Related papers: Quantum structures from association schemes
Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. This is well known and it usually proceeds by partitioning…
Science is rich in abstract concepts that capture complex processes in astonishingly simple ways. A prominent example is the reduction of molecules to simple graphs. This work introduces a design principle for parametrized quantum circuits…
Modern quantum chemistry can make quantitative predictions on an immense array of chemical systems. However, the interpretation of those predictions is often complicated by the complex wave function expansions used. Here we show that an…
We propose a quantum computer structure based on coupled asymmetric single-electron quantum dots. Adjacent dots are strongly coupled by means of electric dipole-dipole interactions enabling rapid computation rates. Further, the asymmetric…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…
This paper proposes groove-like potential structures for the observation of quantum information processing by trapped particles. As an illustration the effect of quantum statistics at a 50-50 beam splitter is investigated. For…
In the present paper, we construct QMC (Quantum Markov Chains) associated with Open Quantum Random Walks such that the transition operator of the chain is defined by OQRW and the restriction of QMC to the commutative subalgebra coincides…
The theory of quantum dynamical semigroups within the mathematically rigorous framework of completely positive dynamical maps is reviewed. First, the axiomatic approach which deals with phenomenological constructions and general…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule,…
We present an integral formalism for constructing scheme transformations in a quantum field theory. We apply this to generate several new useful scheme transformations. A comparative analysis is given of these scheme transformations in…
We summarize different approaches to the theory of quantum graphs and provide several ways to construct concrete examples. First, we classify all undirected quantum graphs on the quantum space $M_2$. Secondly, we apply the theory of…
We study the quantum metric structure arising from length functions on quantum groups and show that for coamenable quantum groups of Kac type, the quantum metric information is captured by the algebra of central functions. Using this, we…
Quantum forces are long-range interactions originating from vacuum fluctuations of mediator fields. Such forces inevitably arise between ordinary matter particles whenever they couple to light mediator species. Conventional computations of…
It is demonstrated that in gate-based quantum computing architectures quantum walk is a natural mathematical description of quantum gates. It originates from field-matter interaction driving the system, but is not attached to specific qubit…
We investigate exponential families of random graph distributions as a framework for systematic quantification of structure in networks. In this paper we restrict ourselves to undirected unlabeled graphs. For these graphs, the counts of…
Discussion of the necessity to use the constructive mathematics as the formalism of quantum theory for systems with many particles.
It is postulated that quantum gravity is a sum over causal structures coupled to matter via scale evolution. Quantized causal structures can be described by studying simple matrix models where matrices are replaced by an algebra of quantum…
We consider the realization of a quantum computer in a chain of nuclear spins coupled by an Ising interaction. Quantum algorithms can be performed with the help of appropriate radio-frequency pulses. In addition to the standard…
Various aspects of the theory of quantum integrable systems are reviewed. Basic ideas behind the construction of integrable ultralocal and nonultralocal quantum models are explored by exploiting the underlying algebraic structures related…
We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way…