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Postprocessing for speeding up general quantum search algorithms

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Title Postprocessing for speeding up general quantum search algorithms
 
Creator TULSI, A
 
Description A general quantum search algorithm aims to evolve a quantum system from a known source state vertical bar s > to an unknown target state vertical bar t >. It uses a diffusion operator D-s that has the source state as one of its eigenstates and I-t, where I-psi denotes the selective phase inversion of the vertical bar psi > state. It evolves vertical bar s > to a particular state vertical bar w >, which we will call the w state, in O(B/alpha) time steps, where alpha is vertical bar < t vertical bar s >vertical bar and B is a characteristic of the diffusion operator. Measuring the w state gives the target state with a success probability of O(1/B-2), and O(B-2) applications of the algorithm can boost it from O(1/B-2) to O(1), making the total time complexity O(B-3/alpha). In the special case of Grover's algorithm, D-s is I-s and B is very close to 1. A more efficient way to boost the success probability is quantum amplitude amplification provided we can efficiently implement I-w. Such an efficient implementation is not known so far. In this paper, we present an efficient algorithm to approximate selective phase inversions of the unknown eigenstates of an operator using a phase estimation algorithm. This algorithm is used to efficiently approximate I-w, which reduces the time complexity of general algorithm to O(B/alpha). Although O(B/alpha) algorithms are known to exist, our algorithm offers physical implementation advantages.
 
Publisher AMER PHYSICAL SOC
 
Date 2016-01-15T08:29:08Z
2016-01-15T08:29:08Z
2015
 
Type Article
 
Identifier PHYSICAL REVIEW A, 92(2)
1050-2947
1094-1622
http://dx.doi.org/10.1103/PhysRevA.92.022353
http://dspace.library.iitb.ac.in/jspui/handle/100/18166
 
Language en