Classical and quantum computing

Abstract

The fundamental limitations of any form of computation can be expressed in terms of the resource requirements of standard computational tasks under it. Within traditional models of computation, such as the Turing machine model, many problems are found to be intractable due to the limited computational capabilities of classical physical systems. However, quantum systems allow the range of tractable computations to be extended beyond that achievable by classical computation because the superposition principle offers a radically different sort of computational parallelism. The quantum circuit model (or gate array model), in which networks composed of quantum logic gates act on sets of qubits, is the dominant model of quantum computation and has an equivalent (quantum) Turing machine model. Both of these models and the general principles of quantum computation are discussed in this chapter. A number of specific algorithms, which illustrate the novel character of quantum computation, are described in the following chapter.