{"title":"图上格罗弗漫步与粗里奇曲率之间的传输距离","authors":"Yasuaki Fujitani, Chusei Kiumi","doi":"10.1007/s11128-024-04373-2","DOIUrl":null,"url":null,"abstract":"<div><p>One direction to investigate the relation between quantum walks and their underlying graphs is to define geometric quantity concerning quantum walks. In order to contribute to this direction, we define a transport distance between Grover walks, which can be seen as a quantum analogue of symmetric random walks. We employ signed optimal transport theory to formulate this distance. Also, we define coarse Ricci curvature induced by Grover walks and investigate its property. It has been found that this coarse Ricci curvature has similar properties to those of coarse Ricci curvature induced by random walks.</p></div>","PeriodicalId":746,"journal":{"name":"Quantum Information Processing","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Transport distance between Grover walks on graphs and coarse Ricci curvature\",\"authors\":\"Yasuaki Fujitani, Chusei Kiumi\",\"doi\":\"10.1007/s11128-024-04373-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>One direction to investigate the relation between quantum walks and their underlying graphs is to define geometric quantity concerning quantum walks. In order to contribute to this direction, we define a transport distance between Grover walks, which can be seen as a quantum analogue of symmetric random walks. We employ signed optimal transport theory to formulate this distance. Also, we define coarse Ricci curvature induced by Grover walks and investigate its property. It has been found that this coarse Ricci curvature has similar properties to those of coarse Ricci curvature induced by random walks.</p></div>\",\"PeriodicalId\":746,\"journal\":{\"name\":\"Quantum Information Processing\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-05-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quantum Information Processing\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11128-024-04373-2\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum Information Processing","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11128-024-04373-2","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
Transport distance between Grover walks on graphs and coarse Ricci curvature
One direction to investigate the relation between quantum walks and their underlying graphs is to define geometric quantity concerning quantum walks. In order to contribute to this direction, we define a transport distance between Grover walks, which can be seen as a quantum analogue of symmetric random walks. We employ signed optimal transport theory to formulate this distance. Also, we define coarse Ricci curvature induced by Grover walks and investigate its property. It has been found that this coarse Ricci curvature has similar properties to those of coarse Ricci curvature induced by random walks.
期刊介绍:
Quantum Information Processing is a high-impact, international journal publishing cutting-edge experimental and theoretical research in all areas of Quantum Information Science. Topics of interest include quantum cryptography and communications, entanglement and discord, quantum algorithms, quantum error correction and fault tolerance, quantum computer science, quantum imaging and sensing, and experimental platforms for quantum information. Quantum Information Processing supports and inspires research by providing a comprehensive peer review process, and broadcasting high quality results in a range of formats. These include original papers, letters, broadly focused perspectives, comprehensive review articles, book reviews, and special topical issues. The journal is particularly interested in papers detailing and demonstrating quantum information protocols for cryptography, communications, computation, and sensing.