Papers
Topics
Authors
Recent
Assistant
AI Research Assistant
Well-researched responses based on relevant abstracts and paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses.
Gemini 2.5 Flash
Gemini 2.5 Flash 173 tok/s
Gemini 2.5 Pro 47 tok/s Pro
GPT-5 Medium 43 tok/s Pro
GPT-5 High 44 tok/s Pro
GPT-4o 94 tok/s Pro
Kimi K2 180 tok/s Pro
GPT OSS 120B 438 tok/s Pro
Claude Sonnet 4.5 36 tok/s Pro
2000 character limit reached

Game Semantics for Higher-Order Unitary Quantum Computation (2404.06646v1)

Published 9 Apr 2024 in cs.PL and quant-ph

Abstract: We develop a symmetric monoidal closed category of games, incorporating sums and products, to model quantum computation at higher types. This model is expressive, capable of representing all unitary operators at base types. It is compatible with base types and realizable by unitary operators.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (26)
  1. Quantum complexity theory. SIAM Journal on Computing, 26(5):1411–1473, 1997.
  2. A Lambda Calculus for Quantum Computation with Classical Control, page 354–368. Springer Berlin Heidelberg, 2005. ISBN 9783540320142. doi: 10.1007/11417170˙26. URL http://dx.doi.org/10.1007/11417170_26.
  3. Applying quantitative semantics to higher-order quantum computing. In Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL ’14, page 647–658, New York, NY, USA, 2014. Association for Computing Machinery. ISBN 9781450325448. doi: 10.1145/2535838.2535879. URL https://doi.org/10.1145/2535838.2535879.
  4. Peter Selinger. Towards a semantics for higher-order quantum computation. In Proceedings of the 2nd International Workshop on Quantum Programming Languages, QPL 2004, Turku, Finland, TUCS General Publication No 33, pages 127–143. Turku Centre for Computer Science, 2004. Expanded version available from http://www.mathstat.dal.ca/~selinger/papers.html#cones.
  5. Interacting quantum observables. In Luca Aceto, Ivan Damgård, Leslie Ann Goldberg, Magnús M. Halldórsson, Anna Ingólfsdóttir, and Igor Walukiewicz, editors, Automata, Languages and Programming, pages 298–310, Berlin, Heidelberg, 2008. Springer Berlin Heidelberg.
  6. Jean-Yves Girard. Between logic and quantic: A tract. In Thomas Ehrhard, editor, Linear Logic in Computer Science, pages 316–346. Cambridge University Press, 2004.
  7. With a few square roots, quantum computing is as easy as pi. Proc. ACM Program. Lang., 8(POPL), jan 2024. URL https://doi.org/10.1145/3632861.
  8. Linear dependent type theory for quantum programming languages. Logical Methods in Computer Science, 18(3:28):1–44, 2022.
  9. Reversible monadic computing. Electronic Notes in Theoretical Computer Science, 319:217–237, 2015. ISSN 1571-0661. doi: https://doi.org/10.1016/j.entcs.2015.12.014. URL https://www.sciencedirect.com/science/article/pii/S157106611500081X. The 31st Conference on the Mathematical Foundations of Programming Semantics (MFPS XXXI).
  10. Samson Abramsky. A structural approach to reversible computation. Theoretical Computer Science, 347(3):441–464, 2005. ISSN 0304-3975. doi: https://doi.org/10.1016/j.tcs.2005.07.002. URL https://www.sciencedirect.com/science/article/pii/S0304397505003804.
  11. The structure of multiplicatives. Archive for Mathematical Logic, 28(3):181–203, 1989. doi: 10.1007/bf01622878.
  12. Jean-Yves Girard. Geometry of interaction 1: Interpretation of system f. In R. Ferro, C. Bonotto, S. Valentini, and A. Zanardo, editors, Logic Colloquium ’88, volume 127 of Studies in Logic and the Foundations of Mathematics, pages 221 – 260. Elsevier, 1989. doi: https://doi.org/10.1016/S0049-237X(08)70271-4. URL http://www.sciencedirect.com/science/article/pii/S0049237X08702714.
