经典和量子分支程序的计算能力

F. Ablayev
{"title":"经典和量子分支程序的计算能力","authors":"F. Ablayev","doi":"10.1117/12.683111","DOIUrl":null,"url":null,"abstract":"We present a classical stochastic simulation technique of quantum Branching programs. This technique allows to prove the following relations among complexity classes: PrQP-BP &subuline; PP-BP and BQP-BP &subuline; PP-BP. Here BPP-BP and PP-BP stands for the classes of functions computable with bounded error and unbounded error respectively by stochastic branching program of polynomial size. BQP-BP and PrQP-BP stands the classes of functions computable with bounded error and unbounded error respectively by quantum branching program of polynomial size. Second. We present two different types, of complexity lower bounds for quantum nonuniform automata (OBDDs). We call them \"metric\" and \"entropic\" lower bounds in according to proof technique used. We present explicit Boolean functions that show that these lower bounds are tight enough. We show that when considering \"almost all Boolean functions\" on n variables our entropic lower bounds gives exponential (2c(δ)(n-log n)) lower bound for the width of quantum OBDDs depending on the error δ allowed.","PeriodicalId":90714,"journal":{"name":"Quantum bio-informatics V : proceedings of the quantum bio-informatics 2011, Tokyo University of Science, Japan, 7-12 March 2011. Quantum Bio-Informatics (Conference) (5th : 2011 : Tokyo, Japan)","volume":"38 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2006-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"On computational power of classical and quantum branching programs\",\"authors\":\"F. Ablayev\",\"doi\":\"10.1117/12.683111\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present a classical stochastic simulation technique of quantum Branching programs. This technique allows to prove the following relations among complexity classes: PrQP-BP &subuline; PP-BP and BQP-BP &subuline; PP-BP. Here BPP-BP and PP-BP stands for the classes of functions computable with bounded error and unbounded error respectively by stochastic branching program of polynomial size. BQP-BP and PrQP-BP stands the classes of functions computable with bounded error and unbounded error respectively by quantum branching program of polynomial size. Second. We present two different types, of complexity lower bounds for quantum nonuniform automata (OBDDs). We call them \\\"metric\\\" and \\\"entropic\\\" lower bounds in according to proof technique used. We present explicit Boolean functions that show that these lower bounds are tight enough. We show that when considering \\\"almost all Boolean functions\\\" on n variables our entropic lower bounds gives exponential (2c(δ)(n-log n)) lower bound for the width of quantum OBDDs depending on the error δ allowed.\",\"PeriodicalId\":90714,\"journal\":{\"name\":\"Quantum bio-informatics V : proceedings of the quantum bio-informatics 2011, Tokyo University of Science, Japan, 7-12 March 2011. Quantum Bio-Informatics (Conference) (5th : 2011 : Tokyo, Japan)\",\"volume\":\"38 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-05-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quantum bio-informatics V : proceedings of the quantum bio-informatics 2011, Tokyo University of Science, Japan, 7-12 March 2011. Quantum Bio-Informatics (Conference) (5th : 2011 : Tokyo, Japan)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1117/12.683111\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum bio-informatics V : proceedings of the quantum bio-informatics 2011, Tokyo University of Science, Japan, 7-12 March 2011. Quantum Bio-Informatics (Conference) (5th : 2011 : Tokyo, Japan)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1117/12.683111","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2

摘要

提出了一种经典的量子分支程序随机模拟技术。该技术允许证明复杂性类之间的以下关系:PrQP-BP & subline;PP-BP和BQP-BP & subline;PP-BP。其中BPP-BP和PP-BP分别表示可通过多项式大小的随机分支规划计算有界误差和无界误差的函数类。BQP-BP和PrQP-BP分别表示多项式大小的量子分支规划可计算有界误差和无界误差的函数类。第二。提出了两种不同类型的量子非均匀自动机(obdd)的复杂度下界。根据所使用的证明技术,我们称它们为“度规”和“熵”下界。我们给出了明确的布尔函数来证明这些下界是足够紧密的。我们表明,当考虑n个变量上的“几乎所有布尔函数”时,我们的熵下界根据允许的误差δ给出了量子obdd宽度的指数下界(2c(δ)(n-log n))。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On computational power of classical and quantum branching programs
We present a classical stochastic simulation technique of quantum Branching programs. This technique allows to prove the following relations among complexity classes: PrQP-BP &subuline; PP-BP and BQP-BP &subuline; PP-BP. Here BPP-BP and PP-BP stands for the classes of functions computable with bounded error and unbounded error respectively by stochastic branching program of polynomial size. BQP-BP and PrQP-BP stands the classes of functions computable with bounded error and unbounded error respectively by quantum branching program of polynomial size. Second. We present two different types, of complexity lower bounds for quantum nonuniform automata (OBDDs). We call them "metric" and "entropic" lower bounds in according to proof technique used. We present explicit Boolean functions that show that these lower bounds are tight enough. We show that when considering "almost all Boolean functions" on n variables our entropic lower bounds gives exponential (2c(δ)(n-log n)) lower bound for the width of quantum OBDDs depending on the error δ allowed.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信