Related papers: Computing an Integer Prime Factoring in O(n^2.5)

We withdraw our paper as the factorizability of the correlation functions is unproven.

This paper has been withdrawn due to a critical error discovered in Theorem 4.21. Anyone with a historical or pragamatic interest in prior "negative results", however - e.g., failed proof attempts relating to the (in)consistency of ZF or…

Unfortunately, after an imprudent sumbission of the paper to the e-print archive, I discovered in it many serious mistakes. So I draw back it .

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…

This paper has been withdrawn by the authors due to a crucial error.

This paper has been withdrawn by the author due to an error in section 7. There is a new version: arXiv:1011.3352.

The paper was retracted.

The paper was withdrawn by the author. It contained various errors.

It is widely known that the lower bound for the algorithmic complexity of square matrix multiplication resorts to at least $n^2$ arithmetic operations. The justification builds upon the following reasoning: given that there are $2 n^2$…

This paper has been withdrawn by the authors due to crucial error in the main proof (located in Section 2.4). The authors apologize for any inconveniences.

This paper was withdrawn by the author due to a fatal error.

The algorithm reduces the running time of an algorithm of Frieze from O(n^{1.5)) to O(n^(4/3 + o)). It also introduces the concept of admissible permutations that is used in algorithms for obtaining solutions to the AP and the TSP.

This paper has been withdrawn due to a crucial theoretical error.

This paper has been withdrawn by the author.

This paper has been withdrawn by the authors pending corrections.

We present a randomized quantum algorithm for polynomial factorization over finite fields. For polynomials of degree $n$ over a finite field $\F_q$, the average-case complexity of our algorithm is an expected $O(n^{1 + o(1)} \log^{2 +…

In this note, we show the mistake which has been made in quant-ph/0609176. Further more, we provide a sketch of proof to show the impossibility of the effort of such kind toward improving the efficiency of Grover's Algorithm.

The paper has been withdrawn by the author due to a crucial error.

This paper has been withdrawn by the author due to a crucial error.

This paper has been withdrawn. See published paper http://arxiv.org/math.HO/0512390