47 research outputs found
Instanton effects and Witten complex in supersymmetric quantum mechanics on SO(4)
We examine supersymmetric quantum mechanics on 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 . 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
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
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
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
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