Related papers: Dynamical Vector Fields on the Manifold of Quantum…
Quantum kernel methods offer significant theoretical benefits by rendering classically inseparable features separable in quantum space. Yet, the practical application of Quantum Machine Learning (QML), currently constrained by the…
Physical constraints such as positivity endow the set of quantum states with a rich geometry if the system dimension is greater than two. To shed some light on the complicated structure of the set of quantum states, we consider a…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is employed to address the hitherto nonrenormalizable gravitational interaction following which the…
The state vector evolution in the interaction of measured pure state with the collective quantum system or the field is analyzed in a nonperturbative QED formalism. As the model example the measurement of the electron final state scattered…
The quantum walks in the lattice spaces are represented as unitary evolutions. We find a generator for the evolution and apply it to further understand the walks. We first extend the discrete time quantum walks to continuous time walks.…
We investigate the question of unitarity of evolution between hypersurfaces in quantum field theory in curved spacetime from the perspective of the general boundary formulation. Unitarity thus means unitarity of the quantum operator that…
We construct quantum evolution operators on the space of states, that is represented by the vertices of the n-dimensional unit hypercube. They realize the metaplectic representation of the modular group SL(2,Z(2^n)). By construction this…
We review results on GKSL-type equations with multi-modal generators which are quadratic in bosonic or fermionic creation and annihilation operators. General forms of such equations are presented. The Gaussian solutions are obtained in…
A new approach to quantum walks is presented. Considering a quantum system undergoing some unitary discrete-time evolution in a directed graph G, we think of the vertices of G as sites that are occupied by the quantum system, whose internal…
In the present paper we propose a new approach to quantum fields in terms of category algebras and states on categories. We define quantum fields and their states as category algebras and states on causal categories with partial involution…
Intense terahertz laser field is shown to have a profound effect on the electronic and optical properties of quantum rings, where the isotropic and anisotropic quantum rings can now be treated on equal footing. We have demonstrated that in…
The geometric measure of entanglement of variational quantum states is studied on the basis of its relation with the mean value of spin. We examine n-qubit quantum states prepared by a variational circuit with a layer formed by the…
In this series of papers we aim to provide a mathematically comprehensive framework to the Hamiltonian pictures of quantum field theory in curved spacetimes. Our final goal is to study the kinematics and the dynamics of the theory from the…
In this paper, we study the distributions and the affine distributions of the quantum mechanical system. Also, we discuss the controllability of the quantum mechanical system with the related question concerning the minimum time needed to…
We provide a class of quantum evolution beyond Markovian semigroup. This class is governed by a hybrid Davies like generator such that dissipation is controlled by a suitable memory kernel and decoherence by standard GKLS generator. These…
The geometrical description of Quantum Mechanics is reviewed and proposed as an alternative picture to the standard ones. The basic notions of observables, states, evolution and composition of systems are analised from this perspective, the…
We develop a rigorous formalism for the description of the evolution of observables of quantum systems of particles in the mean-field scaling limit. The corresponding asymptotics of a solution of the initial-value problem of the dual…
We consider superfluidity and quantum vorticity in rotating spacetimes. The system is described by a complex scalar satisfying a nonlinear Klein-Gordon equation. Rotation terms are identified and found to lead to the transfer of angular…
We analyze the transformation of quantum fields under conformal coordinate transformations from inertial to accelerated frames, in the simple case of scalar massless fields in a two-dimensional spacetime, through the transformation of…