Related papers: Fourier Analytic Approach to Quantum Estimation of…
Quantum algorithms for diverse problems, including search and optimization problems, require the implementation of a reflection operator over a target state. Commonly, such reflections are approximately implemented using phase estimation.…
We address precision of optical interferometers fed by Gaussian states and involving passive and/or active elements, such as beam splitters, photodetectors and optical parametric amplifiers. We first address the ultimate bounds to precision…
Quantum measurements are our eyes to the quantum systems consisting of a multitude of microscopic degrees of freedom. However, the intrinsic uncertainty of quantum measurements and the exponentially large Hilbert space pose natural barriers…
The main goal is to interpret the Askey-Wilson function and the corresponding transform pair on the quantum SU(1,1) group. A weight on the C^*-algebra of continuous functions vanishing at infinity on the quantum SU(1,1) group is studied,…
The Quantum Fourier Transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing Quantum Fourier Transform adders and multipliers and propose some modifications that extend their…
{\em Quantum Fourier analysis} is a new subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estimates. This provides interesting tools to investigate phenomena such as quantum…
This work introduces novel numerical algorithms for computational quantum mechanics, grounded in a representation of the Laplace operator -- frequently used to model kinetic energy in quantum systems -- via the heat semigroup. The key…
We establish the renormalization group equation for the running action in the context of a one quantum particle system. This equation is deduced by integrating each fourier mode after the other in the path integral formalism. It is free of…
In this paper, we propose a general analysis framework for inexact power iteration, which can be used to efficiently solve high dimensional eigenvalue problems arising from quantum many-body problems. Under the proposed framework, we…
On a locally compact group we introduce covariant quantization schemes and analogs of phase space representations as well as mixed-state localization operators. These generalize corresponding notions for the affine group and the Heisenberg…
A new approach to group classification problems and more general investigations on transformational properties of classes of differential equations is proposed. It is based on mappings between classes of differential equations, generated by…
The physical interpretation of the main notions of the quantum group theory (coproduct, representations and corepresentations, action and coaction) is discussed using the simplest examples of $q$-deformed objects (quantum group…
We propose a quantum inverse iteration algorithm which can be used to estimate the ground state properties of a programmable quantum device. The method relies on the inverse power iteration technique, where the sequential application of the…
We consider $\mathbb{R}^3$ as a homogeneous manifold for the action of the motion group given by rotations and translations. For an arbitrary $\tau\in \widehat{SO(3)}$, let $E_\tau$ be the homogeneous vector bundle over $\mathbb{R}^3$…
Let $\mathbb{F}_q$ denote the finite field with $q$ elements where $q=p^l$ is a prime power. Using Fourier analytic tools with a third moment method, we obtain sum-product type estimates for subsets of $\mathbb{F}_q$. In particular, we…
A class of (1+2)-dimensional diffusion-convection equations (nonlinear Kolmogorov equations) with time-dependent coefficients is studied with Lie symmetry point of view. The complete group classification is achieved using a gauging of…
We investigate quantum corrections in non-commutative gauge theory on fuzzy sphere. We study translation invariant models which classically favor a single fuzzy sphere with U(1) gauge group. We evaluate the effective actions up to the two…
This paper explores an efficient method for entanglement quantification in two-qubit and qubit-qutrit quantum systems based upon the framework of collective measurements in conjunction with machine learning. We introduce an adaptive…
Using the theory of representations of the symmetric group, we propose an algorithm to compute the invariant ring of a permutation group. Our approach have the goal to reduce the amount of linear algebra computations and exploit a thinner…
We present the view of quantum algorithms as a search-theoretic problem. We show that the Fourier transform, used to solve the Abelian hidden subgroup problem, is an example of an efficient elimination observable which eliminates a constant…