Shor ’ s Algorithm for Factoring Large Integers ∗
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چکیده
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.
منابع مشابه
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.
متن کاملSome remarks on consequences of Shor’s Factoring Algorithm
The algorithm of Shor for factoring integers into primes shows that factoring can be done by a quantum computer in polynomial time. The question if this can also be achieved by a classical Turing machine, i.e. if the Shor algorithm is inherently quantum mechanical or if a classical system could do equally well, is still unresolved but linked to two of the most important open problems of mathema...
متن کاملQuantum algorithms for algebraic problems
Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for classical computers. Understanding what other computational problems can be solved significantly faster using quantum algorithms is one of the major challenges ...
متن کامل1 Ju n 20 04 A precise estimation of the computational complexity in Shor ’ s factoring algorithm
Abstract. A precise estimation of the computational complexity in Shor’s factoring algorithm under the condition that the large integer we want to factorize is composed by the product of two prime numbers, is derived by the results related to number theory. Compared with Shor’s original estimation, our estimation shows that one can obtain the solution under such a condition, by less computation...
متن کاملFactoring Multivariate Polynomials over Algebraic Number Fields
The algorithm for factoring polynomials over the integers by Wang and Rothschild is generalized to an algorithm for the irreducible factorization of multivariate polynomials over any given algebraic number field. The extended method makes use of recent ideas in factoring univariate polynomials over large finite fields due to Berlekamp and Zassenhaus. The procedure described has been implemented...
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تاریخ انتشار 2003