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

Parameterized Model-Checking for Timed-Systems with Conjunctive Guards (Extended Version)

In this work we extend the Emerson and Kahlon's cutoff theorems for process skeletons with conjunctive guards to Parameterized Networks of Timed Automata, i.e. systems obtained by an \emph{apriori} unknown number of Timed Automata instantiated from a finite set $U_1, \dots, U_n$ of Timed Automata templates. In this way we aim at giving a tool to universally verify software systems where an unknown number of software components (i.e. processes) interact with continuous time temporal constraints. It is often the case, indeed, that distributed algorithms show an heterogeneous nature, combining dynamic aspects with real-time aspects. In the paper we will also show how to model check a protocol that uses special variables storing identifiers of the participating processes (i.e. PIDs) in Timed Automata with conjunctive guards. This is non-trivial, since solutions to the parameterized verification problem often relies on the processes to be symmetric, i.e. indistinguishable. On the other side, many popular distributed algorithms make use of PIDs and thus cannot directly apply those solutions

NGC1333/IRAS4: A multiple star formation laboratory

We present SCUBA observations of the protomultiple system NGC1333/IRAS4 at 450um and 850um. The 850um map shows significant extended emission which is most probably a remnant of the initial cloud core. At 450um, the component 4A is seen to have an elongated shape suggestive of a disk. Also we confirm that in addition to the 4A and 4B system, there exists another component 4C, which appears to lie out of the plane of the system and of the extended emission. Deconvolution of the beam reveals a binary companion to IRAS4B. Simple considerations of binary dynamics suggest that this triple 4A-4BI-4BII system is unstable and will probably not survive in its current form. Thus IRAS4 provides evidence that systems can evolve from higher to lower multiplicity as they move towards the main sequence. We construct a map of spectral index from the two wavelengths, and comment on the implications of this for dust evolution and temperature differences across the map. There is evidence that in the region of component 4A the dust has evolved, probably by coagulating into larger or more complex grains. Furthermore, there is evidence from the spectral index maps that dust from this object is being entrained in its associated outflow.Comment: 10 pages, 10 figures. To appear in MNRAS. Uses mn.sty. Also available at http://www.astro.phys.ethz.ch/papers/smith/smith_p_m.htm

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

Organ failure, outcomes and deprivation status among critically ill cirrhosis patients — a one-year cohort study

No abstract available

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

Words are vectors, dependencies are matrices: Learning word embeddings from dependency graphs

Distributional Semantic Models (DSMs) construct vector representations of word meanings based on their contexts. Typically, the contexts of a word are defined as its closest neighbours, but they can also be retrieved from its syntactic dependency relations. In this work, we propose a new dependency-based DSM. The novelty of our model lies in associating an independent meaning representation, a matrix, with each dependency-label. This allows it to capture specifics of the relations between words and contexts, leading to good performance on both intrinsic and extrinsic evaluation tasks. In addition to that, our model has an inherent ability to represent dependency chains as products of matrices which provides a straightforward way of handling further contexts of a word

Characterization of complex quantum dynamics with a scalable NMR information processor

We present experimental results on the measurement of fidelity decay under contrasting system dynamics using a nuclear magnetic resonance quantum information processor. The measurements were performed by implementing a scalable circuit in the model of deterministic quantum computation with only one quantum bit. The results show measurable differences between regular and complex behaviour and for complex dynamics are faithful to the expected theoretical decay rate. Moreover, we illustrate how the experimental method can be seen as an efficient way for either extracting coarse-grained information about the dynamics of a large system, or measuring the decoherence rate from engineered environments.Comment: 4pages, 3 figures, revtex4, updated with version closer to that publishe