Science

The Usefulness of NMR Quantum Computing

Warren S. Warren

Published Sep 12, 1997• 253 citations

Abstract

Quantum computing—the manipulation of a quantum mechanical system to do information processing—has attracted considerable recent attention, largely triggered by Shor's proposed algorithm for finding prime factors in polynomial instead of exponential time ([1][1]). The importance of this problem

DOI: 10.1126/science.277.5332.1688

Related papers

Quantum Computing

Susan Loepp, William K. Wootters

Introduction In an ordinary computer, information is stored in a collection of tiny circuits each of which is designed to have two stable and easily distinguishable configurations: each represents a bit . In our study of quantum cryptography, we have seen how it can be useful to express information not in ordinary bits but in qubits . Whereas a bit can have only two values, say 0 and 1, a qubit can be in any quantum superposition of ∣0〉 and ∣1〉. Moreover, a qubit can be entangled with other qubits. Thus one might wonder whether a quantum computer, in which the basic elements for storing and processing information are qubits, can outperform an ordinary (classical) computer in certain ways. This question was addressed by researchers starting in the 1980s. In terms of practical consequences, perhaps the most dramatic answer has been given by Peter Shor in his 1994 factoring algorithm for a quantum computer, an algorithm that is exponentially faster than any known classical algorithm. As we have seen in Chapter 1, the difficulty of factoring a product of two large primes is the basis of the security of the RSA cryptosystem. So if one could build a large enough quantum computer – and there is no reason in principle why this could not be done – the RSA system would be rendered ineffective. In this chapter we present the basics of quantum computation and then focus on Shor's factoring algorithm.

Cambridge University Press eBooksJul 10, 20060 citations

The Use of NMR for Solving the Problems of Quantum Computers

Vladimir V. Voronov

The analysis of papers on usage NMR in quantum computations is provided and the probable direction of the future investigations are considered.

arXiv:quant-ph/0102021Feb 5, 20012 citations

Qubits and quantum dots

Yuli V. Nazarov, Yaroslav M. Blanter

It is difficult nowadays to graduate from a department of natural sciences and not hear anything about quantum computing, most likely about the fascinating prospects of it. Quantum computing by its origin is a rather abstract discipline, a branch of math or information science. It has emerged from a persistent search for more efficient ways to process information when quantum mechanics made it to the scope of the search. Being an abstract discipline, quantum computing approximates a physical quantum system with a number of axioms and explores the consequences of these axioms, precisely as conventional math has been. These activities begun in the 1970s, and for a long time it was not obvious why quantum calculational schemes have to be any better than common computer algorithms. This extensive work was rewarded with a break-through in 1994, when Peter Shor discovered a remarkable quantum algorithm for the factorization of large numbers into prime ones. This sounds quite abstract, but many public key cryptosystems will become obsolete if Shor's algorithm is ever implemented in a practical quantum computer. Modern communication security is based on the fact that the factorization is a tough problem for a classical computer: it takes too long to crack a code. The proposed algorithm speeds up the factorization enormously. The discovery by Shor has brought quantum computing to the scientific and even public attention. This progress has motivated a massive research effort towards the manipulation of individual quantum systems, the practical realization of quantum computing schemes being one of the most attractive goals. This chapter describes this goal, the quantum transport systems suitable for it, and the achievements made so far.

Cambridge University Press eBooksMay 28, 20090 citations

A prime factorization based on quantum dynamics on a spin ensemble (I)

Xijia Miao

In this paper it has been described how to use the unitary dynamics of quantum mechanics to solve the prime factorization problem on a spin ensemble without any quantum entanglement. The ensemble quantum computation for the prime factorization is based on the basic principle that both a closed quantum system and its ensemble obey the same unitary dynamics of quantum mechanics if there is not any decoherence effect in both the quantum system and its ensemble. It uses the NMR multiple-quantum measurement techniques to output the quantum computational results that are the inphase multiple-quantum spectra of the spin ensemble. It has been shown that the inphase NMR multiple-quantum spectral intensities used to search for the period of the modular exponential function may reduce merely in a polynomial form as the qubit number of the spin ensemble. The time evolution process of the modular exponential operation on the quantum computer obeys the unitary dynamics of quantum mechanics and hence the computational output is governed by the quantum dynamics. This essential difference between the quantum computer and the classical one could be the key point for the quantum computation outperforming the classical one in the prime factorization on a spin ensemble without any quantum entanglement. It has been shown that the prime factorization based on the quantum dynamics on a spin ensemble is locally efficient at least. This supports the conjecture that the quantum dynamics could play an important role for the origin of power of quantum computation and quantum entanglement could not be a unique resource to achieve power of quantum computation in the prime factorization.

arXiv:quant-ph/0302153Feb 20, 20032 citations

NMR Quantum Computation

Jonathan A. Jones

In this article I will describe how NMR techniques may be used to build simple quantum information processing devices, such as small quantum computers, and show how these techniques are related to more conventional NMR experiments.

arXiv:quant-ph/0009002Sep 1, 20001 citation

Shor's factorization algorithm

E. Desurvire

This chapter describes what is generally considered to be one of the most important and historical contributions to the field of quantum computing, namely Shor's factorization algorithm . As its name indicates, this algorithm makes it possible to factorize numbers, which consists in their decomposition into a unique product of prime numbers. Other classical factorization algorithms previously developed have a complexity or computing time that increases exponentially with the number size, making the task intractable if not hopeless for large numbers. In contrast, Shor's algorithm is able to factor a number of any size in polynomial time , making the factorization problem tractable should a quantum computer ever be realized in the future. Since Shor's algorithm is based on several nonintuitive properties and other mathematical subtleties, this chapter presents a certain level of difficulty. With the previous chapters and tools readily assimilated, and some patience in going through the different preliminary steps required, such a difficulty is, however, quite surmountable. I have sought to make this description of Shor's algorithm as mathematically complete as possible and crack-free, while avoiding some academic considerations that may not be deemed necessary from any engineering perspective. Eventually, Shor's algorithm is described in only a few basic instructions. What is conceptually challenging is to grasp why it works so well, and also to feel comfortable with the fact that its implementation actually takes a fair amount of trial and error. The two preliminaries of Shor's algorithm are the phase estimation and the related order-finding algorithms.

Cambridge University Press eBooksFeb 19, 20090 citations