Convergence Conditions for Random Quantum Circuits

Efficient methods for generating pseudo-randomly distributed unitary operators are needed for the practical application of Haar distributed random operators in quantum communication and noise estimation protocols. We develop a theoretical framework for analyzing pseudo-random ensembles generated through a random circuit composition. We prove that the measure over random circuits converges exponentially (with increasing circuit length) to the uniform (Haar) measure on the unitary group and describe how the rate of convergence may be calculated for specific applications.Comment: 4 pages (revtex), comments welcome. v2: reference added, title changed; v3: published version, minor changes, references update

Efficient Symmetry Reduction and the Use of State Symmetries for Symbolic Model Checking

One technique to reduce the state-space explosion problem in temporal logic model checking is symmetry reduction. The combination of symmetry reduction and symbolic model checking by using BDDs suffered a long time from the prohibitively large BDD for the orbit relation. Dynamic symmetry reduction calculates representatives of equivalence classes of states dynamically and thus avoids the construction of the orbit relation. In this paper, we present a new efficient model checking algorithm based on dynamic symmetry reduction. Our experiments show that the algorithm is very fast and allows the verification of larger systems. We additionally implemented the use of state symmetries for symbolic symmetry reduction. To our knowledge we are the first who investigated state symmetries in combination with BDD based symbolic model checking

The NIR structure of the barred galaxy NGC253 from VISTA

[abridged] We used J and Ks band images acquired with the VISTA telescope as part of the science verification to quantify the structures in the stellar disk of the barred Sc galaxy NGC253. Moving outward from the galaxy center, we find a nuclear ring within the bright 1 kpc diameter nucleus, then a bar, a ring with 2.9 kpc radius. From the Ks image we obtain a new measure of the deprojected length of the bar of 2.5 kpc. The bar's strength, as derived from the curvature of the dust lanes in the J-Ks image, is typical of weak bars. From the deprojected length of the bar, we establish the corotation radius (R_CR=3 kpc) and bar pattern speed (Omega_b = 61.3 km /s kpc), which provides the connection between the high-frequency structures in the disk and the orbital resonances induced by the bar. The nuclear ring is located at the inner Lindblad resonance. The second ring does not have a resonant origin, but it could be a merger remnant or a transient structure formed during an intermediate stage of the bar formation. The inferred bar pattern speed places the outer Lindblad resonance within the optical disk at 4.9 kpc, in the same radial range as the peak in the HI surface density. The disk of NGC253 has a down-bending profile with a break at R~9.3 kpc, which corresponds to about 3 times the scale length of the inner disk. We discuss the evidence for a threshold in star formation efficiency as a possible explanation of the steep gradient in the surface brightness profile at large radii. The NIR photometry unveils the dynamical response of the NGC253 stellar disk to its central bar. The formation of the bar may be related to the merger event that determined the truncation of stars and gas at large radii and the perturbation of the disk's outer edge.Comment: Accepted for publication in Astronomy & Astrphysics. High resolution pdf file is available at the following link: https://www.dropbox.com/s/4o4cofs1lyjrtpv/NGC253.pd

Sistem Informasi Penjualan pada Karo Rumah Mode di Simalingkar Berbasis Web

This study discusses the web-based sales information system at the Rumah Mode Karo store which has a collection of different men\u27s and women\u27s clothing products for sale. In addition to selling clothing collections, karo fashion houses also sell Tupperware. Karo Rumah Mode currently still sells directly and does not have a sales information system so that it causes problems such as recording the Karo Rumah Mode sales transaction data still manually, the store is difficult to control all products that have been sold and those that have not been sold, nor is the store know how much stock is still available for each type of product, who receives money on the sale of a product is also not well-documented and clear. Then from the problems that arise the proposed solution to overcome this problem is to build a sales information system that uses the PHP programming language and MYSQL as the database. The goal is a web-based information system that is built can make sales both online and directly in the store and facilitate users in sales transactions, report inventory and receipt of money against sales transactions are well-documented and clear. The method used in this study is literature study and interviews / case studies at fashion house karo stores

Randomized benchmarking of single and multi-qubit control in liquid-state NMR quantum information processing

Being able to quantify the level of coherent control in a proposed device implementing a quantum information processor (QIP) is an important task for both comparing different devices and assessing a device's prospects with regards to achieving fault-tolerant quantum control. We implement in a liquid-state nuclear magnetic resonance QIP the randomized benchmarking protocol presented by Knill et al (PRA 77: 012307 (2008)). We report an error per randomized $\frac{\pi}{2}$ pulse of $1.3 \pm 0.1 \times 10^{-4}$ with a single qubit QIP and show an experimentally relevant error model where the randomized benchmarking gives a signature fidelity decay which is not possible to interpret as a single error per gate. We explore and experimentally investigate multi-qubit extensions of this protocol and report an average error rate for one and two qubit gates of $4.7 \pm 0.3 \times 10^{-3}$ for a three qubit QIP. We estimate that these error rates are still not decoherence limited and thus can be improved with modifications to the control hardware and software.Comment: 10 pages, 6 figures, submitted versio

