Hybrid solid state qubits: the powerful role of electron spins

We review progress on the use of electron spins to store and process quantum information, with particular focus on the ability of the electron spin to interact with multiple quantum degrees of freedom. We examine the benefits of hybrid quantum bits (qubits) in the solid state that are based on coupling electron spins to nuclear spin, electron charge, optical photons, and superconducting qubits. These benefits include the coherent storage of qubits for times exceeding seconds, fast qubit manipulation, single qubit measurement, and scalable methods for entangling spatially separated matter-based qubits. In this way, the key strengths of different physical qubit implementations are brought together, laying the foundation for practical solid-state quantum technologies.Comment: 54 pages, 7 figure

Implementation of Quantum Gates via Optimal Control

Starting with the basic control system model often employed in NMR pulse design, we derive more realistic control system models taking into account effects such as off-resonant excitation for systems with fixed inter-qubit coupling controlled by globally applied electromagnetic fields, as well as for systems controlled by a combination of a global fields and local control electrodes. For both models optimal control is used to find controls that implement a set of two- and three-qubit gates with fidelity greater than 99.99%. While in some cases the optimal pulses obtained appear to be surprisingly simple and experimentally realistic, the results also show that the "optimal" pulses obtained in other cases are experimentally infeasible, and more sophisticated parametrization of the control fields and numerical algorithms are needed.Comment: 10 pages, 4 figure

Block-block entanglement and quantum phase transitions in one-dimensional extended Hubbard model

In this paper, we study block-block entanglement in the ground state of one-dimensional extended Hubbard model. Our results show that the phase diagram derived from the block-block entanglement manifests richer structure than that of the local (single site) entanglement because it comprises nonlocal correlation. Besides phases characterized by the charge-density-wave, the spin-density-wave, and phase-separation, which can be sketched out by the local entanglement, singlet superconductivity phase could be identified on the contour map of the block-block entanglement. Scaling analysis shows that ${\rm log}_2(l)$ behavior of the block-block entanglement may exist in both non-critical and the critical regions, while some local extremum are induced by the finite-size effect. We also study the block-block entanglement defined in the momentum space and discuss its relation to the phase transition from singlet superconducting state to the charge-density-wave state.Comment: 8 pages, 9 figure

Conformally rescaled spacetimes and Hawking radiation

We study various derivations of Hawking radiation in conformally rescaled metrics. We focus on two important properties, the location of the horizon under a conformal transformation and its associated temperature. We find that the production of Hawking radiation cannot be associated in all cases to the trapping horizon because its location is not invariant under a conformal transformation. We also find evidence that the temperature of the Hawking radiation should transform simply under a conformal transformation, being invariant for asymptotic observers in the limit that the conformal transformation factor is unity at their location.Comment: 22 pages, version submitted to journa

Entanglement and quantum phase transition in the extended Hubbard model

We study quantum entanglement in one-dimensional correlated fermionic system. Our results show, for the first time, that entanglement can be used to identify quantum phase transitions in fermionic systems.Comment: 5 pages, 4 figure

A multi-domain Chebyshev collocation method for predicting ultrasonic field parameters in complex material geometries

The use of ultrasound to measure elastic field parameters as well as to detect cracks in solid materials has received much attention, and new important applications have been developed recently, e.g., the use of laser generated ultrasound in non-destructive evaluation (NDE). To model such applications requires a realistic calculation of field parameters in complex geometries with discontinuous, layered materials. In this paper we present an approach for solving the elastic wave equation in complex geometries with discontinuous layered materials. The approach is based on a pseudospectral elastodynamic formulation, giving a direct solution of the time-domain elastodynamic equations. A typical calculation is performed by decomposing the global computational domain into a number of subdomains. Every subdomain is then mapped on a unit square using transfinite blending functions and spatial derivatives are calculated efficiently by a Chebyshev collocation scheme. This enables that the elastodynamic equations can be solved within spectral accuracy, and furthermore, complex interfaces can be approximated smoothly, hence avoiding staircasing. A global solution is constructed from the local solutions by means of characteristic variables. Finally, the global solution is advanced in time using a fourth order Runge-Kutta scheme. Examples of field prediction in discontinuous solids with complex geometries are given and related to ultrasonic NDE. (C) 2002 Elsevier Science B.V. All rights reserved

Special Values of Generalized Polylogarithms

We study values of generalized polylogarithms at various points and relationships among them. Polylogarithms of small weight at the points 1/2 and -1 are completely investigated. We formulate a conjecture about the structure of the linear space generated by values of generalized polylogarithms.Comment: 32 page