Artur K. Ekert and Richard Jozsa. Shor's quantum algorithm for factorising numbers. To appear in Rev. Mod. Phys. Preprint at ftp://eve.physics.ox.ac.uk/Archive/Numbered/EJ95/EJ95.ps.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....repitition period (which is the answer we are looking for) with high probability. The details of exactly how and why this all works are of course very complex, and beyond the scope of this short survey paper. For more detailed expositions of Shor s algorithm, see Ekert and Jozsa s description in [23, 22], and Shor s original papers [37, 38] 3.3 Consequences of Shor s Discovery Shor s algorithm provides the strongest evidence to date that quantum computers may be more powerful than classical computers in a realistic way. Of course, the current level of technology for manipulating quantum states ....

Artur K. Ekert and Richard Jozsa. Shor's quantum algorithm for factorising numbers. To appear in Rev. Mod. Phys. Preprint at ftp://eve.physics.ox.ac.uk/Archive/Numbered/EJ95/EJ95.ps.

....N be given with prime factorization N = p # 1 1 p # 2 2 p # k k for k 1, which is not of the form 2p # . Suppose that y N chosen at random satis es gcd(y, N) 1. Let r be the order of y in Z # N . Then Prob(r is even and y r 2 ## 1 (mod N) # 1 1 2 k 1 . Proof. See [29]. By Theorem 3.5.1 the probability of success in Step 4 and Step 5 is at least 1 2. Euler phi function denoted by #(N) is the number of integers less than N which are coprimes to N . Let #(N) denote the number of primes less than or equal to N . We now state two theorems about the estimates for ....

A. Ekert and R. Jozsa, Shor's quantum algorithm for factorising numbers, Rev. Modern Phys. 68 (1996), 733753.

....this inter dependence of decoherence and computation time seems to be a restriction in many current models for quantum computers and leads to the result that the computation time T scales much stronger with L than previously expected. PACS: 42.50.Lc I. Introduction Since Shor s discovery [1, 2] of an algorithm that allows thefactorization of a large number by a quantum computer in polynomial time instead of an exponential time as in classical computing, interest in the practical realization of a quantum computer has been much enhanced. Recent advances in the preparation and manipulation ....

....of 1000 [6] so that we obtain L T min Gamma max 2 1s 10 Gamma1 s Gamma1 4 259s 1:9 10 Gamma4 s Gamma1 . One observes that even with the rather large value of ae the factorization of a 4 bit number (e.g. 15 which is the smallest composite number for which Shor s algorithm applies [2]) seems to be practically impossible when we take into account that for example the metastable transition in Barium has a lifetime of 45s and therefore Gamma = 0:044s Gamma1 . Note that we have not taken into account the influence of all other possible sources of error such as counterrotating ....

A. Ekert and R. Josza, Shor's Quantum Algorithm for Factorising Numbers, preprint to appear in Rev. Mod. Phys.

....is no known efficient (i.e. polynomial time) classical (even randomised) algorithm. In this talk we describe the essential principles of quantum computation and discuss Shor s quantum factoring algorithm, including a brief review of the (elementary) quantum theory required. For references, see, [8, 17, 22, 24, 65]. Homological methods and word problems Yves Lafont, University of Marseille lafont lmd.univ mrs.fr Complete (or convergent) rewrite systems have been introduced as a tool for solving word problems. Anick and Squier discovered that they can also be used for calculating homological invariants. ....

A. Ekert and R. Jozsa. Shor's quantum algorithm for factorising numbers. Reviews of Modern Physics, to appear 1995.

....attempts to exploit these capabilities for search are not particularly effective, then motivates and describes a new search algorithm. 3. 1 An Overview of Quantum Computers The basic distinguishing feature of a quantum computer (Benioff, 1982; Bernstein Vazirani, 1993; Deutsch, 1985, 1989; Ekert Jozsa, 1995; Feynman, 1986; Jozsa, 1992; Kimber, 1992; Lloyd, 1993; Shor, 1994; Svozil, 1995) is its ability to operate simultaneously on a collection of classical states, thus potentially performing many operations in the time a classical computer would do just one. Alternatively, this quantum parallelism ....

....1995) using a scanning tunneling or atomic force microscope. This possibility of precise manipulation of chemical reactions has also been demonstrated (Muller, Klein, Lee, Clarke, McEuen, Schultz, 1995) There are also a number of other proposals under investigation (Barenco, Deutsch, Ekert, 1995; Sleator Weinfurter, 1995; Cirac Zoller, 1995) including the possibility of multiple simultaneous quantum operations (Margolus, 1990) A simple computation on a quantum bit is the logical NOT operation, i.e. NOT(j0i) j1i and NOT(j1i) j0i. This operator simply exchanges the state ....

Ekert, A., & Jozsa, R. (1995). Shor's quantum algorithm for factorising numbers. Rev.

No context found.

Rev. A 51, 1015--1022. A. Ekert and R. Jozsa (1995) "Shor's quantum algorithm for factorising numbers," Rev.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC