Skip to main content

Space Complexity of Streaming Algorithms on Universal Quantum Computers

  • Conference paper
  • First Online:
Theory and Applications of Models of Computation (TAMC 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12337))

Abstract

Universal quantum computers are the only general purpose quantum computers known that can be implemented as of today. These computers consist of a classical memory component which controls the quantum memory. In this paper, the space complexity of some data stream problems, such as PartialMOD and Equality, is investigated on universal quantum computers. The quantum algorithms for these problems are believed to outperform their classical counterparts. Universal quantum computers, however, need classical bits for controlling quantum gates in addition to qubits. Our analysis shows that the number of classical bits used in quantum algorithms is equal to or even larger than that of classical bits used in corresponding classical algorithms. These results suggest that there is no advantage of implementing certain data stream problems on universal quantum computers instead of classical computers when space complexity is considered.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Ablayev, F., Gainutdinova, A., Karpinski, M., Moore, C., Pollett, C.: On the computational power of probabilistic and quantum branching program. Inf. Comput. 203(2), 145–162 (2005)

    Article  MathSciNet  Google Scholar 

  2. Ablayev, F., Gainutdinova, A., Khadiev, K., Yakaryılmaz, A.: Very narrow quantum OBDDs and width hierarchies for classical OBDDs. In: Jürgensen, H., Karhumäki, J., Okhotin, A. (eds.) DCFS 2014. LNCS, vol. 8614, pp. 53–64. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09704-6_6

    Chapter  Google Scholar 

  3. Ablayev, F., Khasianov, A., Vasiliev, A.: On complexity of quantum branching programs computing equality-like Boolean functions. Electronic Colloquium on Computational Complexity (2010)

    Google Scholar 

  4. Alon, N., Matias, Y., Szegedy, M.: The space complexity of approximating the frequency moments. In: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing. STOC (1996)

    Google Scholar 

  5. Ambainis, A., Yakaryılmaz, A.: Superiority of exact quantum automata for promise problems. Inf. Process. Lett. 112(7), 289–291 (2012)

    Article  MathSciNet  Google Scholar 

  6. Babai, L., Kimmel, P.G.: Randomized simultaneous messages: solution of a problem of Yao in communication complexity. In: Proceedings of the 12th Annual IEEE Conference on Computational Complexity. CCC (1997)

    Google Scholar 

  7. Buhrman, H., Cleve, R., Watrous, J., de Wolf, R.: Quantum fingerprinting. Phys. Rev. Lett. 87, 167902 (2001)

    Article  Google Scholar 

  8. Dawson, C.M., Nielsen, M.A.: The Solovay-Kitaev algorithm. Quantum Inf. Comput. 6(1), 81–95 (2006)

    MathSciNet  MATH  Google Scholar 

  9. Gavinsky, D., Kempe, J., Kerenidis, I., Raz, R., de Wolf, R.: Exponential separations for one-way quantum communication complexity, with applications to cryptography. In: Proceedings of the Thirty-Ninth Annual ACM Symposium on Theory of Computing. STOC (2007)

    Google Scholar 

  10. Guan, J.Y., et al.: Observation of quantum fingerprinting beating the classical limit. Phys. Rev. Lett. 116, 240502 (2016)

    Article  Google Scholar 

  11. Harrow, A.W., Recht, B., Chuang, I.L.: Efficient discrete approximations of quantum gates. J. Math. Phys. 43(9), 4445–4451 (2002)

    Article  MathSciNet  Google Scholar 

  12. Karp, R.M., Rabin, M.O.: Efficient randomized pattern-matching algorithms. IBM J. Res. Dev. 31(2), 249–260 (1987)

    Article  MathSciNet  Google Scholar 

  13. Khadiev, K., Khadieva, A., Kravchenko, D., Rivosh, A.: Quantum versus Classical Online Algorithms with Advice and Logarithmic Space (2017)

    Google Scholar 

  14. Khadiev, K., Khadieva, A., Mannapov, I.: Quantum online algorithms with respect to space complexity. Lobachevskii J. Math. 39, 1377–1387 (2017)

    Article  MathSciNet  Google Scholar 

  15. Khadiev, K., Ziatdinov, M., Mannapov, I., Khadieva, A., Yamilov, R.: Quantum Online Streaming Algorithms with Constant Number of Advice Bits (2018)

    Google Scholar 

  16. Kitaev, A.Y., Shen, A., Vyalyi, M.N.: Classical and Quantum Computation. American Mathematical Society, Boston (2002)

    Book  Google Scholar 

  17. Le Gall, F.: Exponential separation of quantum and classical online space complexity. Theory Comput. Syst. 45, 188–202 (2009)

    Article  MathSciNet  Google Scholar 

  18. Newman, I., Szegedy, M.: Public vs. private coin flips in one round communication games (extended abstract). In: Proceedings of the Twenty-eighth Annual ACM Symposium on Theory of Computing. STOC (1996)

    Google Scholar 

  19. Nielsen, M.A., Chuang, I.L.: Programmable quantum gate arrays. Phys. Rev. Lett. 79, 321 (1997)

    Article  MathSciNet  Google Scholar 

  20. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th, Anniversary Edition. Cambridge University Press, Cambridge (2010)

    Book  Google Scholar 

  21. Sauerhoff, M., Sieling, D.: Quantum branching programs and space-bounded nonuniform quantum complexity. Theoret. Comput. Sci. 334(1), 177–225 (2005)

    Article  MathSciNet  Google Scholar 

  22. Watrous, J.H.: Space-bounded quantum computation. Ph.D. thesis, The University of Wisconsin, Madison (1998)

    Google Scholar 

  23. Yao, A.C.C.: Some complexity questions related to distributive computing (preliminary report). In: Proceedings of the Eleventh Annual ACM Symposium on Theory of Computing. STOC (1979)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Darya Melnyk .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Hu, Y., Melnyk, D., Wang, Y., Wattenhofer, R. (2020). Space Complexity of Streaming Algorithms on Universal Quantum Computers. In: Chen, J., Feng, Q., Xu, J. (eds) Theory and Applications of Models of Computation. TAMC 2020. Lecture Notes in Computer Science(), vol 12337. Springer, Cham. https://doi.org/10.1007/978-3-030-59267-7_24

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-59267-7_24

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-59266-0

  • Online ISBN: 978-3-030-59267-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics