Probabilistic implementation of universal quantum processors

We present a probabilistic quantum processor for qudits. The processor itself is represented by a fixed array of gates. The input of the processor consists of two registers. In the program register the set of instructions (program) is encoded. This program is applied to the data register. The processor can perform any operation on a single qudit of the dimension N with a certain probability. If the operation is unitary, the probability is in general 1/N^2, but for more restricted sets of operators the probability can be higher. In fact, this probability can be independent of the dimension of the qudit Hilbert space of the qudit under some conditions.Comment: 7 revtex pages, 1 eps figur

Superconducting p-branes and Extremal Black Holes

In Einstein-Maxwell theory, magnetic flux lines are `expelled' from a black hole as extremality is approached, in the sense that the component of the field strength normal to the horizon goes to zero. Thus, extremal black holes are found to exhibit the sort of `Meissner effect' which is characteristic of superconducting media. We review some of the evidence for this effect, and do present new evidence for it using recently found black hole solutions in string theory and Kaluza-Klein theory. We also present some new solutions, which arise naturally in string theory, which are non-superconducting extremal black holes. We present a nice geometrical interpretation of these effects derived by looking carefully at the higher dimensional configurations from which the lower dimensional black hole solutions are obtained. We show that other extremal solitonic objects in string theory (such as p-branes) can also display superconducting properties. In particular, we argue that the relativistic London equation will hold on the worldvolume of `light' superconducting p-branes (which are embedded in flat space), and that minimally coupled zero modes will propagate in the adS factor of the near-horizon geometries of `heavy', or gravitating, superconducting p-branes.Comment: 22 pages, 2 figure

A quantum gate array can be programmed to evaluate the expectation value of any operator

A programmable gate array is a circuit whose action is controlled by input data. In this letter we describe a special--purpose quantum circuit that can be programmed to evaluate the expectation value of any operator $O$ acting on a space of states of $N$ dimensions. The circuit has a program register whose state $|\Psi(O)>_P$ encodes the operator $O$ whose expectation value is to be evaluated. The method requires knowledge of the expansion of $O$ in a basis of the space of operators. We discuss some applications of this circuit and its relation to known instances of quantum state tomography.Comment: 4 pages, 3 figures include

Probabilistic instantaneous quantum computation

The principle of teleportation can be used to perform a quantum computation even before its quantum input is defined. The basic idea is to perform the quantum computation at some earlier time with qubits which are part of an entangled state. At a later time a generalized Bell state measurement is performed jointly on the then defined actual input qubits and the rest of the entangled state. This projects the output state onto the correct one with a certain exponentially small probability. The sufficient conditions are found under which the scheme is of benefit.Comment: 4 pages, 1 figur

Accelerating cycle expansions by dynamical conjugacy

Periodic orbit theory provides two important functions---the dynamical zeta function and the spectral determinant for the calculation of dynamical averages in a nonlinear system. Their cycle expansions converge rapidly when the system is uniformly hyperbolic but greatly slowed down in the presence of non-hyperbolicity. We find that the slow convergence can be associated with singularities in the natural measure. A properly designed coordinate transformation may remove these singularities and results in a dynamically conjugate system where fast convergence is restored. The technique is successfully demonstrated on several examples of one-dimensional maps and some remaining challenges are discussed

Models of Neutrino Masses: Anarchy versus Hierarchy

We present a quantitative study of the ability of models with different levels of hierarchy to reproduce the solar neutrino solutions, in particular the LA solution. As a flexible testing ground we consider models based on SU(5)xU(1)_F. In this context, we have made statistical simulations of models with different patterns from anarchy to various types of hierachy: normal hierarchical models with and without automatic suppression of the 23 (sub)determinant and inverse hierarchy models. We find that, not only for the LOW or VO solutions, but even in the LA case, the hierarchical models have a significantly better success rate than those based on anarchy. The normal hierachy and the inverse hierarchy models have comparable performances in models with see-saw dominance, while the inverse hierarchy models are particularly good in the no see-saw versions. As a possible distinction between these categories of models, the inverse hierarchy models favour a maximal solar mixing angle and their rate of success drops dramatically as the mixing angle decreases, while normal hierarchy models are far more stable in this respect.Comment: v1: 28 pages, 12 figures; v2: 34 pages, 14 figures, updated previous analysis with the inclusion of recent SNO result

Minimal Scenarios for Leptogenesis and CP Violation

The relation between leptogenesis and CP violation at low energies is analyzed in detail in the framework of the minimal seesaw mechanism. Working, without loss of generality, in a weak basis where both the charged lepton and the right-handed Majorana mass matrices are diagonal and real, we consider a convenient generic parametrization of the Dirac neutrino Yukawa coupling matrix and identify the necessary condition which has to be satisfied in order to establish a direct link between leptogenesis and CP violation at low energies. In the context of the LMA solution of the solar neutrino problem, we present minimal scenarios which allow for the full determination of the cosmological baryon asymmetry and the strength of CP violation in neutrino oscillations. Some specific realizations of these minimal scenarios are considered. The question of the relative sign between the baryon asymmetry and CP violation at low energies is also discussed.Comment: 36 pages, 5 figures; minor corrections and references updated. Final version to appear in Phys. Rev.

