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The router is a key element for a network. We describe a scheme to realize genuine quantum routing of single-photon pulses based on cascading of conditional quantum gates in a Mach-Zehnder interferome...
We propose a scheme to realize scalable quantum computation in a planar ion crystal confined by a Paul trap. We show that the inevitable in-plane micromotion affects the gate design via three separate...
Let V be a symplectic vector space and LG be the Lagrangian Grassmannian which parametrizes maximal isotropic subspaces in V . We give a presentation for the (small) quantum cohomology ring QH¤(LG) ...
Let V be a vector space with a nondegenerate symmetric form and OG be the orthogonal Grassmannian which parametrizes maximal isotropic subspaces in V . We give a presentation for the (small) quantum...
This is the written version of my ˉve lectures at the Banach Center mini-school on `Schubert Varieties', in Warsaw, Poland, May 18{22, 2003.
Let G be a classical Lie group and P a maximal parabolic subgroup. We describe a quantum Pieri rule which holds in the small quantum cohomology ring of G=P. We also give a presentation of this ring i...
Let G be a semisimple complex algebraic group and P a parabolic subgroup of G. The homogeneous space X = G=P is a projective complex manifold. My aim in this lecture is to survey what is known about...
We study the three point genus zero Gromov-Witten invariants on the Grassmannians which parametrize non-maximal isotropic subspaces in a vector space equipped with a nondegenerate symmetric or skew-...
Let X be a symplectic or odd orthogonal Grassmannian which parametrizes isotropic subspaces in a vector space equipped with a nondegenerate (skew) symmetric form. We prove quantum Giambelli formulas ...
A new study has found a link between abrupt ocean warming at the end of the last ice age and the sudden onset of low-oxygen, or hypoxic conditions that led to vast marine dead zones.Results of the stu...
Models of quantum computing rely on transformations of the states of a quantum memory. We study mathematical aspects of a model proposed by Wu in which the memory state is changed via the scattering o...
Seeing Quantum Motion     Quantum Motion       < 2015/9/8
Consider the pendulum of a grandfather clock. If you forget to wind it, you will eventually find the pendulum at rest, unmoving. However, this simple observation is only valid at the level of classica...
We consider the problem of detecting the true quantum state among r possible ones, based onmeasurements performed on n of copies of a finite dimensional quantum system. It is known that the exponent f...
We consider the problem of detecting the true quantum state among r possible ones, based of measurements performed on n copies of a finitedimensional quantum system. A special case is the problem of d...
We consider the decision problem between a finite numberof states of a finite quantum system, when an arbitrarily large number of copies of the system is available for measurements. We provide an uppe...

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