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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
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)
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
Ablayev, F., Khasianov, A., Vasiliev, A.: On complexity of quantum branching programs computing equality-like Boolean functions. Electronic Colloquium on Computational Complexity (2010)
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)
Ambainis, A., Yakaryılmaz, A.: Superiority of exact quantum automata for promise problems. Inf. Process. Lett. 112(7), 289–291 (2012)
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)
Buhrman, H., Cleve, R., Watrous, J., de Wolf, R.: Quantum fingerprinting. Phys. Rev. Lett. 87, 167902 (2001)
Dawson, C.M., Nielsen, M.A.: The Solovay-Kitaev algorithm. Quantum Inf. Comput. 6(1), 81–95 (2006)
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)
Guan, J.Y., et al.: Observation of quantum fingerprinting beating the classical limit. Phys. Rev. Lett. 116, 240502 (2016)
Harrow, A.W., Recht, B., Chuang, I.L.: Efficient discrete approximations of quantum gates. J. Math. Phys. 43(9), 4445–4451 (2002)
Karp, R.M., Rabin, M.O.: Efficient randomized pattern-matching algorithms. IBM J. Res. Dev. 31(2), 249–260 (1987)
Khadiev, K., Khadieva, A., Kravchenko, D., Rivosh, A.: Quantum versus Classical Online Algorithms with Advice and Logarithmic Space (2017)
Khadiev, K., Khadieva, A., Mannapov, I.: Quantum online algorithms with respect to space complexity. Lobachevskii J. Math. 39, 1377–1387 (2017)
Khadiev, K., Ziatdinov, M., Mannapov, I., Khadieva, A., Yamilov, R.: Quantum Online Streaming Algorithms with Constant Number of Advice Bits (2018)
Kitaev, A.Y., Shen, A., Vyalyi, M.N.: Classical and Quantum Computation. American Mathematical Society, Boston (2002)
Le Gall, F.: Exponential separation of quantum and classical online space complexity. Theory Comput. Syst. 45, 188–202 (2009)
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)
Nielsen, M.A., Chuang, I.L.: Programmable quantum gate arrays. Phys. Rev. Lett. 79, 321 (1997)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th, Anniversary Edition. Cambridge University Press, Cambridge (2010)
Sauerhoff, M., Sieling, D.: Quantum branching programs and space-bounded nonuniform quantum complexity. Theoret. Comput. Sci. 334(1), 177–225 (2005)
Watrous, J.H.: Space-bounded quantum computation. Ph.D. thesis, The University of Wisconsin, Madison (1998)
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)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
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)