1 Ju n 20 04 A precise estimation of the computational complexity in Shor ’ s factoring algorithm

ar X iv : q ua nt - p h / 04 06 14 5 v 2 1 3 A ug 2 00 5 A precise estimation of the computational complexity in Shor ’ s factoring algorithm

P.W.Shor proposed the algorithm to solve the factorization into prime factors within polynomial time by using the quantum computer [1, 2]. See also [5], on the recent advances of the Shor’s factoring algorithm. In his paper, the number of the computational steps was estimated. Through this paper, we consider the case that we factorize n into finite prime numbers pi, (i = 1, · · · , k). We deriv...

ua nt - p h / 03 06 19 6 v 1 2 9 Ju n 20 03 On Shor ’ s channel extension and constrained channels

Adaptive search area for fast motion estimation

In this paper a new method for determining the search area for motion estimation algorithm based on block matching is suggested. In the proposed method the search area is adaptively found for each block of a frame. This search area is similar to that of the full search (FS) algorithm but smaller for most blocks of a frame. Therefore, the proposed algorithm is analogous to FS in terms of reg...

ua nt - p h / 02 01 09 5 v 1 2 2 Ja n 20 02 QUANTUM HIDDEN SUBGROUP ALGORITHMS : A MATHEMATICAL PERSPECTIVE

The ultimate objective of this paper is to create a stepping stone to the development of new quantum algorithms. The strategy chosen is to begin by focusing on the class of abelian quantum hidden subgroup algorithms, i.e., the class of abelian algorithms of the Shor/Simon genre. Our strategy is to make this class of algorithms as mathematically transparent as possible. By the phrase “mathematic...

ar X iv : c s / 03 10 04 6 v 2 [ cs . C C ] 1 4 Ju n 20 04 Theory of One Tape Linear Time Turing Machines ∗

A theory of one-tape linear-time Turing machines is quite different from its polynomial-time counterpart since one-tape linear-time Turing machines are closely related to finite state automata. This paper discusses structural-complexity issues of one-tape Turing machines of various types (deterministic, nondeterministic, reversible, alternating, probabilistic, counting, and quantum Turing machi...