OPTIMAL DATABASE SEARCH: WAVES AND CATALYSIS

2006 ◽  
Vol 04 (05) ◽  
pp. 815-825 ◽  
Author(s):  
APOORVA PATEL

Grover's database search algorithm, although discovered in the context of quantum computation, can be implemented using any system that allows superposition of states. A physical realization of this algorithm is described using coupled simple harmonic oscillators, which can be exactly solved in both classical and quantum domains. Classical wave algorithms are far more stable against decoherence compared to their quantum counterparts. In addition to providing convenient demonstration models, they may have a role in practical situations, such as catalysis.

PROTEOMICS ◽  
2009 ◽  
Vol 9 (7) ◽  
pp. 1763-1770 ◽  
Author(s):  
Hua Xu ◽  
Liwen Wang ◽  
Larry Sallans ◽  
Michael A. Freitas

2011 ◽  
Vol 09 (06) ◽  
pp. 1363-1381 ◽  
Author(s):  
YUJI TANAKA ◽  
TSUBASA ICHIKAWA ◽  
MASAHITO TADA-UMEZAKI ◽  
YUKIHIRO OTA ◽  
MIKIO NAKAHARA

We present a systematic construction of quantum circuits implementing Grover's database search algorithm for arbitrary number of targets. We introduce a new operator which flips the sign of the targets and evaluate its circuit complexity. We find the condition under which the circuit complexity of the database search algorithm based on this operator is less than that of the conventional one.


2015 ◽  
Vol 125 ◽  
pp. 89-97 ◽  
Author(s):  
Hao Chi ◽  
Kun He ◽  
Bing Yang ◽  
Zhen Chen ◽  
Rui-Xiang Sun ◽  
...  

2009 ◽  
Vol 8 (6) ◽  
pp. 3198-3205 ◽  
Author(s):  
Rovshan G. Sadygov ◽  
David M. Good ◽  
Danielle L. Swaney ◽  
Joshua J. Coon

2006 ◽  
Vol 84 (6-7) ◽  
pp. 645-651 ◽  
Author(s):  
D Ahrensmeier

Adiabatic quantum computation provides an alternative approach to quantum computation using a time-dependent Hamiltonian. The time evolution of entanglement during the adiabatic quantum search algorithm is studied, and its relevance as a resource is discussed.PACS Nos.: 03.67.–a, 03.67.Lx, 03.67.Mn


2011 ◽  
Vol 10 (10) ◽  
pp. M111.007658 ◽  
Author(s):  
Peter G. Slade ◽  
Michelle V. Williams ◽  
Alison Chiang ◽  
Elizabeth Iffrig ◽  
Steven R. Tannenbaum ◽  
...  

2002 ◽  
Vol 2 (2) ◽  
pp. 97-116
Author(s):  
T.M. Forcer ◽  
A.J.G. Hey ◽  
D.A. Ross ◽  
P.G.R. Smith

The paper examines the roles played by superposition and entanglement in quantum computing. The analysis is illustrated by discussion of a "classical" electronic implementation of Grover's quantum search algorithm. It is shown explicitly that the absence of multi-particle entanglement leads to exponentially rising resources for implementing such quantum algorithms.


2010 ◽  
Vol 9 (7) ◽  
pp. 3384-3393 ◽  
Author(s):  
Hua Xu ◽  
Pang-Hung Hsu ◽  
Liwen Zhang ◽  
Ming-Daw Tsai ◽  
Michael A. Freitas

Author(s):  
Sergey Ulyanov ◽  
Andrey Reshetnikov ◽  
Olga Tyatyushkina

Models of Grover’s search algorithm is reviewed to build the foundation for the other algorithms. Thereafter, some preliminary modifications of the original algorithms by others are stated, that increases the applicability of the search procedure. A general quantum computation on an isolated system can be represented by a unitary matrix. In order to execute such a computation on a quantum computer, it is common to decompose the unitary into a quantum circuit, i.e., a sequence of quantum gates that can be physically implemented on a given architecture. There are different universal gate sets for quantum computation. Here we choose the universal gate set consisting of CNOT and single-qubit gates. We measure the cost of a circuit by the number of CNOT gates as they are usually more difficult to implement than single qubit gates and since the number of single-qubit gates is bounded by about twice the number of CNOT’s.


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