Information-theoretic equilibration: the appearance of irreversibility under complex quantum dynamics

The question of how irreversibility can emerge as a generic phenomena when the underlying mechanical theory is reversible has been a long-standing fundamental problem for both classical and quantum mechanics. We describe a mechanism for the appearance of irreversibility that applies to coherent, isolated systems in a pure quantum state. This equilibration mechanism requires only an assumption of sufficiently complex internal dynamics and natural information-theoretic constraints arising from the infeasibility of collecting an astronomical amount of measurement data. Remarkably, we are able to prove that irreversibility can be understood as typical without assuming decoherence or restricting to coarse-grained observables, and hence occurs under distinct conditions and time-scales than those implied by the usual decoherence point of view. We illustrate the effect numerically in several model systems and prove that the effect is typical under the standard random-matrix conjecture for complex quantum systems.Comment: 15 pages, 7 figures. Discussion has been clarified and additional numerical evidence for information theoretic equilibration is provided for a variant of the Heisenberg model as well as one and two-dimensional random local Hamiltonian

Complexity of Manipulative Actions When Voting with Ties

Most of the computational study of election problems has assumed that each voter's preferences are, or should be extended to, a total order. However in practice voters may have preferences with ties. We study the complexity of manipulative actions on elections where voters can have ties, extending the definitions of the election systems (when necessary) to handle voters with ties. We show that for natural election systems allowing ties can both increase and decrease the complexity of manipulation and bribery, and we state a general result on the effect of voters with ties on the complexity of control.Comment: A version of this paper will appear in ADT-201

Control Plane Compression

We develop an algorithm capable of compressing large networks into a smaller ones with similar control plane behavior: For every stable routing solution in the large, original network, there exists a corresponding solution in the compressed network, and vice versa. Our compression algorithm preserves a wide variety of network properties including reachability, loop freedom, and path length. Consequently, operators may speed up network analysis, based on simulation, emulation, or verification, by analyzing only the compressed network. Our approach is based on a new theory of control plane equivalence. We implement these ideas in a tool called Bonsai and apply it to real and synthetic networks. Bonsai can shrink real networks by over a factor of 5 and speed up analysis by several orders of magnitude.Comment: Extended version of the paper appearing in ACM SIGCOMM 201

Model Checking CTL is Almost Always Inherently Sequential

The model checking problem for CTL is known to be P-complete (Clarke, Emerson, and Sistla (1986), see Schnoebelen (2002)). We consider fragments of CTL obtained by restricting the use of temporal modalities or the use of negations---restrictions already studied for LTL by Sistla and Clarke (1985) and Markey (2004). For all these fragments, except for the trivial case without any temporal operator, we systematically prove model checking to be either inherently sequential (P-complete) or very efficiently parallelizable (LOGCFL-complete). For most fragments, however, model checking for CTL is already P-complete. Hence our results indicate that, in cases where the combined complexity is of relevance, approaching CTL model checking by parallelism cannot be expected to result in any significant speedup. We also completely determine the complexity of the model checking problem for all fragments of the extensions ECTL, CTL+, and ECTL+

Preliminary results for RR Lyrae stars and Classical Cepheids from the Vista Magellanic Cloud (VMC) Survey

The Vista Magellanic Cloud (VMC, PI M.R. Cioni) survey is collecting $K_S$-band time series photometry of the system formed by the two Magellanic Clouds (MC) and the "bridge" that connects them. These data are used to build $K_S$-band light curves of the MC RR Lyrae stars and Classical Cepheids and determine absolute distances and the 3D geometry of the whole system using the $K$-band period luminosity ($PLK_S$), the period - luminosity - color ($PLC$) and the Wesenhiet relations applicable to these types of variables. As an example of the survey potential we present results from the VMC observations of two fields centered respectively on the South Ecliptic Pole and the 30 Doradus star forming region of the Large Magellanic Cloud. The VMC $K_S$-band light curves of the RR Lyrae stars in these two regions have very good photometric quality with typical errors for the individual data points in the range of $\sim$ 0.02 to 0.05 mag. The Cepheids have excellent light curves (typical errors of $\sim$ 0.01 mag). The average $K_S$ magnitudes derived for both types of variables were used to derive $PLK_S$ relations that are in general good agreement within the errors with the literature data, and show a smaller scatter than previous studies.Comment: 7 pages, 6 figure. Accepted for publication in Astrophysics and Space Science. Following a presentation at the conference "The Fundamental Cosmic Distance Scale: State of the Art and the Gaia Perspective", Naples, May 201