Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance
Abstract
The number of steps any classical computer requires in order to find the prime factors of an ldigit integer N increases exponentially with l, at least using algorithms known at present. Factoring large integers is therefore conjectured to be intractable classically, an observation underlying the security of widely used cryptographic codes. Quantum computers, however, could factor integers in only polynomial time, using Shor's quantum factoring algorithm. Although important for the study of quantum computers, experimental demonstration of this algorithm has proved elusive. Here we report an implementation of the simplest instance of Shor's algorithm: factorization of <italic>N</italic> = 15 (whose prime factors are 3 and 5). We use seven spin1/2 nuclei in a molecule as quantum bits, which can be manipulated with room temperature liquidstate nuclear magnetic resonance techniques. This method of using nuclei to store quantum information is in principle scalable to systems containing many quantum bits, but such scalability is not implied by the present work. The significance of our work lies in the demonstration of experimental and theoretical techniques for precise control and modelling of complex quantum computers. In particular, we present a simple, parameterfree but predictive model of decoherence effects in our system.
 Publication:

Nature
 Pub Date:
 December 2001
 DOI:
 10.1038/414883a
 arXiv:
 arXiv:quantph/0112176
 Bibcode:
 2001Natur.414..883V
 Keywords:

 Quantum Physics
 EPrint:
 accepted version