Quantum adiabatic elimination at arbitrary order for photon number measurement

AbstractWe develop a geometrically intrinsic formulation of the arbitrary-order Virtual Element Method (VEM) on polygonal cells for the numerical solution of elliptic surface partial differential equations (PDEs). The PDE is first written in covariant form using an appropriate local reference system. The knowledge of the local parametrization allows us to consider the two-dimensional VEM scheme, without any explicit approximation of the surface geometry. The theoretical properties of the classical VEM are extended to our framework by taking into consideration the highly anisotropic character of the final discretization. These properties are extensively tested on triangular and polygonal meshes using a manufactured solution. The limitations of the scheme are verified as functions of the regularity of the surface and its approximation.

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Procedure via cross-Kerr nonlinearities for encoding single logical qubit information onto four-photon decoherence-free states

Scientific Reports ◽

10.1038/s41598-021-89809-w ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Jino Heo ◽

Seong-Gon Choi

Keyword(s):

Quantum Information ◽

Quantum Information Processing ◽

Photon Number ◽

Optical Devices ◽

Quantum Bus ◽

Reliable Procedure ◽

Optical Gates ◽

Photon Loss ◽

Decoherence Effect ◽

Logical Qubit

AbstractWe propose a photonic procedure using cross-Kerr nonlinearities (XKNLs) to encode single logical qubit information onto four-photon decoherence-free states. In quantum information processing, a decoherence-free subspace can secure quantum information against collective decoherence. Therefore, we design a procedure employing nonlinear optical gates, which are composed of XKNLs, quantum bus beams, and photon-number-resolving measurements with linear optical devices, to conserve quantum information by encoding quantum information onto four-photon decoherence-free states (single logical qubit information). Based on our analysis in quantifying the affection (photon loss and dephasing) of the decoherence effect, we demonstrate the experimental condition to acquire the reliable procedure of single logical qubit information having the robustness against the decoherence effect.

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Polyanalytic boundary value problems for planar domains with harmonic Green function

Analysis and Mathematical Physics ◽

10.1007/s13324-021-00569-2 ◽

2021 ◽

Vol 11 (3) ◽

Author(s):

Heinrich Begehr ◽

Bibinur Shupeyeva

Keyword(s):

Green Function ◽

Boundary Value Problems ◽

Arbitrary Order ◽

Boundary Value ◽

Planar Domains ◽

Schwarz Problem ◽

Bianalytic Functions ◽

Neumann Type ◽

The Neumann Problem ◽

Well Posed

AbstractThere are three basic boundary value problems for the inhomogeneous polyanalytic equation in planar domains, the well-posed iterated Schwarz problem, and further two over-determined iterated problems of Dirichlet and Neumann type. These problems are investigated in planar domains having a harmonic Green function. For the Schwarz problem, treated earlier [Ü. Aksoy, H. Begehr, A.O. Çelebi, AV Bitsadze’s observation on bianalytic functions and the Schwarz problem. Complex Var Elliptic Equ 64(8): 1257–1274 (2019)], just a modification is mentioned. While the Dirichlet problem is completely discussed for arbitrary order, the Neumann problem is just handled for order up to three. But a generalization to arbitrary order is likely.

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Horndeski genesis: consistency of classical theory

Journal of High Energy Physics ◽

10.1007/jhep12(2020)107 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Yulia Ageeva ◽

Pavel Petrov ◽

Valery Rubakov

Keyword(s):

Strong Coupling ◽

Dimensional Analysis ◽

Classical Theory ◽

Arbitrary Order ◽

Specific Model ◽

Power Counting ◽

Coupling Energy ◽

Classical Description ◽

Higher Order Terms ◽

The Universe

Abstract Genesis within the Horndeski theory is one of possible scenarios for the start of the Universe. In this model, the absence of instabilities is obtained at the expense of the property that coefficients, serving as effective Planck masses, vanish in the asymptotics t → −∞, which signalizes the danger of strong coupling and inconsistency of the classical treatment. We investigate this problem in a specific model and extend the analysis of cubic action for perturbations (arXiv:2003.01202) to arbitrary order. Our study is based on power counting and dimensional analysis of the higher order terms. We derive the latter, find characteristic strong coupling energy scales and obtain the conditions for the validity of the classical description. Curiously, we find that the strongest condition is the same as that obtained in already examined cubic case.

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Towards an MID-based Delayed Design for Arbitrary-order Dynamical Systems with a Mechanical Application

IFAC-PapersOnLine ◽

10.1016/j.ifacol.2020.12.065 ◽

2020 ◽

Vol 53 (2) ◽

pp. 4375-4380

Author(s):

Tamas Balogh ◽

Tamas Insperger ◽

Islam Boussaada ◽

Silviu-Iulian Niculescu

Keyword(s):

Dynamical Systems ◽

Arbitrary Order

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General Fractional Dynamics

Mathematics ◽

10.3390/math9131464 ◽

2021 ◽

Vol 9 (13) ◽

pp. 1464

Author(s):

Vasily E. Tarasov

Keyword(s):

Fractional Calculus ◽

Exact Solutions ◽

Arbitrary Order ◽

Nonlinear Dynamical Systems ◽

Fractional Integrals ◽

Fractional Dynamics ◽

Fractional Systems ◽

Nonlinear Dynamical ◽

Fractional Differential ◽

Solutions Of Equations

General fractional dynamics (GFDynamics) can be viewed as an interdisciplinary science, in which the nonlocal properties of linear and nonlinear dynamical systems are studied by using general fractional calculus, equations with general fractional integrals (GFI) and derivatives (GFD), or general nonlocal mappings with discrete time. GFDynamics implies research and obtaining results concerning the general form of nonlocality, which can be described by general-form operator kernels and not by its particular implementations and representations. In this paper, the concept of “general nonlocal mappings” is proposed; these are the exact solutions of equations with GFI and GFD at discrete points. In these mappings, the nonlocality is determined by the operator kernels that belong to the Sonin and Luchko sets of kernel pairs. These types of kernels are used in general fractional integrals and derivatives for the initial equations. Using general fractional calculus, we considered fractional systems with general nonlocality in time, which are described by equations with general fractional operators and periodic kicks. Equations with GFI and GFD of arbitrary order were also used to derive general nonlocal mappings. The exact solutions for these general fractional differential and integral equations with kicks were obtained. These exact solutions with discrete timepoints were used to derive general nonlocal mappings without approximations. Some examples of nonlocality in time are described.

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