Scattering theory in relation to quantum computing

Much of the theory of quantum computing assumes the capacity to apply a chosen sequence of unitary trans-formations to the state of a quantum register (sometimes called a memory). It is widely recognized that this '' application of a unitary transformation '' requires an external influence. Here we relate the physics of external influences to the well established framework of quantum-mechanical scattering problems, in order to show how scattering is conceptually necessary to quantum computers, even in the idealization of zero temperature and no imperfections. For a single-qubit quantum register, infinitely slow limiting cases are shown in which scattering indeed results in a unitary transformation of the register. Implications for '' transformation-induced decoherence '' are developed and related to questions of errors and error correction.