10 May 2007 Scattering theory in relation to quantum computing
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Abstract
Much of the theory of quantum computing assumes the capacity to apply a chosen sequence of unitary transformations 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.
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John M. Myers, Tai Tsun Wu, "Scattering theory in relation to quantum computing", Proc. SPIE 6573, Quantum Information and Computation V, 657306 (10 May 2007); doi: 10.1117/12.721693; https://doi.org/10.1117/12.721693
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