Related papers: Quantum Diagonalization Method in the Tavis-Cummin…
In the geometry of quantum-mechanical processes, the time-varying curvature coefficient of a quantum evolution is specified by the magnitude squared of the covariant derivative of the tangent vector to the state vector. In particular, the…
We solve the problem of Fourier transformation for the one-dimensional $q$-deformed Heisenberg algebra. Starting from a matrix representation of this algebra we observe that momentum and position are unbounded operators in the Hilbert…
Semiclassical Mechanics allows for a description of quantum systems which preserves their phase information, while using only the system's classical dynamics as an input. Over the time an identification has been developed between stationary…
We present a quantum algorithm for efficiently sampling transformed Gaussian random fields on $d$-dimensional domains, based on an enhanced version of the classical moving average method. Pointwise transformations enforcing boundedness are…
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…
We present a simple way to quantize the well-known Margulis expander map. The result is a quantum expander which acts on discrete Wigner functions in the same way the classical Margulis expander acts on probability distributions. The…
We develop a mathematically rigorous path integral representation of the time evolution operator for a model of (1+1) quantum gravity that incorporates factor ordering ambiguity. In obtaining a suitable integral kernel for the…
Partial symplectic conditional and joint probability representations of quantum mechanics are considered. The correspondence rules for most interesting physical operators are found and the expressions of the dual symbols of operators are…
There is a sub-class of the solutions to Quantum Tetrahedron Equation related to the algebraical Pentagon Equation. The Quantum Tetrahedron Equation defines an evolution operator in wholly discrete three dimensional space-time. In this…
Quantization of electromagnetic fields is investigated in the framework of stochastic variational method (SVM). Differently from the canonical quantization, this method does not require canonical form and quantization can be performed…
This work proposes double-bracket iterations as a framework for obtaining diagonalizing quantum circuits. Their implementation on a quantum computer consists of interlacing evolutions generated by the input Hamiltonian with diagonal…
This is a non-standard exposition of the main notions of quantum mechanics and quantum field theory including some recent results. It is based on the algebraic approach where the starting point is a star-algebra and on the geometric…
We explore the main processes involved in the evolution of general quantum systems by means of Diagrams of States, a novel method to graphically represent and analyze how quantum information is elaborated during computations performed by…
We propose quantum algorithms, purely quantum in nature, for calculating the determinant and inverse of an $(N-1)\times (N-1)$ matrix (depth is $O(N^2\log N)$) which is a simple modification of the algorithm for calculating the determinant…
A general formulation of noncommutative or quantum derivatives for operators in a Banach space is given on the basis of the Leibniz rule, irrespective of their explicit representations such as the G\^ateaux derivative or commutators. This…
In an amended version of non-Hermitian interaction picture we propose to work with the states $\psi(t)$ in a dyadic representation. The control of evolution via two conjugate Schr\"{o}diner equations then renders the usual necessity of the…
We provide a definition of the quantum distances of correlated many fermion wave functions in terms of the expectation values of certain operators that we call exchange operators. We prove that the distances satisfy the triangle…
Mathematical analysis of the spectral properties of the time evolution operator in quantum walks is essential for understanding key dynamical behaviors such as localization and long-term evolution. The inhomogeneous three-state case, in…
A model Hamiltonian is proposed in order to understand the localization-delocalization transition in a quantum dot, where there are two gate voltages: top and side. Considering energetically favorable degrees of freedom only, we achieve a…
We study the diagonalization problem of certain discrete quantum integrable models by the method of Baxter's T-Q relation from the algebraic geometry aspect. Among those the Hofstadter type model (with the rational magnetic flux), discrete…