Scalable Noise Estimation with Random Unitary Operators

We describe a scalable stochastic method for the experimental measurement of generalized fidelities characterizing the accuracy of the implementation of a coherent quantum transformation. The method is based on the motion reversal of random unitary operators. In the simplest case our method enables direct estimation of the average gate fidelity. The more general fidelities are characterized by a universal exponential rate of fidelity loss. In all cases the measurable fidelity decrease is directly related to the strength of the noise affecting the implementation -- quantified by the trace of the superoperator describing the non--unitary dynamics. While the scalability of our stochastic protocol makes it most relevant in large Hilbert spaces (when quantum process tomography is infeasible), our method should be immediately useful for evaluating the degree of control that is achievable in any prototype quantum processing device. By varying over different experimental arrangements and error-correction strategies additional information about the noise can be determined.Comment: 8 pages; v2: published version (typos corrected; reference added

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

Characterization of solar-grade silicon produced by the SiF4-Na process

A process was developed for producing low cost solar grade silicon by the reaction between SiF4 gas and sodium metal. The results of the characterization of the silicon are presented. These results include impurity levels, electronic properties of the silicon after crystal growth, and the performance of solar photovoltaic cells fabricated from wafers of the single crystals. The efficiency of the solar cells fabricated from semiconductor silicon and SiF4-Na silicon was the same

Effects of rarefaction on cavity flow in the slip regime

The Navier-Stokes-Fourier equations, with boundary conditions that account for the effects of velocity-slip and temperature-jump, are compared to the direct simulation Monte Carlo method for the case of a lid-driven micro-cavity. Results are presented for Knudsen numbers within the slip-flow regime where the onset of nonequilibrium effects are usually observed. Good agreement is found in predicting the general features of the velocity field and the recirculating flow. However, although the steady-state pressure distributions along the walls of the driven cavity are generally in good agreement with the Monte Carlo data, there is some indication that the results are starting to show noticeable differences, particularly at the separation and reattachment points. The modified Navier-Stokes-Fourier equations consistently overpredict the maximum and minimum pressure values throughout the slip regime. This highlights the need for alternative boundary formulations or modeling techniques that can provide accurate and computationally economic solutions over a wider range of Knudsen numbers

Micro-scale cavities in the slip - and transition - flow regimes

Differences between Navier-Stokes-Fourier (NSF) slip/jump solutions and direct simulation Monte-Carlo (DSMC) computations are highlighted for a micro lid-driven cavity problem. The results indicate a need for better modelling techniques which at the same time retain low computational cost of NSF models. We also highlight the fact thatmany micro-flows that have been considered are simple planar flows and typical classification systems are defined on such flows. We show that for complex flows, such as thedriven cavity, non-equilibrium effects are more appreciable and their onset occurs at lower Knudsen numbers than expected

Symmetrised Characterisation of Noisy Quantum Processes

A major goal of developing high-precision control of many-body quantum systems is to realise their potential as quantum computers. Probably the most significant obstacle in this direction is the problem of "decoherence": the extreme fragility of quantum systems to environmental noise and other control limitations. The theory of fault-tolerant quantum error correction has shown that quantum computation is possible even in the presence of decoherence provided that the noise affecting the quantum system satisfies certain well-defined theoretical conditions. However, existing methods for noise characterisation have become intractable already for the systems that are controlled in today's labs. In this paper we introduce a technique based on symmetrisation that enables direct experimental characterisation of key properties of the decoherence affecting a multi-body quantum system. Our method reduces the number of experiments required by existing methods from exponential to polynomial in the number of subsystems. We demonstrate the application of this technique to the optimisation of control over nuclear spins in the solid state.Comment: About 12 pages, 5 figure

When images work faster than words: The integration of content-based image retrieval with the Northumbria Watermark Archive

Information on the manufacture, history, provenance, identification, care and conservation of paper-based artwork/objects is disparate and not always readily available. The Northumbria Watermark Archive will incorporate such material into a database, which will be made freely available on the Internet providing an invaluable resource for conservation, research and education. The efficiency of a database is highly dependant on its search mechanism. Text based mechanisms are frequently ineffective when a range of descriptive terminologies might be used i.e. when describing images or translating from foreign languages. In such cases a Content Based Image Retrieval (CBIR) system can be more effective. Watermarks provide paper with unique visual identification characteristics and have been used to provide a point of entry to the archive that is more efficient and effective than a text based search mechanism. The research carried out has the potential to be applied to any numerically large collection of images with distinctive features of colour, shape or texture i.e. coins, architectural features, picture frame profiles, hallmarks, Japanese artists stamps etc. Although the establishment of an electronic archive incorporating a CBIR system can undoubtedly improve access to large collections of images and related data, the development is rarely trouble free. This paper discusses some of the issues that must be considered i.e. collaboration between disciplines; project management; copying and digitising objects; content based image retrieval; the Northumbria Watermark Archive; the use of standardised terminology within a database as well as copyright issues

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