{"title":"晶格上反应-扩散系统的数字量子模拟","authors":"Louie Hong Yao","doi":"10.1140/epjb/s10051-025-00930-5","DOIUrl":null,"url":null,"abstract":"<p>The quantum computer offers significant advantages in simulating physical systems, particularly those with exponentially large state spaces, such as quantum systems. Stochastic reaction–diffusion systems, characterized by their stochastic nature, also exhibit exponential growth in the dimension of the state space, posing challenges for simulation at a probability distribution level. We explore the quantum simulation of stochastic reaction–diffusion systems on a digital quantum computer, directly simulating the system at the master equation level. Leveraging a spin representation of the system, we employ Trotterization and probabilistic imaginary time evolution (PITE) to simulate the probability distribution directly. We illustrate this approach through four diverse examples, ranging from simple single-lattice site generation-annihilation processes to a system featuring active-absorbing phase transition.</p>","PeriodicalId":787,"journal":{"name":"The European Physical Journal B","volume":"98 5","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2025-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1140/epjb/s10051-025-00930-5.pdf","citationCount":"0","resultStr":"{\"title\":\"Digital quantum simulation of reaction–diffusion systems on lattice\",\"authors\":\"Louie Hong Yao\",\"doi\":\"10.1140/epjb/s10051-025-00930-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The quantum computer offers significant advantages in simulating physical systems, particularly those with exponentially large state spaces, such as quantum systems. Stochastic reaction–diffusion systems, characterized by their stochastic nature, also exhibit exponential growth in the dimension of the state space, posing challenges for simulation at a probability distribution level. We explore the quantum simulation of stochastic reaction–diffusion systems on a digital quantum computer, directly simulating the system at the master equation level. Leveraging a spin representation of the system, we employ Trotterization and probabilistic imaginary time evolution (PITE) to simulate the probability distribution directly. We illustrate this approach through four diverse examples, ranging from simple single-lattice site generation-annihilation processes to a system featuring active-absorbing phase transition.</p>\",\"PeriodicalId\":787,\"journal\":{\"name\":\"The European Physical Journal B\",\"volume\":\"98 5\",\"pages\":\"\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2025-05-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1140/epjb/s10051-025-00930-5.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The European Physical Journal B\",\"FirstCategoryId\":\"4\",\"ListUrlMain\":\"https://link.springer.com/article/10.1140/epjb/s10051-025-00930-5\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, CONDENSED MATTER\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The European Physical Journal B","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1140/epjb/s10051-025-00930-5","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, CONDENSED MATTER","Score":null,"Total":0}
Digital quantum simulation of reaction–diffusion systems on lattice
The quantum computer offers significant advantages in simulating physical systems, particularly those with exponentially large state spaces, such as quantum systems. Stochastic reaction–diffusion systems, characterized by their stochastic nature, also exhibit exponential growth in the dimension of the state space, posing challenges for simulation at a probability distribution level. We explore the quantum simulation of stochastic reaction–diffusion systems on a digital quantum computer, directly simulating the system at the master equation level. Leveraging a spin representation of the system, we employ Trotterization and probabilistic imaginary time evolution (PITE) to simulate the probability distribution directly. We illustrate this approach through four diverse examples, ranging from simple single-lattice site generation-annihilation processes to a system featuring active-absorbing phase transition.