Table of contents

The article proposes a new method of proving theorems from [1], [2], based on the principle of duality.

Contents §1. Introduction §2. Affine classification of points of multidimensional surfaces 2.1. Main results 2.2. Proof of Theorem 2.1.1 2.3. Classification of points of 3-dimensional submanifolds §3. Strongly parabolic submanifolds 3.1. Local structure of a strongly parabolic surface in Riemannian space 3.2. Local structure of a strongly parabolic surface in Euclidean space 3.3. Complete strongly parabolic multidimensional surfaces in Euclidean space 3.4. Conditions under which complete strongly parabolic submanifolds in spherical space are totally geodesic 3.5. Strongly parabolic submanifolds in Lobachevskii space 3.6. Strongly parabolic submanifolds in pseudo-Euclidean and pseudo-Riemannian spaces of constant curvature 3.7. Strongly parabolic submanifolds and minimal surfaces

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Contents §0. Introduction §1. Abelian problem on the stabilizer §2. Classical models of computations 2.1. Boolean schemes and sequences of operations 2.2. Reversible computations §3. Quantum formalism 3.1. Basic notions and notation 3.2. Transformations of mixed states 3.3. Accuracy §4. Quantum models of computations 4.1. Definitions and basic properties 4.2. Construction of various operators from the elements of a basis 4.3. Generalized quantum control and universal schemes §5. Measurement operators §6. Polynomial quantum algorithm for the stabilizer problem §7. Computations with perturbations: the choice of a model §8. Quantum codes (definitions and general properties) 8.1. Basic notions and ideas 8.2. One-to-one codes 8.3. Many-to-one codes §9. Symplectic (additive) codes 9.1. Algebraic preparation 9.2. The basic construction 9.3. Error correction procedure 9.4. Torus codes §10. Error correction in the computation process: general principles 10.1. Definitions and results 10.2. Proofs §11. Error correction: concrete procedures 11.1. The symplecto-classical case 11.2. The case of a complete basis

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Contents Introduction §1. Newton polygons, the Pascal relation, and the Vieta relation §2. Newton polygons and Weil numbers §3. Parametrization of one-dimensional orbits on a torus surface §4. Curves on a torus surface §5. Polygons without interior integer-valued points §6. Polygon Δ_D with an interior integer-valued point §7. Polygon Δ_D without interior integer-valued points §8. Meromorphic vector functions on compact curves §9. Refinement of Weil's theorem §10. Abel's theorem and the Vieta relation §11. Singularities of the characteristic curve and Newton polygons

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