scholarly journals Entanglement and adiabatic quantum computation

2006 ◽  
Vol 84 (6-7) ◽  
pp. 645-651 ◽  
Author(s):  
D Ahrensmeier
Keyword(s):  
Quantum Computation ◽  
Time Evolution ◽  
Search Algorithm ◽  
Time Dependent ◽  
Quantum Search ◽  
Quantum Search Algorithm ◽  
Adiabatic Quantum Computation ◽  
Alternative Approach ◽  
03.67 Mn

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

scholarly journals The dynamics of entanglement in the adiabatic search and Deutsch algorithms

2007 ◽  
Vol 85 (10) ◽  
pp. 995-1021 ◽  
Author(s):  
K Choy ◽  
G Passante ◽  
D Ahrensmeier ◽  
M E Carrington ◽  
T Fugleberg ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Time Evolution ◽  
Search Algorithm ◽  
The Other ◽  
Running Time ◽  
Adiabatic Quantum Computation ◽  
Other Hand ◽  
03.67 Mn

The goal of this paper is to study the effect of entanglement on the running time of a quantum computation. Adiabatic quantum computation is suited to this kind of study, since it allows us to explicitly calculate the time evolution of the entanglement throughout the calculation. On the other hand, however, the adiabatic formalism makes it impossible to study the roles of entanglement and fidelity separately, which means that results have to be interpreted carefully. We study two algorithms: the search algorithm and the Deutsch–Jozsa algorithm. We find some evidence that entanglement can be considered a resource in quantum computation. PACS Nos.: 03.67.Mn, 03.67.Lx

Superposition, entanglement and quantum computation

2002 ◽  
Vol 2 (2) ◽  
pp. 97-116
Author(s):  
T.M. Forcer ◽  
A.J.G. Hey ◽  
D.A. Ross ◽  
P.G.R. Smith
Keyword(s):  
Quantum Computing ◽  
Quantum Computation ◽  
Search Algorithm ◽  
Quantum Algorithms ◽  
Quantum Search ◽  
Quantum Search Algorithm ◽  
Electronic Implementation

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.

scholarly journals Continuous-time quantum search and time-dependent two-level quantum systems

2019 ◽  
Vol 17 (03) ◽  
pp. 1950025 ◽  
Author(s):  
Carlo Cafaro ◽  
Paul M. Alsing
Keyword(s):  
Continuous Time ◽  
Transition Probabilities ◽  
Search Algorithm ◽  
Quantum Systems ◽  
Time Dependent ◽  
Quantum Search ◽  
Quantum Search Algorithm ◽  
Time Quantum ◽  
Characteristic Features ◽  
External Time

It was recently emphasized by Byrnes, Forster and Tessler [Phys. Rev. Lett. 120 (2018) 060501] that the continuous-time formulation of Grover’s quantum search algorithm can be intuitively understood in terms of Rabi oscillations between the source and the target subspaces. In this work, motivated by this insightful remark and starting from the consideration of a time-independent generalized quantum search Hamiltonian as originally introduced by Bae and Kwon [Phys. Rev. A 66 (2002) 012314], we present a detailed investigation concerning the physical connection between quantum search Hamiltonians and exactly solvable time-dependent two-level quantum systems. Specifically, we compute in an exact analytical manner the transition probabilities from a source state to a target state in a number of physical scenarios specified by a spin-[Formula: see text] particle immersed in an external time-dependent magnetic field. In particular, we analyze both the periodic oscillatory as well as the monotonic temporal behaviors of such transition probabilities and, moreover, explore their analogy with characteristic features of Grover-like and fixed-point quantum search algorithms, respectively. Finally, we discuss from a physics standpoint the connection between the schedule of a search algorithm, in both adiabatic and nonadiabatic quantum mechanical evolutions, and the control fields in a time-dependent driving Hamiltonian.

A quantum search algorithm for future spacecraft attitude determination

2011 ◽  
Vol 68 (7-8) ◽  
pp. 1208-1218 ◽  
Author(s):  
Jack Tsai ◽  
Fu-Yuen Hsiao ◽  
Yi-Ju Li ◽  
Jen-Fu Shen
Keyword(s):  
Attitude Determination ◽  
Search Algorithm ◽  
Spacecraft Attitude ◽  
Quantum Search ◽  
Quantum Search Algorithm

How significant are the known collision and element distinctness quantum algorithms?

2004 ◽  
Vol 4 (3) ◽  
pp. 201-206
Author(s):  
L. Grover ◽  
T. Rudolph
Keyword(s):  
Search Algorithm ◽  
Quantum Algorithms ◽  
Search Space ◽  
Space Complexity ◽  
Quantum Search ◽  
Quantum Search Algorithm ◽  
Time Space ◽  
Simple Quantum ◽  
Structured Problems ◽  
Better Than

Quantum search is a technique for searching $N$ possibilities for a desired target in $O(\sqrt{N})$ steps. It has been applied in the design of quantum algorithms for several structured problems. Many of these algorithms require significant amount of quantum hardware. In this paper we propose the criterion that an algorithm which requires $O(S)$ hardware should be considered significant if it produces a speedup of better than $O\left(\sqrt{S}\right)$ over a simple quantum search algorithm. This is because a speedup of $O\left(\sqrt{S}\right)$ can be trivially obtained by dividing the search space into $S$ separate parts and handing the problem to $S$ independent processors that do a quantum search (in this paper we drop all logarithmic factors when discussing time/space complexity). Known algorithms for collision and element distinctness exactly saturate the criterion.

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