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arXiv:quant-ph/0605040 · Canadian Journal of Physics

The dynamics of entanglement in the adiabatic search and Deutsch algorithms

K Choy, G Passante, D Ahrensmeier, M E Carrington, T Fugleberg, R. Kobes, G. Kunstatter

Published Oct 1, 2007• 2 citations
arXivHTMLPDF

Abstract

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

DOI
10.1139/p07-084

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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
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.
Quantum entanglement is widely considered as one of the key resources for quantum-computational power. However, present interpretations of entanglement in speeding up of quantum algorithms remain far from complete. We analyze and compare the behaviors of entanglement during the adiabatic evolution of Grover's quantum search algorithms with complexity [Formula: see text] and O(1), respectively. Our results show that entanglement has a significant impact on the computational efficiency of both algorithms. That is, the greater the entanglement, the higher is the quantum computation, and vice versa. Furthermore, the correlations between entanglement and energy are discussed. It is observed that for the algorithm with complexity O(1), its entanglement degree becomes larger when the energy input into the quantum system increases, thus making the algorithm more efficient.
In the adiabatic quantum computation model, a computational procedure is described by the continuous time evolution of a time dependent Hamiltonian. Classically, the unstructured search problem can be solved only in a running time of order O(G). However, by modifying the structure of local Hamiltonian or using specific interpolating functions, it is possible to do the calculation in constant time for a quantum computer. This paper reveals the cause that lead to the speedup. We analyze two kinds of specific adiabatic quantum models, and conclude that the value of relevant elements in back-diagonal of the local Hamiltonian is the main factors affecting the time complexity of adiabatic quantum algorithms. According to the speedup mechanism, we have proposed two kinds of adiabatic quantum algorithms to make a constant time complexity.