By Topic

The quantum complexity of set membership

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
Radhakrishnan, J. ; Sch. of Technol. & Comput. Sci., Tata Inst. of Fundamental Res., Mumbai, India ; Sen, P. ; Venkatesh, S.

Studies the quantum complexity of the static set membership problem: given a subset S (|S|⩽n) of a universe of size m(≫n), store it as a table, T:(0,1)r→(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 bit-probe model”. We assume that access to the table T is provided by means of a black-box (oracle) unitary transform OT that takes the basis state (y,b) to the basis state |y,b⊕T(y)⟩. The query algorithm is allowed to apply OT on any superposition of basis states. We show tradeoff results between the space (defined as 2r) 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 bit-probe model. These bounds almost match the classical upper bounds. Our lower bounds are proved using linear algebraic arguments

Published in:

Foundations of Computer Science, 2000. Proceedings. 41st Annual Symposium on

Date of Conference: