{"title":"几何因果关系:将费曼积分引入量子算法","authors":"German Fabricio Roberto Sborlini","doi":"10.31349/suplrevmexfis.4.021103","DOIUrl":null,"url":null,"abstract":"The calculation of higher-order corrections in Quantum Field Theories is a challenging task. In particular, dealing with multiloop and multileg Feynman amplitudes leads to severe bottlenecks and a very fast scaling of the computational resources required to perform the calculation. With the purpose of overcoming these limitations, we discuss efficient strategies based on the Loop-Tree Duality, its manifestly causal representation and the underlying geometrical interpretation. In concrete, we exploit the geometrical causal selection rules to define a Hamiltonian whose ground-state is directly related to the terms contributing to the causal representation. In this way, the problem can be translated into a minimization one and implemented in a quantum computer to search for a potential speed-up.","PeriodicalId":210091,"journal":{"name":"Suplemento de la Revista Mexicana de Física","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Geometrical causality: casting Feynman integrals into quantum algorithms\",\"authors\":\"German Fabricio Roberto Sborlini\",\"doi\":\"10.31349/suplrevmexfis.4.021103\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The calculation of higher-order corrections in Quantum Field Theories is a challenging task. In particular, dealing with multiloop and multileg Feynman amplitudes leads to severe bottlenecks and a very fast scaling of the computational resources required to perform the calculation. With the purpose of overcoming these limitations, we discuss efficient strategies based on the Loop-Tree Duality, its manifestly causal representation and the underlying geometrical interpretation. In concrete, we exploit the geometrical causal selection rules to define a Hamiltonian whose ground-state is directly related to the terms contributing to the causal representation. In this way, the problem can be translated into a minimization one and implemented in a quantum computer to search for a potential speed-up.\",\"PeriodicalId\":210091,\"journal\":{\"name\":\"Suplemento de la Revista Mexicana de Física\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Suplemento de la Revista Mexicana de Física\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.31349/suplrevmexfis.4.021103\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Suplemento de la Revista Mexicana de Física","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31349/suplrevmexfis.4.021103","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Geometrical causality: casting Feynman integrals into quantum algorithms
The calculation of higher-order corrections in Quantum Field Theories is a challenging task. In particular, dealing with multiloop and multileg Feynman amplitudes leads to severe bottlenecks and a very fast scaling of the computational resources required to perform the calculation. With the purpose of overcoming these limitations, we discuss efficient strategies based on the Loop-Tree Duality, its manifestly causal representation and the underlying geometrical interpretation. In concrete, we exploit the geometrical causal selection rules to define a Hamiltonian whose ground-state is directly related to the terms contributing to the causal representation. In this way, the problem can be translated into a minimization one and implemented in a quantum computer to search for a potential speed-up.