Entangling characterization of (SWAP)1/m and Controlled unitary gates

We study the entangling power and perfect entangler nature of (SWAP)1/m, for m>=1, and controlled unitary (CU) gates. It is shown that (SWAP)1/2 is the only perfect entangler in the family. On the other hand, a subset of CU which is locally equivalent to CNOT is identified. It is shown that the subset, which is a perfect entangler, must necessarily possess the maximum entangling power.Comment: 12 pages, 1 figure, One more paragraph added in Introductio

Disorder, spin-orbit, and interaction effects in dilute Ga1−xMnxAs{\rm Ga}_{1-x}{\rm Mn}_x{\rm As}

We derive an effective Hamiltonian for ${\rm Ga}_{1-x}{\rm Mn}_x {\rm As}$ in the dilute limit, where ${\rm Ga}_{1-x}{\rm Mn}_x {\rm As}$ can be described in terms of spin $F=3/2$ polarons hopping between the {\rm Mn} sites and coupled to the local {\rm Mn} spins. We determine the parameters of our model from microscopic calculations using both a variational method and an exact diagonalization within the so-called spherical approximation. Our approach treats the extremely large Coulomb interaction in a non-perturbative way, and captures the effects of strong spin-orbit coupling and Mn positional disorder. We study the effective Hamiltonian in a mean field and variational calculation, including the effects of interactions between the holes at both zero and finite temperature. We study the resulting magnetic properties, such as the magnetization and spin disorder manifest in the generically non-collinear magnetic state. We find a well formed impurity band fairly well separated from the valence band up to $x_{\rm active} \lesssim 0.015$ for which finite size scaling studies of the participation ratios indicate a localization transition, even in the presence of strong on-site interactions, where $x_{\rm active}<x_{\rm nom}$ is the fraction of magnetically active Mn. We study the localization transition as a function of hole concentration, Mn positional disorder, and interaction strength between the holes.Comment: 15 pages, 12 figure

Probabilistic abstract interpretation: From trace semantics to DTMC’s and linear regression

In order to perform probabilistic program analysis we need to consider probabilistic languages or languages with a probabilistic semantics, as well as a corresponding framework for the analysis which is able to accommodate probabilistic properties and properties of probabilistic computations. To this purpose we investigate the relationship between three different types of probabilistic semantics for a core imperative language, namely Kozen’s Fixpoint Semantics, our Linear Operator Semantics and probabilistic versions of Maximal Trace Semantics. We also discuss the relationship between Probabilistic Abstract Interpretation (PAI) and statistical or linear regression analysis. While classical Abstract Interpretation, based on Galois connection, allows only for worst-case analyses, the use of the Moore-Penrose pseudo inverse in PAI opens the possibility of exploiting statistical and noisy observations in order to analyse and identify various system properties

A Taxonomy of Causality-Based Biological Properties

We formally characterize a set of causality-based properties of metabolic networks. This set of properties aims at making precise several notions on the production of metabolites, which are familiar in the biologists' terminology. From a theoretical point of view, biochemical reactions are abstractly represented as causal implications and the produced metabolites as causal consequences of the implication representing the corresponding reaction. The fact that a reactant is produced is represented by means of the chain of reactions that have made it exist. Such representation abstracts away from quantities, stoichiometric and thermodynamic parameters and constitutes the basis for the characterization of our properties. Moreover, we propose an effective method for verifying our properties based on an abstract model of system dynamics. This consists of a new abstract semantics for the system seen as a concurrent network and expressed using the Chemical Ground Form calculus. We illustrate an application of this framework to a portion of a real metabolic pathway

Single-qubit gates and measurements in the surface acoustic wave quantum computer

In the surface acoustic wave quantum computer, the spin state of an electron trapped in a moving quantum dot comprises the physical qubit of the scheme. Via detailed analytic and numerical modeling of the qubit dynamics, we discuss the effect of excitations into higher-energy orbital states of the quantum dot that occur when the qubits pass through magnetic fields. We describe how single-qubit quantum operations, such as single-qubit rotations and single-qubit measurements, can be performed using only localized static magnetic fields. The models provide useful parameter regimes to be explored experimentally when the requirements on semiconductor gate fabrication and the nanomagnetics technology are met in the future.Comment: 13 pages, 10 figures, submitted to Phys. Rev.

Topological Charge and The Spectrum of Exactly Massless Fermions on the Lattice

The square root of the positive definite hermitian operator $D_w^{\dagger} D_w$ in Neuberger's proposal of exactly massless quarks on the lattice is implemented by the recursion formula $Y_{k+1} = {1/2} (Y_k + D_w^{\dagger} D_w Y_k^{-1})$ with Y_0 = \Id, where $Y_k^2$ converges to $D_w^{\dagger} D_w$ quadratically. The spectrum of the lattice Dirac operator for single massless fermion in two dimensional background U(1) gauge fields is investigated. For smooth background gauge fields with non-zero topological charge, the exact zero modes with definite chirality are reproduced to a very high precision on a finite lattice and the Index Theorem is satisfied exactly. The fermionic determinants are also computed and they are in good agreement with the continuum exact solution.Comment: 18 pages (LaTeX), 2 figures (EPS

Using standard typing algorithms incrementally

Modern languages are equipped with static type checking/inference that helps programmers to keep a clean programming style and to reduce errors. However, the ever-growing size of programs and their continuous evolution require building fast and efficient analysers. A promising solution is incrementality, aiming at only re-typing the diffs, i.e. those parts of the program that change or are inserted, rather than the entire codebase. We propose an algorithmic schema that drives an incremental usage of existing, standard typing algorithms with no changes. Ours is a grey-box approach: just the shape of the input, that of the results and some domain-specific knowledge are needed to instantiate our schema. Here, we present the foundations of our approach and the conditions for its correctmess. We show it at work to derive two different incremental typing algorithms. The first type checks an imperative language to detect information flow and non-interference, and the second infers types for a functional language. We assessed our proposal on a prototypical imple- mentation of an incremental type checker. Our experiments show that using the type checker incrementally is (almost) always rewardin

Using Standard Typing Algorithms Incrementally

Modern languages are equipped with static type checking/inference that helps programmers to keep a clean programming style and to reduce errors. However, the ever-growing size of programs and their continuous evolution require building fast and efficient analysers. A promising solution is incrementality, so one only re-types those parts of the program that are new, rather than the entire codebase. We propose an algorithmic schema driving the definition of an incremental typing algorithm that exploits the existing, standard ones with no changes. Ours is a grey-box approach, meaning that just the shape of the input, that of the results and some domain-specific knowledge are needed to instantiate our schema. Here, we present the foundations of our approach and we show it at work to derive three different incremental typing algorithms. The first two implement type checking and inference for a functional language. The last one type-checks an imperative language to detect information flow and non-interference. We assessed our proposal on a prototypical implementation of an incremental type checker. Our experiments show that using the type checker incrementally is (almost) always rewarding.Comment: corrected and updated; experimental results adde