Related papers: Closed Systems of Invertible Maps

Reversible Boolean Circuits are an interesting computational model under many aspects and in different fields, ranging from Reversible Computing to Quantum Computing. Our contribution is to describe a specific class of Reversible Boolean…

The reversible implementation of classical functions accounts for the bulk of most known quantum algorithms. As a result, a number of reversible circuit constructions over the Clifford+$T$ gate set have been developed in recent years which…

In this paper we present an equivalent statement to the Jacobian conjecture. For a polynomial map F on an affine space of dimension n, we define recursively n finite sequences of polynomials. We give an equivalent condition to the…

We prove that every clone of operations on a finite set A, if it contains a Malcev operation, is finitely related -- i.e., identical with the clone of all operations respecting R for some finitary relation R over A. It follows that for a…

Efficient decomposition of permutation unitaries is vital as they frequently appear in quantum computing. In this paper, we identify the key properties that impact the decomposition process of permutation unitaries. Then, we classify these…

We develop a compositional framework for generalized reversible computing using copy-discard categories and resource theories. We introduce partitioned matrices between partitioned sets as subdistribution matrices which preserve the…

We extend the circuit model of quantum computation so that the wiring between gates is soft-coded within registers inside the gates. The addresses in these registers can be manipulated and put into superpositions. This aims at capturing…

In this paper we show that it is possible to adapt a qudit scheme for creating a controlled-Toffoli created by Ralph et al. [Phys. Rev. A 75 011213] to be applicable to qubits. While this scheme requires more gates than standard schemes for…

It has long been known that to minimise the heat emitted by a deterministic computer during it's operation it is necessary to make the computation act in a logically reversible manner\cite{Lan61}. Such logically reversible operations…

We establish a relation between fully extended $2$-dimensional TQFTs and recognisable weighted formal languages, rational biprefix codes and lattice TFTs. We show the equivalence of $2D$ closed TFTs and rational exchangeable series and we…

We describe the additive subgroups of fields which are closed with respect to taking inverses. In particular, in characteristic different from two any such subgroup is either a subfield or the kernel of the trace map of a quadratic…

Reversible computation is an unconventional form of computing that extends the standard forward-only mode of computation with the ability to execute a sequence of operations in reverse at any point during computation. As such, in this…

This paper investigates some issues arising in categorical models of reversible logic and computation. Our claim is that the structural (coherence) isomorphisms of these categorical models, although generally overlooked, have decidedly…

It is well-known that deciding equivalence of logic circuits is a coNP-complete problem. As a corollary, the problem of deciding weak equivalence of reversible circuits, i.e. ignoring the ancilla bits, is also coNP-complete. The complexity…

Reversible forms of computations are often interesting from an energy efficiency point of view. When the computation device in question is an automaton, it is known that the minimal reversible automaton recognizing a given language is not…

Reversible or information-lossless circuits have applications in digital signal processing, communication, computer graphics and cryptography. They are also a fundamental requirement in the emerging field of quantum computation. We…

Substructural type systems, such as affine (and linear) type systems, are type systems which impose restrictions on copying (and discarding) of variables, and they have found many applications in computer science, including quantum…

We define a family of maps on lattice paths, called sweep maps, that assign levels to each step in the path and sort steps according to their level. Surprisingly, although sweep maps act by sorting, they appear to be bijective in general.…

In this paper we examine the topology of inverse limit spaces generated by maps of finite graphs. In particular we explore the way in which the structure of the orbits of the turning points affects the inverse limit. We show that if $f$ has…

We study the computational strength of resetting $\alpha$-register machines, a model of transfinite computability introduced by P. Koepke in \cite{K1}. Specifically, we prove the following strengthening of a result from \cite{C}: For an…