47 research outputs found

    Instanton effects and Witten complex in supersymmetric quantum mechanics on SO(4)

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    We examine supersymmetric quantum mechanics on SO(4)SO(4) to realize Witten's idea. We find instanton solutions connecting approximate vacuums. We calculate Hessian matrices for these solutions to determine true vacuums. Our result is in agreement with de Rham cohomology of SO(4)SO(4). We also give a criterion for cancellation of instanton effects for a pair of instanton paths.Comment: 26pages, Late

    Simple procedure for classical signal-procession in cluster-state quantum computation

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    We exhibit a simple procedure to find how classical signals should be processed in cluster-state quantum computation. Using stabilizers characterizing a cluster state, we can easily find a precise classical signal-flow that is required in performing cluster-state computation.Comment: 5pages, 5figure

    De Rham Cohomology of SO(n) by Supersymmetric Quantum Mechanics

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    We give an elementary derivation of the de Rham cohomology of SO(n) in terms of supersymmetric quantum mechanics. Our analysis is based on Witten's Morse theory. We show reflection symmetries of the theory are useful to select true vacuums. The number of the selected vacuums will agree with the de Rham cohomology of SO(n).Comment: 7pages, latex, no figure

    de Rham cohomology of SO(n) and some related manifolds by supersymmetric quantum mechanics

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    We study supersymmetric quantum mechanics on RP_{n},SO(n),G_{2} and U(2) to examine Witten's Morse theory concretely. We confirm the simple instanton picture of the de Rham cohomology that has been given in a previous paper. We use a reflection symmetry of each theory to select the true vacuums. The number of selected vacuums agrees with the de Rham cohomology for each of the above manifolds.Comment: 18pages,Late

    Proper magnetic fields for nonadiabatic geometric quantum gates in NMR

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    In a scheme of nonadiabatic purely geometric quantum gates in nuclear magnetic resonance(NMR) systems we propose proper magnitudes of magnetic fields that are suitable for an experiment. We impose a natural condition and reduce the degree of freedom of the magnetic fields to the extent. By varying the magnetic fields with essentially one-dimensional degree of freedom, any spin state can acquire arbitrary purely geometric phase \phi_{g}=-2\pi(1-cos{theta}), 0 < cos{\theta} < 1. This is an essential ingredient for constructing universal geometric quantum gates.Comment: LaTeX, 4page
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