Grover’s algorithm and the secant varieties
نویسندگان
چکیده
منابع مشابه
Secant varieties
The goal of this talk is to introduce secant varieies and show connections of secant varieties of Veronese variety to the Waring problem. 1 Secant varieties Let X ⊂ P be a variety over k, where k is algebraically closed field of characteristic 0 (or just assume k = C). Definition 1.1. For s ≥ 1 the s-th higher secant variety of X is
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If X is a smooth projective toric variety of dimension n we give explicit conditions on characters of the torus giving an embedding X →֒ Pr that guarantee dimSecX = 2n+ 1. We also give necessary and sufficient conditions for a general point of SecX to lie on a unique secant line when X is embedded into Pr using a complete linear system. For X of dimension 2 and 3 we give formulas for deg SecX in...
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Let X be a semi-stable arithmetic surface over the spectrum S of the ring of integers in a number field K. We assume that the generic fiber XK is geometrically irreducible and has positive genus. Consider a line bundle L on X , which is non-negative on every vertical fiber and equipped with an admissible metric (in the sense of Arakelov [A]) of positive curvature. In [S] we have shown that any ...
متن کاملGrassmannians of Secant Varieties
For an irreducible projective variety X, we study the family of h-planes contained in the secant variety Sec k (X), for 0 < h < k. These families have an expected dimension and we study varieties for which the expected dimension is not attained; for these varieties, making general consecutive projections to lower dimensional spaces, we do not get the expected singularities. In particular, we ex...
متن کاملCombinatorial Secant Varieties
The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant ideals are obstructions to graph colorings, and this leads to a commutative algebra version of the Strong Perfect Graph Theorem. Given any projective variety and any term order, we explore whether the initial ideal o...
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ژورنال
عنوان ژورنال: Quantum Information Processing
سال: 2016
ISSN: 1570-0755,1573-1332
DOI: 10.1007/s11128-016-1445-2