Results 1 
3 of
3
Towards quantumresistant cryptosystems from supersingular elliptic curve isogenies
"... ..."
(Show Context)
Quantum Walks
, 2008
"... Abstract. Quantum walks can be considered as a generalized version of the classical random walk. There are two classes of quantum walks, that is, the discretetime (or coined) and the continuoustime quantum walks. This manuscript treats the discrete case in Part I and continuous case in Part II, re ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
Abstract. Quantum walks can be considered as a generalized version of the classical random walk. There are two classes of quantum walks, that is, the discretetime (or coined) and the continuoustime quantum walks. This manuscript treats the discrete case in Part I and continuous case in Part II, respectively. Most of the contents are based on our results. Furthermore, papers on quantum walks are listed in References. Studies of discretetime walks appeared from the late 1980s from Gudder (1988), for example. Meyer (1996) investigated the model as a quantum lattice gas automaton. Nayak and Vishwanath (2000) and Ambainis et al. (2001) studied intensively the behaviour of discretetime walks, in particular, the Hadamard walk. In contrast with the central limit theorem for the classical random walks, Konno (2002a, 2005a) showed a new type of weak limit theorems for the onedimensional lattice. Grimmett, Janson, and Scudo (2004) extended the limit theorem to a wider range of the walks. On the other hand, the continuoustime quantum walk was introduced and studied by Childs, Farhi, and Gutmann (2002). Excellent reviews on quantum walks are
Continuous Time Quantum Walks (CTQW)
, 2015
"... Quantum computing became a prominent area of research with publications such as Feynman’s 1986 paper suggesting a construction for a Hamiltonian that can implement any quantum circuit [1]. Some of the key results in quantum information science such as Shor’s algorithm [2] and Grover’s algorithm [3] ..."
Abstract
 Add to MetaCart
(Show Context)
Quantum computing became a prominent area of research with publications such as Feynman’s 1986 paper suggesting a construction for a Hamiltonian that can implement any quantum circuit [1]. Some of the key results in quantum information science such as Shor’s algorithm [2] and Grover’s algorithm [3] which show speed up over classical algorithms for integer factorisation and database searching have motivated a wealth