Related papers: Volume and Quantizations
We show a significant reduction of the number of quantum operations and the improvement of the circuit depth for the realization of the Toffoli gate by using qudits. This is done by establishing a general relation between the dimensionality…
This Perspective focuses on the several overlaps between quantum algorithms and Monte Carlo methods in the domains of physics and chemistry. We will analyze the challenges and possibilities of integrating established quantum Monte Carlo…
This work presents a selective review of results concerning the mathematical interface between the classical and quantum aspects encountered in problems such as the nuclear mean-field dynamics or quantum Brownian motion. It is shown that…
We review quantum chaos on graphs. We construct a unitary operator which represents the quantum evolution on the graph and study its spectral and wavefunction statistics. This operator is the analogue of the classical evolution operator on…
We introduce several notions of random positive operator valued measures (POVMs), and we prove that some of them are equivalent. We then study statistical properties of the effect operators for the canonical examples, obtaining limiting…
In this article we introduce a new operator representing the three-dimensional scalar curvature in loop quantum gravity. Our construction does not apply to the entire kinematical Hilbert space of loop quantum gravity; instead, the operator…
The elements of the class of non-homogeneous differential operators which are based on the same vector field, when viewed as acting on appropriate Hilbert spaces, are shown to be isomorphic to each other. It shown that the replacement of a…
The goal of this article is to give a positive answer to Rockafellar's maximality of the sum conjecture in the linear multi-valued operator case.
Rovelli's argument against the realistic interpretation of quantum states and in favor of an ontology of quantum events is refuted.
The success of quantum physics in description of various physical interaction phenomena relies primarily on the accuracy of analytical methods used. In quantum mechanics, many of such interactions such as those found in quantum…
A formula is written down for the annhilation operator(bose or fermi) in terms of the corresponding observable bilinears namely currents and densities. The Fock space representation of these formulas is clarified. A conjecture is written…
We examine spectrum of the physical volume operator within the non-standard loop quantum cosmology. The spectrum is discrete with equally distant levels defining a quantum of the volume. The discreteness may imply a foamy structure of…
We present a survey on the mathematical structure of zero- and single scale quantities and the associated calculation methods and function spaces in higher order perturbative calculations in relativistic renormalizable quantum field…
The present article is devoted to the generalized Salem functions, the generailed shift operator, and certain related problems. A description of further investigations of the author of this article is given.These investigations (in terms of…
Simulating molecules is believed to be one of the early-stage applications for quantum computers. Current state-of-the-art quantum computers are limited in size and coherence, therefore optimizing resources to execute quantum algorithms is…
In loop quantum cosmology, the Hamiltonian reduces to a finite difference operator. We study the initial singularity and the large volume limit against the ambiguities in the discretisation and the operator ordering within a homogeneous,…
Costello and Gwilliam have given both 1) a general definition of perturbative quantum gauge theory on a manifold M and 2) a construction of a factorization algebra of quantum observables assigned to every quantum gauge theory. In this…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
We present a mathematical framework that unifies the quantum causal history formalism from theoretical high energy physics and the directed graph operator framework from the theory of operator algebras. The approach involves completely…
A general formulation of classical relativistic particle mechanics is presented, with an emphasis on the fact that superluminal velocities and nonlocal interactions are compatible with relativity. Then a manifestly relativistic-covariant…