Quantum walks based on an interferometric analogy

There are presently two models for quantum walks on graphs. The "coined" walk uses discrete time steps, and contains, besides the particle making the walk, a second quantum system, the coin, that determines the direction in which the particle will move. The continuous walk operates with continuous time. Here a third model for a quantum walk is proposed, which is based on an analogy to optical interferometers. It is a discrete-time model, and the unitary operator that advances the walk one step depends only on the local structure of the graph on which the walk is taking place. No quantum coin is introduced. This type of walk allows us to introduce elements, such as phase shifters, that have no counterpart in classical random walks. Walks on the line and cycle are discussed in some detail, and a probability current for these walks is introduced. The relation to the coined quantum walk is also discussed. The paper concludes by showing how to define these walks for a general graph.Comment: Latex,18 pages, 5 figure

Energy downconversion between classical electromagnetic fields via a quantum mechanical SQUID ring

We consider the interaction of a quantum mechanical SQUID ring with a classical resonator (a parallel LC tank circuit). In our model we assume that the evolution of the ring maintains its quantum mechanical nature, even though the circuit to which it is coupled is treated classically. We show that when the SQUID ring is driven by a classical monochromatic microwave source, energy can be transferred between this input and the tank circuit, even when the frequency ratio between them is very large. Essentially, these calculations deal with the coupling between a single macroscopic quantum object (the SQUID ring) and a classical circuit measurement device where due account is taken of the nonperturbative behavior of the ring and the concomitant nonlinear interaction of the ring with this device

Characterising a solid state qubit via environmental noise

We propose a method for characterising the energy level structure of a solid state qubit by monitoring the noise level in its environment. We consider a model persistent current qubit in a lossy reservoir and demonstrate that the noise in a classical bias field is a sensitive function of the applied field

Noninvasive imaging of signals in digital circuits

In this article we describe the construction and use of a noninvasive (noncontact) electric potential probe to measure time delays of signals propagating through digital circuits. As we show, by incorporating such probes into a scanning microscope system we have been able to create time delay images of these signals.We suggest that future developments of this technique may lead to real time, high resolution imaging of digital pulses across complex very large scale integrated circuits

A review of quantitative structure-activity relationship modelling approaches to predict the toxicity of mixtures

Exposure to chemicals generally occurs in the form of mixtures. However, the great majority of the toxicity data, upon which chemical safety decisions are based, relate only to single compounds. It is currently unfeasible to test a fully representative proportion of mixtures for potential harmful effects and, as such, in silico modelling provides a practical solution to inform safety assessment. Traditional methodologies for deriving estimations of mixture effects, exemplified by principles such as concentration addition (CA) and independent action (IA), are limited as regards the scope of chemical combinations to which they can reliably be applied. Development of appropriate quantitative structure-activity relationships (QSARs) has been put forward as a solution to the shortcomings present within these techniques – allowing for the potential formulation of versatile predictive tools capable of capturing the activities of a full contingent of possible mixtures. This review addresses the current state-of-the-art as regards application of QSAR towards mixture toxicity, discussing the challenges inherent in the task, whilst considering the strengths and limitations of existing approaches. Forty studies are examined within – through reference to several characteristic elements including the nature of the chemicals and endpoints modelled, the form of descriptors adopted, and the principles behind the statistical techniques employed. Recommendations are in turn provided for practices which may assist in further advancing the field, most notably with regards to ensuring confidence in the acquired predictions.publishedVersio

Mesoscopic Josephson arrays interacting with non-classical electromagnetic fields and their applications

A ring made from a Josephson array in the insulating phase is considered. The ring contains a ‘dual Josephson junction’ (Josephson junction for vortices). External non-classical electromagnetic fields are coupled to the device and interact with the vortices that circulate the ring. The time evolution of ths two-mode fully quantum mechanical system is studied. The effect of the quantum statistics of the photons on the quantum statistics of the vortices is discussed. The entanglement between the two systems is quantified

Persistent entanglement in the classical limit

The apparent difficulty in recovering classical nonlinear dynamics and chaos from standard quantum mechanics has been the subject of a great deal of interest over the last 20 years. For open quantum systems—those coupled to a dissipative environment and/or a measurement device—it has been demonstrated that chaotic-like behaviour can be recovered in the appropriate classical limit. In this paper, we investigate the entanglement generated between two nonlinear oscillators, coupled to each other and to their environment. Entanglement—the inability to factorize coupled quantum systems into their constituent parts—is one of the defining features of quantum mechanics. Indeed, it underpins many of the recent developments in quantum technologies. Here, we show that the entanglement characteristics of two 'classical' states (chaotic and periodic solutions) differ significantly in the classical limit. In particular, we show that significant levels of entanglement are preserved only in the chaotic-like solutions

Quantum statistics and entanglement of two electromagnetic field modes coupled via a mesoscopic SQUID ring

In this paper we investigate the behavior of a fully quantum mechanical system consisting of a mesoscopic SQUID ring coupled to one or two electromagnetic field modes. We show that we can use a static magnetic flux threading the SQUID ring to control the transfer of energy, the entanglement and the statistical properties of the fields coupled to the ring. We also demonstrate that at, and around, certain values of static flux the effective coupling between the components of the system is large. The position of these regions in static flux is dependent on the energy level structure of the ring and the relative field mode frequencies, In these regions we find that the entanglement of states in the coupled system, and the energy transfer between its components, is strong

Pinch resonances in a radio-frequency-driven superconducting-quantum-interference-device ring-resonator system

In this paper we present experimental data on the frequency domain response of a superconducting-quantum-interference-device ring (a Josephson weak link enclosed by a thick superconducting ring) coupled to a radio frequency tank circuit resonator. We show that with the ring weakly hysteretic the resonance line shape of this coupled system can display opposed fold bifurcations that appear to touch (pinch off). We demonstrate that for appropriate circuit parameters these pinchoff line shapes exist as solutions of the nonlinear equations of motion for the system