Related papers: Modular Double of Quantum Group
We outline the recent classification of differential structures for all main classes of quantum groups. We also outline the algebraic notion of `quantum manifold' and `quantum Riemannian manifold' based on quantum group principal bundles, a…
By encoding a qudit in a harmonic oscillator and investigating the infinite limit, we give an entirely new realization of continuous-variable quantum computation. The generalized Pauli group is generated by number and phase operators for…
Differential calculus on the quantum quaternionic group GL(1,H$_q$) is introduced.
We define a convenient $\infty$-operad parametrizing modules over commutative algebras in $\infty$-categories.
Two hierarchies of quantum principal bundles over quantum real projective spaces are constructed. One hierarchy contains bundles with U(1) as a structure group, the other has the quantum group $SU_q(2)$ as a fibre. Both hierarchies are…
It is shown that in one spatial dimension the quantum oscillator is dual to the charged particle situated in the field described by the superposition of Coulomb and Calogero-Sutherland potentials.
This document contains supporting material for our paper ``The Quantum Advantage in Binary Teams and the Coordination Dilemma''
The quantum field theory of extended objects is employed to address the hitherto nonrenormalizable Pauli interaction. This is achieved by quantizing the Dirac field using the infinite dimensional generalization of the extended object…
An universal quantum network which can implement a general quantum computing is proposed. In this sense, it can be called the quantum central processing unit (QCPU). For a given quantum computing, its realization of QCPU is just its quantum…
An alternative model to describe the electronic and thermal properties of quantum dot based on triangle geometry is proposed. The model predicts characteristics and limitations of the system by controlling the magnetic field and…
Quantum Fourier transformation is important in many quantum algorithms. In this paper, we generalize quantum Fourier transformation over the Abelian group $\mathbb{Z}_N$ from two different points to get more efficient unitary…
Fix a smooth, complete algebraic curve $X$ over an algebraically closed field $k$ of characteristic zero. To a reductive group $G$ over $k$, we associate an algebraic stack $\operatorname{Par}_G$ of quantum parameters for the geometric…
Complementarity was originally introduced as a qualitative concept for the discussion of properties of quantum mechanical objects that are classically incompatible. More recently, complementarity has become a \emph{quantitative} relation…
A new method for computing sums on a quantum computer is introduced. This technique uses the quantum Fourier transform and reduces the number of qubits necessary for addition by removing the need for temporary carry bits. This approach also…
We reaffirm the claim of Lee et al. [preceding Comment, Phys. Rev. A 108, 066401 (2023)] that the expression of quantum dual total correlation of a multipartite system in terms of quantum relative entropy as proposed in previous work [A.…
Like quantum groups, quantum groupoids frequently appear in pairs of mutually dual objects. We develop a general Pontrjagin duality theory for quantum groupoids in the algebraic setting that extends Van Daele's duality theory for multiplier…
We give a formula for the modular operator and modular conjugation in terms of matrix coefficients of corepresentations of a quantum group in the sense of Kustermans and Vaes. As a consequence, the modular autmorphism group of a unimodular…
Quantum comparators and modular arithmetic are fundamental in many quantum algorithms. Current research mainly focuses on operations between two quantum states. However, various applications, such as integer factorization, optimization,…
We introduce a novel quantum programming language featuring higher-order programs and quantum controlflow which ensures that all qubit transformations are unitary. Our language boasts a type system guaranteeingboth unitarity and…
Modular double of quantum group U_q (sl(2)) with deformation parameter q=e^{i\pi\tau} is a natural object explicitly taking into account the duality \tau -> 1/\tau. The use of the modular double in CFT allows to consider the region 1<c<25…