Introduction to Grassmann manifolds and quantum computation

“…Fujii [15], [16] in the context of Holonomic Quantum Computation. In a forthcoming paper we want to point out a deeper relation between the gauge theory and some quantum computation (Cavity QED quantum computation if possible).…”

Section: Discussionmentioning

confidence: 99%

Universal Yang–mills Action on Four-Dimensional Manifolds

Fujii

Ôike²,

Suzuki

2006

Int. J. Geom. Methods Mod. Phys.

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The usual action of Yang-Mills theory is given by the quadratic form of curvatures of a principal G bundle defined on four dimensional manifolds. The non-linear generalization which is known as the Born-Infeld action has been given. * E-mail address : fujii@yokohama-cu.ac.jp † E-mail address : oike@tea.ocn.ne.jp ‡ E-mail address : suzukita@gm.math.waseda.ac.jp 1In this paper we give another non-linear generalization on four dimensional manifolds and call it a universal Yang-Mills action.The advantage of our model is that the action splits automatically into two parts consisting of self-dual and anti-self-dual directions. Namely, we have automatically the self-dual and anti-self-dual equations without solving the equations of motion as in a usual case.Our method may be applicable to recent non-commutative Yang-Mills theories studied widely.

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“…As another definition of the Grassmann manifold the following one in terms of projections is also well-known. See [5] and [6] as an elementery introduction and [7] as an advanced one.…”

Section: Reduced Dynamics On Grassmann Manifolds : Reviewmentioning

confidence: 99%

Reduced Dynamics From the Unitary Group to Some Flag Manifolds: Interacting Matrix Riccati Equations

Fujii

Ôike²

2009

Int. J. Geom. Methods Mod. Phys.

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In this paper we treat the time evolution of unitary elements in the N level system and consider the reduced dynamics from the unitary group U (N ) to flag manifolds of the second type (in our terminology). Then we derive a set of differential equations of matrix Riccati types interacting with one another and present an important problem on a nonlinear superposition formula that the Riccati equation satisfies.Our result is a natural generalization of the paper Chaturvedi et al (arXiv :0706.0964 [quant-ph]). *

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Introduction to Grassmann manifolds and quantum computation

Cited by 36 publications

References 21 publications

On the Magic Matrix by Makhlin and the B-C-H Formula in So(4)

On the Magic Matrix by Makhlin and the B-C-H Formula in So(4)

Universal Yang–mills Action on Four-Dimensional Manifolds

Reduced Dynamics From the Unitary Group to Some Flag Manifolds: Interacting Matrix Riccati Equations

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