Related papers: Graphical calculus for quantum vertex operators, I…
We study the minimum cut problem in weighted undirected graphs using variational quantum algorithms in which only feasible cut configurations are explored. Although minimum cut admits efficient classical solutions, it is a fundamental…
We introduce the notion of deformed quantum vertex algebra module associated with a braiding map. We construct two families of braiding maps over the Etingof-Kazhdan quantum vertex algebras associated with the rational $R$-matrices of…
Here we show how universal quantum computers based on the quantum circuit model can handle mathematical analysis calculations for functions with continuous domains, without any digitalization, and with remarkably few qubits. The basic…
In quantum computing, the connectivity of qubits placed on two-dimensional chips limits the scalability and functionality of solid-state quantum computers. This paper presents two approaches to constructing complex quantum networks from…
A finite set can be supplied with a group structure which can then be used to select (classes of) differential calculi on it via the notions of left-, right- and bicovariance. A corresponding framework has been developed by Woronowicz, more…
The form factor of a quantum graph is a function measuring correlations within the spectrum of the graph. It can be expressed as a double sum over the periodic orbits on the graph. We propose a scheme which allows one to evaluate the…
Graphical calculi such as the ZH-calculus are powerful tools in the study and analysis of quantum processes, with links to other models of quantum computation such as quantum circuits, measurement-based computing, etc. A somewhat compact…
Diagrammatic techniques for reasoning about monoidal categories provide an intuitive understanding of the symmetries and connections of interacting computational processes. In the context of categorical quantum mechanics, Coecke and…
A new model of quantum computing has recently been proposed which, in analogy with a classical lambda-calculus, exploits quantum processes which operate on other quantum processes. One such quantum meta-operator takes N unitary…
In this paper we present a new construction of analytic analogues of quantum groups over non-Archimedean fields and construct braided monoidal categories of their representations. We do this by constructing analytic Nichols algebras and use…
We construct a finite dimensional quiver algebra from the non-simply laced type $B$ Dynkin diagram, which we call the type $B$ zigzag algebra. This leads to a faithful categorical action of the type $B$ braid group $\mathcal{A}(B)$, acting…
Working towards an algebra for operators of strongly interacting quantum fields, a nonassociative decomposition of field operators is proposed. In the demonstrated case, quantum corrections appear from the possible bracket permutations. A…
We present a detailed synthetic overview of the utilisation of categorical techniques in the study of order structures together with their applications in operational quantum theory. First, after reviewing the notion of residuation and its…
ZX-calculus has proved to be a useful tool for quantum technology with a wide range of successful applications. Most of these applications are of an algebraic nature. However, other tasks that involve differentiation and integration remain…
Quantum computation can be formulated through various models, each highlighting distinct structural and resource-theoretic aspects of quantum computational power. This paper develops a unified categorical framework that encompasses these…
We introduce the Scalable ZX-calculus (SZX-calculus for short), a formal and compact graphical language for the design and verification of quantum computations. The SZX-calculus is an extension of the ZX-calculus, a powerful framework that…
Different graphical calculi have been proposed to represent quantum computation. First the ZX- calculus [4], followed by the ZW-calculus [12] and then the ZH-calculus [1]. We can wonder if new Z*-calculi will continue to be proposed…
We report on our recent breakthrough in the costructionfor q>0 of Hermitean and "tractable" differential operators out of the U_qso(N)-covariant differential calculus on the noncommutative manifolds R_q^N (the socalled "quantum Euclidean…
A diverse collection of fusion categories may be realized by the representation theory of quantum groups. There is substantial literature where one will find detailed constructions of quantum groups, and proofs of the…
MQuantum algorithms of matrix operations are of great significance in many fields in science and technology. In this paper, by leveraging multi-qubit Toffoli gates and basic single-qubit operations, the quantum algorithms of matrix…