计算机科学 ›› 2015, Vol. 42 ›› Issue (7): 134-137.doi: 10.11896/j.issn.1002-137X.2015.07.029

• 2014’全国理论计算机科学年会 • 上一篇    下一篇

两类量子游走组成的非确定型量子程序的终止验证

雷红轩   

  1. 内江师范学院数学与信息科学学院 内江641112 四川省高等学校数值仿真重点实验室 内江641112
  • 出版日期:2018-11-14 发布日期:2018-11-14
  • 基金资助:
    本文受四川省教育厅重点科研项目(14ZA0242),内江师范学院专业核心课程(hk07010201),四川省教育厅科研创新团队基金(14TD0026),教育部数学与应用数学专业综合改革(ZG0464),四川省数学与应用数学专业综合改革(01249)资助

Verification of Termination for Nondeterministic Quantum Programs Constituted by Two Kinds of Quantum Walks

LEI Hong-xuan   

  • Online:2018-11-14 Published:2018-11-14

摘要: 首先给出了C4空间中由量子游走组成的非确定型量子程序的概念,其次讨论了它们从初态运行时在不同的测量算子下的可达集合、终止集合和发散集合。研究表明:非确定型量子程序的终止、发散和可达集合、发散集合与选取的测量算子有密切的关系。程序在不同测量算子作用下从同一个初态运行时可能终止,也可能发散;并且,同一个初态的可达集合中终态和发散态共存。

关键词: 量子游走,非确定型量子程序,终止概率,程序验证

Abstract: Firstly,the model of nondeterministic quantum programs constituted by quantum walks was proposed in C3 and C4.Secondly,the sets of reachable states,terminating states and diverging states of nondeterministic quantum programs starting in initial states under different measurement operators were discussed.It shows that the termination,diverging,the sets of reachable states and diverging states of nondeterministic quantum programs depend closely on the selection of measurement operators.The nondeterministic quantum programs starting in common initial states under different measurement operators is possible to terminate or diverge and the terminating states and diverging states of nondeterministic quantum programs coexist in the sets of reachable states starting in common initial states.

Key words: Quantum walks,Nondeterministic quantum programs,Termination probability,Program verification

[1] Nielsen M A,Chuang I L.Quantum computation and quantum information[M].Cambridge:Cambridge University Press,2000
[2] Abramsky S.High-level methods for quantum computation and information[C]∥Proceedings of 19th Annual IEEE Symposium on Logic in Computer Science (LICS’04).2004:410-414
[3] Knill E H.Conventions for quantum pseudo-code[R].LANL report LAUR-96-2724,1996
[4] Selinger P.Towards a quantum programming language[J].Mathematical Structures in Computer Science,2004,14(4):527-586
[5] Gay S J,Nagarajan R.Communicating quantum processes,An-nual Symposium on Principles of Programming Languages[C]∥Proceedings of 32nd ACM SIGPLANSIGACT symposium on Principles of programming languages.Long Beach,California,USA,2005:145-157
[6] Lalire M,Jorrand P.A Process Algebraic Approach to Concurrent and Distributed Quantum Computation:Operational Semantics[C]∥Proceedings of 2nd International Workshop on Quantum Programming Languages.Turku,Finland,2004
[7] Feng Y,Duan R Y,Ying MS .Bisimulation for quantum processes[C]∥Proceedings of 38th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL).2011:523-534
[8] D’Hondt E,Panangaden P.Quantum weakest preconditions[J/OL].http://arxiv.org/pdf/quant-ph/0501157.pdf
[9] 徐家福,宋方敏.量子程序设计语言初探[J].中国科学E辑:信息科学,2008,38(6):829-842 Xu Jia-fu,Song Fang-min.Study on Quantum Programming Language[J].Science in China(E):Information Science,2008,38(6):829-842
[10] 宋方敏,钱士钧,戴静安,等.量子程序设计语言NDQJava处理系统[J].软件学报,2008,19(1):9-16 Song Fang-min,Qian Shi-jun,Dai Jing-an,et al.Processing System of Quantum Programming Language NDQJava[J].Journal of Software,2008,19(1):9-16
[11] Ying M S,Feng Y,Duan R Y,et al.An Algebra of Quantum Processes[J].ACM Transactions on Computational Logic,2009,10(3):19:36
[12] Li Y J,Yu N K,Ying M S.Termination of NodeterministicQuantum Programs[J].Acta Informatica,2014,51(1):1-24
[13] Feng Y,Duan R Y,Ji Z F,et al.Proof rules for the correctness of quantum programs[J].Theoretical Computer Science,2007,386:151-166
[14] Ying M S,Feng Y.Quantum loop programs[J].Acta Informatica,2010,47(4):221-250
[15] Ying M S,Yu N K,Feng Y,et al.Verification of Quantum programs[J].Science of Computer Programming,2013,78(9):1679-1700
[16] Yu N K,Ying M S.Reachability and Termination Analysis of Concurrent Quantum Programs[DB/OL].http://arXiv.org/abs/1206.1935v1,2012
[17] 雷红轩,席政军,李永明.几种量子程序终止的有效验证[J].计算机科学,2012,39(11):75-78 Lei Hong-xuan,Xi Zheng-jun,Li Yong-ming.Valid Verification of Termination for Some Quantum Programs[J].Computer Science,2012,39(11):75-78
[18] 雷红轩,席政军,李永明.广义量子Loop程序的若干性质[J].电子学报,2013,41(4):727-732 Lei Hong-xuan,Xi Zheng-jun,Li Yong-ming.Some Properties of Generalized Quantum Loop Program[J].Acta Electronica Sinica,2013,41(4):727-732
[19] 雷红轩,席政军,李永明.量子最弱自由前置条件的交换性及其性质[J].软件学报,2013,24(5):933-941 Lei Hong-xuan,Xi Zheng-jun,Li Yong-ming.Commutativity of Quantum Weakest Liberal Precondition and Its Properties [J].Journal of Software,2013,24(5):933-941

No related articles found!
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!