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41st Annual Symposium on Foundations of Computer Science
The quantum complexity of set membership
Redondo Beach, California
November 12November 14
ISBN: 0769508502
ASCII Text  x  
J. Radhakrishnan, P. Sen, S. Venkatesh, "The quantum complexity of set membership," 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pp. 554, 41st Annual Symposium on Foundations of Computer Science, 2000.  
BibTex  x  
@article{ 10.1109/SFCS.2000.892143, author = {J. Radhakrishnan and P. Sen and S. Venkatesh}, title = {The quantum complexity of set membership}, journal ={2013 IEEE 54th Annual Symposium on Foundations of Computer Science}, volume = {0}, year = {2000}, issn = {02725428}, pages = {554}, doi = {http://doi.ieeecomputersociety.org/10.1109/SFCS.2000.892143}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  CONF JO  2013 IEEE 54th Annual Symposium on Foundations of Computer Science TI  The quantum complexity of set membership SN  02725428 SP EP A1  J. Radhakrishnan, A1  P. Sen, A1  S. Venkatesh, PY  2000 KW  quantum computing; computational complexity; set theory; probes; linear algebra; query processing; quantum complexity; static set membership problem; bit table; query answering; lower bounds; upper bounds; quantum bitprobe model; blackbox unitary transform; oracle calls; query algorithm; basis state superposition; spaceprobe tradeoff; linear algebra VL  0 JA  2013 IEEE 54th Annual Symposium on Foundations of Computer Science ER   
Studies the quantum complexity of the static set membership problem: given a subset S (S/spl les/n) of a universe of size m(/spl Gt/n), store it as a table, T:(0,1)/sup r//spl rarr/(0,1), of bits so that queries of the form 'is x in S?' can be answered. The goal is to use a small table and yet answer queries using a few bit probes. This problem was considered by H. Buhrman et al. (2000), who showed lower and upper bounds for this problem in the classical deterministic and randomised models. In this paper, we formulate this problem in the "quantum bitprobe model". We assume that access to the table T is provided by means of a blackbox (oracle) unitary transform O/sub T/ that takes the basis state (y,b) to the basis state y,b/spl oplus/T(y)<. The query algorithm is allowed to apply O/sub T/ on any superposition of basis states. We show tradeoff results between the space (defined as 2/sup r/) and the number of probes (oracle calls) in this model. Our results show that the lower bounds shown by Buhrman et al. for the classical model also hold (with minor differences) in the quantum bitprobe model. These bounds almost match the classical upper bounds. Our lower bounds are proved using linear algebraic arguments.
Index Terms:
quantum computing; computational complexity; set theory; probes; linear algebra; query processing; quantum complexity; static set membership problem; bit table; query answering; lower bounds; upper bounds; quantum bitprobe model; blackbox unitary transform; oracle calls; query algorithm; basis state superposition; spaceprobe tradeoff; linear algebra
Citation:
J. Radhakrishnan, P. Sen, S. Venkatesh, "The quantum complexity of set membership," focs, pp.554, 41st Annual Symposium on Foundations of Computer Science, 2000
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