A critical evaluation what should be expected from quantum computing ideas in terms of applications in physics (quantum optics) and mathematics within the nest few years is evaluated.
In this tutorial we review basic ideas of quantum computing, from quantum bits and state entanglement to quantum gates and quantum networks [1]. In addition, we give an overview over possible physical implementations of quantum gates[2-6], with emphasis on quantum optical systems: this includes ion traps [2,3], and cavity QED in the optical and microwave domain [4-6], Fundamental problems of building quantum computers, in particular the decoherence problem, and error correction schemes for quantum memory elements [7] and quantum gates [8] will be discussed. We conclude with a critical evaluation what should be expected from quantum computing ideas in terms of applications in physics (quantum optics) and mathematics within the nest few years.