nt - p h / 06 09 00 1 v 1 3 1 A ug 2 00 6 Shor ’ s Algorithm on a Nearest - Neighbor Machine Samuel

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

ua nt - p h / 01 04 09 1 v 3 2 6 A ug 2 00 1 Quantum mechanics gives stability to a Nash equilibrium

We consider a slightly modified version of the Rock-Scissors-Paper (RSP) game from the point of view of evolutionary stability. In its classical version the game has a mixed Nash equilibrium (NE) not stable against mutants. We find a quantized version of the RSP game for which the classical mixed NE becomes stable.

ar X iv : h ep - p h / 06 09 07 7 v 1 7 S ep 2 00 6 Hadron multiplicities in e + e − annihilation with heavy primary quarks

ua nt - p h / 03 03 17 5 v 1 2 9 M ar 2 00 3 Shor ’ s Algorithm for Factoring Large Integers ∗

This work is a tutorial on Shor's factoring algorithm by means of a worked out example. Some basic concepts of Quantum Mechanics and quantum circuits are reviewed. It is intended for non-specialists which have basic knowledge on undergraduate Linear Algebra.