Related papers: Closed Systems of Invertible Maps

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We introduce a general procedure called `reverse engineering' that can be used to construct infinite families of smooth 4-manifolds in a given homeomorphism type. As one of the applications of this technique, we produce an infinite family…

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Algorithmic methods for the explicit inversion of the indefinite double covering maps are proposed. These are based on either the Givens decomposition or the polar decomposition of the given matrix in the proper, indefinite orthogonal group…

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We study reversibility and strong reversibility of affine automorphisms of the two-torus, written as $f_{A,\bar{a}}(\bar{x})=A\bar{x}+\bar{a} \ (\mathrm{mod}\ \mathbb{Z}^2)$. We derive explicit criteria for the reversibility of such maps in…

The problem of finding efficient decompositions of multi-qubit gates is of importance for quantum computing, especially, in application to existing noisy intermediate-scale quantum devices, whose resources are substantially limited. Here we…

The controlled-SWAP and controlled-controlled-NOT gates are at the heart of the original proposal of reversible classical computation by Fredkin and Toffoli. Their widespread use in quantum computation, both in the implementation of…

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The results on the inversion of convolution operators as well as Toeplitz (and block Toeplitz) matrices in the $1$-D (one-dimensional) case are classical and have numerous applications. Last year, we considered the $2$-D case of…

Let A be a finitely generated associative algebra over an algebraically closed field. We characterize the finite dimensional modules over A whose orbit closures are regular varieties.

We propose an encoding for topological quantum computation utilizing quantum representations of mapping class groups. Leakage into a non-computational subspace seems to be unavoidable for universality in general. We are interested in the…

Let $A$ be a finite or countable alphabet and let $\theta$ be literal (anti)morphism onto $A^*$ (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under…

A computable ring is a ring equipped with mechanical procedure to add and multiply elements. In most natural computable integral domains, there is a computational procedure to determine if a given element is prime/irreducible. However,…

The method of using concepts and insight from quantum information theory in order to solve problems in reversible classical computing (introduced in Ref. [1]) have been generalized to irreversible classical computing. The method have been…

Universal quantum entangling gates are a crucial building block in the large-scale quantum computation and quantum communication, and it is an important task to find simple ways to implement them. Here an effective quantum circuit for the…

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We take initial steps towards a general framework for constructing logical gates in general quantum CSS codes. Viewing CSS codes as cochain complexes, we observe that cohomology invariants naturally give rise to diagonal logical gates. We…