相关论文: Alternative linear structures for classical and qu…
A generalization of classical gauge theory is presented, in the framework of a noncommutative-geometric formalism of quantum principal bundles over smooth manifolds. Quantum counterparts of classical gauge bundles, and classical gauge…
The use of the quantizer-dequantizer formalism to describe the evolution of a quantum system is reconsidered. We show that it is possible to embed a manifold in the space of quantum states of a given auxiliary system by means of an…
This work studies how a suitably-designed classical system generates with a quantum-like (QL) state space mediated by a graph. The graph plays a special dual role by directing the topology of the classical network and defining a state space…
We have shown that quantum systems on finite-dimensional Hilbert spaces are equivalent under local transformations. Using these transformations give rise to a gauge group that connects the hamiltonian operators associated with each quantum…
The word \textit{proposition} is used in physics with different meanings, which must be distinguished to avoid interpretational problems. We construct two languages $\mathcal{L}^{\ast}(x)$ and $\mathcal{L}(x)$ with classical set-theoretical…
A geometric approach to Sundman transformation defined by basic functions for systems of second-order differential equations is developed and the necessity of a change of the tangent structure by means of the function defining the Sundman…
We develop a new interpretation of quantum theory by combining insights from extended Wigner's friend scenarios and quantum causal modelling. In this interpretation, which synthesizes ideas from relational quantum mechanics and consistent…
A possible causal solution to the problem of providing a spacetime description of the transmission of signals in quantum entangled states is described using a `bimetric' spacetime structure, in which the quantum entanglement measurements…
A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several…
A Lie system is a non-autonomous system of ordinary differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional Lie algebra of vector fields. Lie systems have been generalised…
The purpose of this paper is to study the structure of quantum linear systems in terms of their Kalman canonical form, which was proposed in a recent paper \cite{ZGPG18}. The spectral structure of quantum linear systems is explored, which…
We show how classical and quantum dualities, as well as duality relations that appear only in a sector of certain theories ("emergent dualities"), can be unveiled, and systematically established. Our method relies on the use of morphisms of…
It is demonstrated that the so-called "unavoidable quantum anomalies" can be avoided in the farmework of a special non-linear quantization scheme. A simple example is discussed in detail.
A method for successive synthesis of a Weyl matrix (or Dirichlet-to-Neumann map) of an arbitrary quantum tree is proposed. It allows one, starting from one boundary edge, to compute the Weyl matrix of a whole quantum graph by adding on new…
In the classical world one can construct two identical systems which have identical behavior and give identical measurement results. We show this to be impossible in the quantum domain. We prove that after the same quantum measurement two…
Quantum annealing is a generic algorithm using quantum-mechanical fluctuations to search for the solution of an optimization problem. The present paper first reviews the fundamentals of quantum annealing and then reports on preliminary…
Variational quantum algorithms (VQAs) utilize a hybrid quantum-classical architecture to recast problems of high-dimensional linear algebra as ones of stochastic optimization. Despite the promise of leveraging near- to intermediate-term…
In this work, we proposed a smooth transition wave equation from a quantum to classical regime in the framework of von Neumann formalism for ensembles and then obtained an equivalent scaled equation. This led us to develop a scaled…
We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression that are comparable to their quantum analogues. De-quantizing such algorithms has received a flurry of…
The quantum-to-classical transition is considered from the point of view of contractions of associative algebras. Various methods and ideas to deal with contractions of associative algebras are discussed that account for a large family of…