  13. Andreas Blass. A game semantics for linear logic. Annals of Pure and Applied Logic, 56(1):183–220, 1992. ISSN 0168-0072. doi: https://doi.org/10.1016/0168-0072(92)90073-9. URL https://www.sciencedirect.com/science/article/pii/0168007292900739.
  14. Games and full completeness for multiplicative linear logic. Journal of Symbolic Logic, 59(2):543–574, 1994. doi: 10.2307/2275407.
  15. Full abstraction for pcf. Information and Computation, 163(2):409–470, 2000. ISSN 0890-5401. doi: https://doi.org/10.1006/inco.2000.2930. URL https://www.sciencedirect.com/science/article/pii/S0890540100929304.
  16. On full abstraction for pcf: I, ii, and iii. Information and Computation, 163(2):285–408, 2000. ISSN 0890-5401.
  17. Hanno Nickau. Hereditarily sequential functionals. In Logical Foundations of Computer Science, Third International Symposium, LFCS’94, St. Petersburg, Russia, July 11-14, 1994, Proceedings, pages 253–264, 1994.
  18. Samson Abramsky. Semantics of Interaction: an Introduction to Game Semantics, page 1–32. Publications of the Newton Institute. Cambridge University Press, 1997.
  19. Traced monoidal categories. Mathematical Proceedings of the Cambridge Philosophical Society, 119(3):447–468, 1996. doi: 10.1017/S0305004100074338.
  20. Samson Abramsky. Retracing some paths in process algebra. In Ugo Montanari and Vladimiro Sassone, editors, CONCUR ’96: Concurrency Theory, pages 1–17, Berlin, Heidelberg, 1996. Springer Berlin Heidelberg. ISBN 978-3-540-70625-0.
  21. Geometry of Interaction and the Dynamics of Proof Reduction: A Tutorial. In Bob Coecke, editor, New Structures for Physics, volume 813 of Lecture Notes in Physics, pages 357–417. Springer, Berlin, Heidelberg, 2010. doi: 10.1007/978-3-642-12821-9˙5. URL http://www.site.uottawa.ca/~phil/papers/HS.GoI-tut.33.pdf.
  22. Exhausting strategies, joker games and full completeness for imll with unit. Theoretical Computer Science, 294(1):269–305, 2003. ISSN 0304-3975. doi: https://doi.org/10.1016/S0304-3975(01)00244-4. URL https://www.sciencedirect.com/science/article/pii/S0304397501002444. Category Theory and Computer Science.
  23. Ana C Calderon and Guy A McCusker. Understanding game semantics through coherence spaces. Electronic Notes in Theoretical Computer Science, 265:231–244, September 2010. ISSN 1571-0661. Proceedings of the 26th Conference on the Mathematical Foundations of Programming Semantics (MFPS 2010).
  24. Physical traces: Quantum vs. classical information processing. Electronic Notes in Theoretical Computer Science, 69:1–22, 2003. ISSN 1571-0661. doi: https://doi.org/10.1016/S1571-0661(04)80556-5. URL https://www.sciencedirect.com/science/article/pii/S1571066104805565. CTCS’02, Category Theory and Computer Science.
  25. Julian Schwinger. Unitary operator bases. Proceedings of the National Academy of Sciences of the United States of America, 46(4), 1960. URL http://www.jstor.org/stable/70873.
  26. John Wheeler. Relationships among the unitary bases of weyl, schwinger, werner and oppenheim. From https://www.reed.edu/physics/faculty/wheeler/documents/Miscellaneous

Summary

We haven't generated a summary for this paper yet.

Dice Question Streamline Icon: https://streamlinehq.com

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Lightbulb Streamline Icon: https://streamlinehq.com

Continue Learning

We haven't generated follow-up questions for this paper yet.

List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets

This paper has been mentioned in 1 tweet and received 0 likes.

Upgrade to Pro to view all of the tweets about this paper: