arXiv subjects

K. Paul

Publications and source records attributed to K. Paul.

11 recordsLinked to original sources

arXiv2021

Portfolio Optimization with Digitized-Counterdiabatic Quantum Algorithms

We consider digitized-counterdiabatic quantum computing as an advanced paradigm to approach quantum advantage for industrial applications in the NISQ era. We apply this concept to investigate a discrete mean-variance portfolio optimization problem, showing its usefulness in a key finance application. Our analysis shows a drastic improvement in the success probabilities of the resulting digital quantum algorithm when approximate counterdiabatic techniques are introduced. Along these lines, we discuss the enhanced performance of our methods over variational quantum algorithms like QAOA and DC-QAOA.

quant-ph↗

arXiv2021

Digitized-counterdiabatic quantum approximate optimization algorithm

The quantum approximate optimization algorithm (QAOA) has proved to be an effective classical-quantum algorithm serving multiple purposes, from solving combinatorial optimization problems to finding the ground state of many-body quantum systems. Since QAOA is an ansatz-dependent algorithm, there is always a need to design ansatz for better optimization. To this end, we propose a digitized version of QAOA enhanced via the use of shortcuts to adiabaticity. Specifically, we use a counterdiabatic (CD) driving term to design a better ansatz, along with the Hamiltonian and mixing terms, enhancing the global performance. We apply our digitized-counterdiabatic QAOA to Ising models, classical optimization problems, and the P-spin model, demonstrating that it outperforms standard QAOA in all cases we study.

quant-ph↗

arXiv2020

Numerical radius inequalities of operator matrices from a new norm on $\mathcal{B}(\mathcal{H})$

This paper is a continuation of a recent work on a new norm, christened the $ (\alpha, \beta)$-norm, on the space of bounded linear operators on a Hilbert space. We obtain some upper bounds for the said norm of $n\times n$ operator matrices. As an application of the present study, we estimate bounds for the numerical radius and the usual operator norm of $n\times n$ operator matrices, which generalize the existing ones.

math.FA↗

arXiv2020

On a new norm on $\mathcal{B}({\mathcal{H}})$ and its applications to numerical radius inequalities

We introduce a new norm on the space of bounded linear operators on a complex Hilbert space, which generalizes the numerical radius norm, the usual operator norm and the modified Davis-Wielandt radius. We study basic properties of this norm, including the upper and the lower bounds for it. As an application of the present study, we estimate bounds for the numerical radius of bounded linear operators. We illustrate with examples that our results improve on some of the important existing numerical radius inequalities.

math.FA↗

arXiv2016

Farthest point problem and M-compact sets

In this paper we give an elementary proof of the fact that every uniquely remotal set is singleton in a finite dimensional strictly convex normed linear space. We show that if A is a uniquely remotal M-compact subset with the derived set of A non-empty then the derived set of A is M-compact and uniquely remotal. We also show that if A is a uniquely remotal M-compact set and the derived set of A is compact then A is singleton.

math.FA↗

arXiv2011

Magnetic Field Expansion Out of a Plane: Application to Inverse Cyclotron Muon Cooling

In studies of the dynamics of charged particles in a cyclotron magnetic field, the specified field is generally B_z in the z = 0 midplane where B_r and B_theta are zero. B_r(r, theta, z) and B_theta(r, theta, z) are simple to determine through a linear expansion which assumes that B_z is independent of z. But, an expansion to only first order may not be sufficient for orbit simulations at large z. This paper reviews the expansion of a specified B_z(r, theta, z = 0) out of the z = 0 midplane to arbitrary order, and shows simple examples worked out to 4th order.

physics.acc-ph↗

arXiv2010

Ferromagnetism in defect-ridden oxides and related materials

The existence of high-temperature ferromagnetism in thin films and nanoparticles of oxides containing small quantities of magnetic dopants remains controversial. Some regard these materials as dilute magnetic semiconductors, while others think they are ferromagnetic only because the magnetic dopants form secondary ferromagnetic impurity phases such as cobalt metal or magnetite. There are also reports in d0 systems and other defective oxides that contain no magnetic ions. Here, we investigate TiO2 (rutile) containing 1 - 5% of iron cations and find that the room-temperature ferromagnetism of films prepared by pulsed-laser deposition is not due to magnetic ordering of the iron. The films are neither dilute magnetic semiconductors nor hosts to an iron-based ferromagnetic impurity phase. A new model is developed for defect-related ferromagnetism which involves a spin-split defect band populated by charge transfer from a proximate charge reservoir in the present case a mixture Fe2+ and Fe3+ ions in the oxide lattice. The phase diagram for the model shows how inhomogeneous Stoner ferromagnetism depends on the total number of electrons Ntot, the Stoner exchange integral I and the defect bandwidth W; the band occupancy is governed by the d-d Coulomb interaction U. There are regions of ferromagnetic metal, half-metal and insulator as well as nonmagnetic metal and insulator. A characteristic feature of the high-temperature Stoner magnetism is an an anhysteretic magnetization curve which is practically temperature independent below room temperature. This is related to a wandering ferromagnetic axis which is determined by local dipole fields. The magnetization is limited by the defect concentration, not by the 3d doping. Only 1-2 % of the volume of the films is magnetically ordered.

cond-mat.mtrl-sci↗

arXiv2005

A Cost-Effective Design for a Neutrino Factory

There have been active efforts in the U.S., Europe, and Japan on the design of a Neutrino Factory. This type of facility produces intense beams of neutrinos from the decay of muons in a high energy storage ring. In the U.S., a second detailed Feasibility Study (FS2) for a Neutrino Factory was completed in 2001. Since that report was published, new ideas in bunching, cooling and acceleration of muon beams have been developed. We have incorporated these ideas into a new facility design, which we designate as Study 2B (ST2B), that should lead to significant cost savings over the FS2 design.

physics.acc-ph↗

arXiv2004

Low-energy neutrino beams with an upgraded Fermilab proton driver

The beam properties of low-energy neutrino beams that would be possible at an upgraded 2 MW Fermilab 8 GeV Proton Source are described. In particular three options are considered; (i) a MiniBooNE-like beam using a conventional neutrino horn, (ii) a decay at rest neutrino source, and (iii) a neutrino beam downstream of a solenoid decay channel. In all three cases the fluxes are sufficiently large to provide an interesting physics program. Some physics examples are considered.

hep-ex↗

arXiv2002

Color-flow decomposition of QCD amplitudes

We introduce a new color decomposition for multi-parton amplitudes in QCD, free of fundamental-representation matrices and structure constants. This decomposition has a physical interpretation in terms of the flow of color, which makes it ideal for merging with shower Monte-Carlo programs. The color-flow decomposition allows for very efficient evaluation of amplitudes with many quarks and gluons, many times faster than the standard color decomposition based on fundamental-representation matrices. This will increase the speed of event generators for multi-jet processes, which are the principal backgrounds to signals of new physics at colliders.

hep-ph↗

arXiv2001

Associated production of Higgs and single top at hadron colliders

We study the production of the Higgs boson in association with a single top quark at hadron colliders. The cross sections for the three production processes (t-channel, s-channel, and W-associated) at both the Tevatron and the LHC are presented. We investigate the possibility of detecting a signal for the largest of these processes, the t-channel process at the LHC, via the Higgs decay into b b-bar. The QCD backgrounds are large and difficult to curb, hindering the extraction of the signal. Extensions of our analysis to the production of supersymmetric Higgs bosons are also addressed. The cross section is enhanced for large values of tangent beta, increasing the prospects for extracting a signal.

hep-ph↗