Relativistic Spheres

By analyzing the Einstein's equations for the static sphere, we find that there exists a non-singular static configuration whose radius can approach its corresponding horizon size arbitrarily.Comment: 8 pages revtex, 1 ps figur

Microwave method for high-frequency properties of graphene

Graphene is a remarkable material, which is yet to make the transition from unique laboratory phenomenon to useful industrial material. One missing element in the development process is a quick method of quality control of the electrical properties of graphene which may be applied in, or close to, the graphene growth process on an industrial scale. In this study, the authors describe a non-contact method using microwave resonance which potentially solves this problem. They describe the technique, consider its limitations and accuracy and suggest how the method may have future take up.UK NMS Programme, the EU EMRP project ‘GraphOhm’ and ‘MetNEMS’. The EMRP (European Metrology Research Programme

Fabrication and analogue applications of nanoSQUIDs using Dayem bridge junctions

We report here recent work at the U.K. National Physical Laboratory on developing nanoscale SQUIDs using Dayem bridge Josephson junctions. The advantages are simplicity of fabrication, exceptional low-noise performance, toward the quantum limit, and a range of novel applications. Focused ion beam patterned Nb SQUID, possessing exceptionally low noise (∼200 nΦ0/Hz1/2 above 1 kHz), and operating above 4.2 K can be applied to measurement of nanoscale magnetic objects or coupled to nanoelectromechanical resonators, as well as single particle detection of photons, protons, and ions. The limited operating temperature range may be extended by exposing the Dayem bridges to carefully controlled ion beam implantation, leading to nonreversible changes in junction transition temperature.The work reported here was supported in part by the EMRP projects ‘MetNEMS’ NEW-08 and ‘BioQUART’SIB-06. The EMRP is jointly funded by the EMRP participating countries within EURAMET and the European Union

Condition Monitoring of Power Cables

A National Grid funded research project at Southampton has investigated possible methodologies for data acquisition, transmission and processing that will facilitate on-line continuous monitoring of partial discharges in high voltage polymeric cable systems. A method that only uses passive components at the measuring points has been developed and is outlined in this paper. More recent work, funded through the EPSRC Supergen V, UK Energy Infrastructure (AMPerES) grant in collaboration with UK electricity network operators has concentrated on the development of partial discharge data processing techniques that ultimately may allow continuous assessment of transmission asset health to be reliably determined

Quantum imaging by coherent enhancement

Conventional wisdom dictates that to image the position of fluorescent atoms or molecules, one should stimulate as much emission and collect as many photons as possible. That is, in this classical case, it has always been assumed that the coherence time of the system should be made short, and that the statistical scaling $\sim1/\sqrt{t}$ defines the resolution limit for imaging time $t$. However, here we show in contrast that given the same resources, a long coherence time permits a higher resolution image. In this quantum regime, we give a procedure for determining the position of a single two-level system, and demonstrate that the standard errors of our position estimates scale at the Heisenberg limit as $\sim 1/t$, a quadratic, and notably optimal, improvement over the classical case.Comment: 4 pages, 4 figue

Quantum Inference on Bayesian Networks

Performing exact inference on Bayesian networks is known to be #P-hard. Typically approximate inference techniques are used instead to sample from the distribution on query variables given the values $e$ of evidence variables. Classically, a single unbiased sample is obtained from a Bayesian network on $n$ variables with at most $m$ parents per node in time $\mathcal{O}(nmP(e)^{-1})$, depending critically on $P(e)$, the probability the evidence might occur in the first place. By implementing a quantum version of rejection sampling, we obtain a square-root speedup, taking $\mathcal{O}(n2^mP(e)^{-\frac12})$ time per sample. We exploit the Bayesian network's graph structure to efficiently construct a quantum state, a q-sample, representing the intended classical distribution, and also to efficiently apply amplitude amplification, the source of our speedup. Thus, our speedup is notable as it is unrelativized -- we count primitive operations and require no blackbox oracle queries.Comment: 8 pages, 3 figures. Submitted to PR

Fixed-point quantum search with an optimal number of queries

Grover's quantum search and its generalization, quantum amplitude amplification, provide quadratic advantage over classical algorithms for a diverse set of tasks, but are tricky to use without knowing beforehand what fraction $\lambda$ of the initial state is comprised of the target states. In contrast, fixed-point search algorithms need only a reliable lower bound on this fraction, but, as a consequence, lose the very quadratic advantage that makes Grover's algorithm so appealing. Here we provide the first version of amplitude amplification that achieves fixed-point behavior without sacrificing the quantum speedup. Our result incorporates an adjustable bound on the failure probability, and, for a given number of oracle queries, guarantees that this bound is satisfied over the broadest possible range of $\lambda$.Comment: 4 pages plus references, 2 figure

Optimal arbitrarily accurate composite pulse sequences

Implementing a single qubit unitary is often hampered by imperfect control. Systematic amplitude errors $\epsilon$, caused by incorrect duration or strength of a pulse, are an especially common problem. But a sequence of imperfect pulses can provide a better implementation of a desired operation, as compared to a single primitive pulse. We find optimal pulse sequences consisting of $L$ primitive $\pi$ or $2\pi$ rotations that suppress such errors to arbitrary order $\mathcal{O}(\epsilon^{n})$ on arbitrary initial states. Optimality is demonstrated by proving an $L=\mathcal{O}(n)$ lower bound and saturating it with $L=2n$ solutions. Closed-form solutions for arbitrary rotation angles are given for $n=1,2,3,4$. Perturbative solutions for any $n$ are proven for small angles, while arbitrary angle solutions are obtained by analytic continuation up to $n=12$. The derivation proceeds by a novel algebraic and non-recursive approach, in which finding amplitude error correcting sequences can be reduced to solving polynomial equations.Comment: 12 pages, 5 figures, submitted to Physical Review