential and be of broad interest and importance to one or several sections of the physics community. The presentation should satisfy the specialist, yet remain understandable to the researchers in other fields through a suitable, clearly written introduction and conclusion (if appropriate).
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