相关论文: Thin layer quantization in higher dimensions and c…
The curvature potential arising from confining a particle initially in three-dimensional space onto a curved surface is normally derived in the hard constraint $q \to 0$ limit, with $q$ the degree of freedom normal to the surface. In this…
Quantum communication systems support unique applications in the form of distributed quantum computing, distributed quantum sensing, and several cryptographic protocols. The main enabler in these communication systems is an efficient…
We review the definition of geometric quantization, which begins with defining a mathematical framework for the algebra of observables that holds equally well for classical and quantum mechanics. We then discuss prequantization, and go into…
We explain that a bulk with arbitrary dimensions can be added to the space over which a quantum field theory is defined. This gives a TQFT such that its correlation functions in a slice are the same as those of the original quantum field…
With the ability to directly obtain the Wigner function and density matrix of photon states, quantum tomography (QT) has had a significant impact on quantum optics, quantum computing and quantum information. By an appropriate sequence of…
A detailed account of the Kohn-Sham algorithm from quantum chemistry, formulated rigorously in the very general setting of convex analysis on Banach spaces, is given here. Starting from a Levy-Lieb-type functional, its convex and lower…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
The Schrodinger equation for a charged particle constrained to a curved surface in the presence of a vector potential is derived using the method of forms. In the limit that the particle is brought infinitesimally close to the surface, a…
The general boundary formulation of quantum field theory is applied to a massive scalar field in two dimensional Rindler space. The field is quantized according to both the Schr\"odinger-Feynman quantization prescription and the holomorphic…
With nowadays steadily growing quantum processors, it is required to develop new quantum tomography tools that are tailored for high-dimensional systems. In this work, we describe such a computational tool, based on recent ideas from…
A method is proposed for evaluation of single and double layer potentials of the Laplace and Helmholtz equations on piecewise smooth manifold boundary elements with constant densities. The method is based on a novel two-term decomposition…
Quantum theory predicts probabilities as well as relative phases between different alternatives of the system. A unified description of both probabilities and phases comes through a generalisation of the notion of a density matrix for…
The new scheme of stochastic quantization is proposed. This quantization procedure is equivalent to the deformation of an algebra of observables in the manner of deformation quantization with an imaginary deformation parameter (the Planck…
We show for any oriented surface, possibly with a boundary, how to generalize Kramers-Wannier duality to the world of quantum groups. The generalization is motivated by quantization of Poisson-Lie T-duality from the string theory.…
Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It…
We present a general strategy to simulate a D+1-dimensional quantum system using a D-dimensional one. We analyze in detail a feasible implementation of our scheme using optical lattice technology. The simplest non-trivial realization of a…
Vector quantization via random projection followed by scalar quantization is a fundamental primitive in machine learning, with applications ranging from similarity search to federated learning and KV cache compression. While dense random…
In this paper, we introduce a quantum extension of classical DNN, QDNN. The QDNN consisting of quantum structured layers can uniformly approximate any continuous function and has more representation power than the classical DNN. It still…
The motion of quantum particles homogeneously constrained to a curved surface is affected by a curvature induced geometric potential. Here, we consider the case of inhomogeneous confinement and derive the effective Hamiltonian by extending…
Generalized quantum measurements with N distinct outcomes are used for determining the density matrix, of order d, of an ensemble of quantum systems. The resulting probabilities are represented by a point in an N-dimensional space. It is…