Related papers: A compositional approach to quantum functions
Homomorphism indistinguishability is a way of characterising many natural equivalence relations on graphs. Two graphs $G$ and $H$ are called homomorphism indistinguishable over a graph class $\mathcal{F}$ if for each $F \in \mathcal{F}$,…
We introduce Compositional Quantum Field Theory (CQFT) as an axiomatic model of Quantum Field Theory, based on the principles of locality and compositionality. Our model is a refinement of the axioms of General Boundary Quantum Field…
We introduce a quantum automorphism group for hypergraphs, which turns out to generalize the quantum automorphism group of Bichon for classical graphs. Further, we show that our quantum automorphism group acts on hypergraph C*-algebras as…
In recent years, diagrammatic languages have been shown to be a powerful and expressive tool for reasoning about physical, logical, and semantic processes represented as morphisms in a monoidal category. In particular, categorical quantum…
In this paper a finite dimensional unital associative algebra is presented, and its group of algebra automorphisms is detailed. The studied algebra can physically be understood as the creation operator algebra in a formal quantum field…
This paper initiates a systematic study of quantum functions, which are (partial) functions defined in terms of quantum mechanical computations. Of all quantum functions, we focus on resource-bounded quantum functions whose inputs are…
The primary goal of this paper is to abstract notions, results and constructions from the theory of categories to the broader setting of plots. Loosely speaking, a plot can be thought of as a non-associative non-unital category with a…
The symmetries of a finite graph are described by its automorphism group; in the setting of Woronowicz's quantum groups, a notion of a quantum automorphism group has been defined by Banica capturing the quantum symmetries of the graph. In…
The problem of discriminating between many quantum channels with certainty is analyzed under the assumption of prior knowledge of algebraic relations among possible channels. It is shown, by explicit construction of a novel family of…
We present a uniform framework for the treatment of a large class of toy models of quantum theory. Specifically, we will be interested in theories of wavefunctions valued in commutative involutive semirings, and which give rise to some…
In recent years, the import of quantum information techniques in quantum gravity opened new perspectives in the study of the microscopic structure of spacetime. We contribute to such a program by establishing a precise correspondence…
We consider commutative Frobenius pseudomonoids in the bicategory of spans, and we show that they are in correspondence with 2-Segal cosymmetric sets. Such a structure can be interpreted as a coherent 2-dimensional topological quantum field…
We introduce an equivariant version of contextuality with respect to a symmetry group, which comes with natural applications to quantum theory. In the equivariant setting, we construct cohomology classes that can detect contextuality. This…
We introduce the coherent algebra of a compact metric measure space by analogy with the corresponding concept for a finite graph. As an application we show that upon topologizing the collection of isomorphism classes of compact metric…
The study of graph C*-algebras has a long history in operator algebras. Surprisingly, their quantum symmetries have never been computed so far. We close this gap by proving that the quantum automorphism group of a finite, directed graph…
We show that the quantum family of all maps from a finite space to a finite dimensional compact quantum semigroup has a canonical quantum semigroup structure.
Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…
Quantum computing (QC) is a new computational paradigm whose foundations relate to quantum physics. Notable progress has been made, driving the birth of a series of quantum-based algorithms that take advantage of quantum computational…
In this paper we consider a generalization of quantum hash functions for arbitrary groups. We show that quantum hash function exists for arbitrary abelian group. We construct a set of "good" automorphisms --- a key component of quantum hash…
In this paper, we first propose two types of concepts of almost automorphic functions on the quantum time scale. Secondly, we study some basic properties of almost automorphic functions on the quantum time scale. Then, we introduce a…