Single-atom entropy squeezing for two two-level atoms interacting with a single-mode radiation field

In this paper we consider a system of two two-level atoms interacting with a single-mode quantized electromagnetic field in a lossless resonant cavity via $l$-photon-transition mechanism. The field and the atoms are initially prepared in the coherent state and the excited atomic states, respectively. For this system we investigate the entropy squeezing, the atomic variances, the von Neumann entropy and the atomic inversions for the single-atom case. We show that the more the number of the parties in the system the less the amounts of the nonclassical effects exhibited in the entropy squeezing. The entropy squeezing can give information on the corresponding von Neumann entropy. Also the nonclassical effects obtained form the asymmetric atoms are greater than those obtained form the symmetric atoms. Finally, the entropy squeezing gives better information than the atomic variances only for the asymmetric atoms.Comment: 15 pages, 4 figures, comments are most welcom

The ODD protocol for describing agent-based and other simulation models: A second update to improve clarity, replication, and structural realism

© 2020, University of Surrey. All rights reserved. The Overview, Design concepts and Details (ODD) protocol for describing Individual-and Agent-Based Models (ABMs) is now widely accepted and used to document such models in journal articles. As a standardized document for providing a consistent, logical and readable account of the structure and dynamics of ABMs, some research groups also find it useful as a workflow for model design. Even so, there are still limitations to ODD that obstruct its more widespread adoption. Such limitations are discussed and addressed in this paper: the limited availability of guidance on how to use ODD; the length of ODD documents; limitations of ODD for highly complex models; lack of sufficient details of many ODDs to enable reimplementation without access to the model code; and the lack of provision for sections in the document structure covering model design ratio-nale, the model’s underlying narrative, and the means by which the model’s fitness for purpose is evaluated. We document the steps we have taken to provide better guidance on: structuring complex ODDs and an ODD summary for inclusion in a journal article (with full details in supplementary material; Table 1); using ODD to point readers to relevant sections of the model code; update the document structure to include sections on model rationale and evaluation. We also further advocate the need for standard descriptions of simulation experiments and argue that ODD can in principle be used for any type of simulation model. Thereby ODD would provide a lingua franca for simulation modelling

Probing the seesaw mechanism with neutrino data and leptogenesis

In the framework of the seesaw mechanism with three heavy right-handed Majorana neutrinos and no Higgs triplets we carry out a systematic study of the structure of the right-handed neutrino sector. Using the current low-energy neutrino data as an input and assuming hierarchical Dirac-type neutrino masses $m_{Di}$, we calculate the masses $M_i$ and the mixing of the heavy neutrinos. We confront the inferred properties of these neutrinos with the constraints coming from the requirement of a successful baryogenesis via leptogenesis. In the generic case the masses of the right-handed neutrinos are highly hierarchical: $M_i \propto m_{Di}^2$; the lightest mass is $M_1 \approx 10^3 - 10^6$ GeV and the generated baryon-to-photon ratio $\eta_B\lesssim 10^{-14}$ is much smaller than the observed value. We find the special cases which correspond to the level crossing points, with maximal mixing between two quasi-degenerate right-handed neutrinos. Two level crossing conditions are obtained: ${m}_{ee}\approx 0$ (1-2 crossing) and $d_{12}\approx 0$ (2-3 crossing), where ${m}_{ee}$ and $d_{12}$ are respectively the 11-entry and the 12-subdeterminant of the light neutrino mass matrix in the basis where the neutrino Yukawa couplings are diagonal. We show that sufficient lepton asymmetry can be produced only in the 1-2 crossing where $M_1 \approx M_2 \approx 10^{8}$ GeV, $M_3 \approx 10^{14}$ GeV and $(M_2 - M_1)/ M_2 \lesssim 10^{-5}$.Comment: 30 pages, 2 eps figures, JHEP3.cls, typos corrected, note (and references) added on non-thermal leptogenesi