Ranee Brylinski

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In this paper we study universality for quantum gates acting on qudits. Qudits are states in a Hilbert space of dimension d where d can be any integer ≥ 2. We determine which 2-qudit gates V have the properties (i) the collection of all 1-qudit gates together with V produces all n-qudit gates up to arbitrary precision, or (ii) the collection of all 1-qudit(More)
Let M be a G-covering of a nilpotent orbit in g where G is a complex semisimple Lie group and g = Lie(G). We prove that under Poisson bracket the space R[2] of homogeneous functions on M of degree 2 is the unique maximal semisimple Lie subalgebra of R = R(M) containing g. The action of g ′ ≃ R[2] exponentiates to an action of the corresponding Lie group G ′(More)
We construct a unique G-equivariant graded star product on the algebra S (g)/I of polynomial functions on the minimal nilpotent coadjoint orbit O min of G where G is a complex simple Lie group and g = sl(2, C). This strengthens the result of Arnal, Benamor and Cahen. Our main result is to compute, for G classical, the star product of a momentum function µ x(More)
Let O be the minimal nilpotent adjoint orbit in a classical complex semisim-ple Lie algebra g. O is a smooth quasi-affine variety stable under the Eu-ler dilation action C * on g. The algebra of differential operators on O is D(O) = D(Cl(O)) where the closure Cl(O) is a singular cone in g. See [J] and [B-K1] for some results on the geometry and quantization(More)
Let X R be a (generalized) flag manifold of a non-compact real semisimple Lie group G R , where X R and G R have complexifications X and G. We investigate the problem of constructing a graded star product on Pol(T * X R) which corresponds to a G R-equivariant quantization of symbols into smooth differential operators acting on half-densities on X R. We show(More)