Grover's search algorithm with an entangled database state

Paul M. Alsing; Nathan McDonald

doi:10.1117/12.883092

3 June 2011 Grover's search algorithm with an entangled database state

Paul M. Alsing, Nathan McDonald

Proceedings Volume 8057, Quantum Information and Computation IX; 80570R (2011) https://doi.org/10.1117/12.883092
Event: SPIE Defense, Security, and Sensing, 2011, Orlando, Florida, United States

Abstract

Grover's oracle based unstructured search algorithm is often stated as "given a phone number in a directory, find the associated name." More formally, the problem can be stated as "given as input a unitary black box Uf for computing an unknown function f:{0,1}n →{0,1}find x=x0 an element of {0,1}n such that f(x0) =1, (and zero otherwise). The crucial role of the externally supplied oracle Uf (whose inner workings are unknown to the user) is to change the sign of the solution 0 x , while leaving all other states unaltered. Thus, Uf depends on the desired solution x0. This paper examines an amplitude amplification algorithm in which the user encodes the directory (e.g. names and telephone numbers) into an entangled database state, which at a later time can be queried on one supplied component entry (e.g. a given phone number t0) to find the other associated unknown component (e.g. name x0). For N=2n names x with N associated phone numbers t , performing amplitude amplification on a subspace of size N of the total space of size N2 produces the desired state 0 0 x t in √N steps. We discuss how and why sequential (though not concurrent parallel) searches can be performed on multiple database states. Finally, we show how this procedure can be generalized to databases with more than two correlated lists (e.g. x t s r ...).

Citation Download Citation

Paul M. Alsing and Nathan McDonald "Grover's search algorithm with an entangled database state", Proc. SPIE 8057, Quantum Information and Computation IX, 80570R (3 June 2011); https://doi.org/10.1117/12.883092

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