Quantum computing and quantum information science are two recently discovered and rapidly growing fields of physics that show substantial promise in providing new and valuable technologies in the foreseeable future. Large-scale quantum computers, if ever realized experimentally, are likely to outperform their classical counterparts in a number of important computational tasks, the most importan...

The Church-Turing thesis says that a digital computer is a universal computational device; that is, it is able to simulate any physically realizable computational device. It has generally been believed that this simulation can be made eecient so that it entails at most a polynomial increase in computation time. This may not be true if quantum mechanics is taken into consideration. A quantum com...

Quantum mechanics requires the operation of quantum computers to be unitary, and thus makes it important to have general techniques for developing fast quantum algorithms for computing unitary transforms. A quantum routine for computing a generalized Kronecker product is given. Applications include re-development of the networks for computing the Walsh-Hadamard and the quantum Fourier transform...

Quantum computing, if realized on a large and commercial scale, will provide significantly more powerful computers that could threaten global information security. Modern methods for encrypting data could become obsolete as quantum computing methods break methods used now by more traditional computing techniques. Commercial machines that make use of quantum algorithms to reduce problem sizes of...

I. Introduction This paper is a quick introduction to key relationships between the theories of knots,links, three-manifold invariants and the structure of quantum mechanics. In section 2 we review the basic ideas and principles of quantum mechanics. Section 3 shows how the idea of a quantum amplitude is applied to the construction of invariants of knots and links. Section 4 explains how the ge...

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The discovery of an algorithm for factoring which runs in polynomial time on a quantum computer has given rise to a concerted effort to understand the principles, advantages, and limitations of quantum computing. At the same time, many different quantum systems are being explored for their suitability to serve as a physical substrate for the quantum computer of the future. I discuss some of the...

There are quantum algorithms that can efficiently simulate quantum physics, factor large numbers and estimate integrals. As a result, quantum computers can solve otherwise intractable computational problems. One of the main problems of experimental quantum computing is to preserve fragile quantum states in the presence of errors. It is known that if the needed elementary operations (gates) can ...

We survey the emerging field of quantum computing by showing its motivations and founding principles, and by presenting the most significant results in some selected areas. In particular, we outline the topics of quantum information, quantum algorithms, quantum cryptography, quantum finite automata, quantum error correction, and the physical realizations of quantum computing systems.