Qudit versions of the qubit "pi-over-eight" gate

When visualised as an operation on the Bloch sphere, the qubit "pi-over-eight" gate corresponds to one-eighth of a complete rotation about the vertical axis. This simple gate often plays an important role in quantum information theory, typically in situations for which Pauli and Clifford gates are insufficient. Most notably, when it supplements the set of Clifford gates then universal quantum computation can be achieved. The "pi-over-eight" gate is the simplest example of an operation from the third level of the Clifford hierarchy (i.e., it maps Pauli operations to Clifford operations under conjugation). Here we derive explicit expressions for all qudit (d-level, where d is prime) versions of this gate and analyze the resulting group structure that is generated by these diagonal gates. This group structure differs depending on whether the dimensionality of the qudit is two, three or greater than three. We then discuss the geometrical relationship of these gates (and associated states) with respect to Clifford gates and stabilizer states. We present evidence that these gates are maximally robust to depolarizing and phase damping noise, in complete analogy with the qubit case. Motivated by this and other similarities we conjecture that these gates could be useful for the task of qudit magic-state distillation and, by extension, fault-tolerant quantum computing. Very recent, independent work by Campbell, Anwar and Browne confirms the correctness of this intuition, and we build upon their work to characterize noise regimes for which noisy implementations of these gates can (or provably cannot) supplement Clifford gates to enable universal quantum computation.Comment: Version 2 changed to reflect improved distillation routines in arXiv:1205.3104v2. Minor typos fixed. 12 Pages,2 Figures,3 Table

Percolative shunting on electrified surface

The surface discharge of electrified dielectrics at high humidity is considered. The percolative nature of charge transport in electrets is established. Particular attention is given to the phenomena of adsorption and nucleation of electrically conducting phase in the cause of percolation cluster growth on electrified surface. The critical index of the correlation lenght for percolation cluster is found, and its value is in good agreement with the known theoretical estimations.Comment: 4 pages with 1 figure, revtex, published in Tech. Phys. Lett. 25 (1999) 877-879 with one additional figur

Equivalence of operator-splitting schemes for the integration of the Langevin equation

We investigate the equivalence of different operator-splitting schemes for the integration of the Langevin equation. We consider a specific problem, so called the directed percolation process, which can be extended to a wider class of problems. We first give a compact mathematical description of the operator-splitting method and introduce two typical splitting schemes that will be useful in numerical studies. We show that the two schemes are essentially equivalent through the map that turns out to be an automorphism. An associated equivalent class of operator-splitting integrations is also defined by generalizing the specified equivalence.Comment: 4 page

Transport on Directed Percolation Clusters

We study random lattice networks consisting of resistor like and diode like bonds. For investigating the transport properties of these random resistor diode networks we introduce a field theoretic Hamiltonian amenable to renormalization group analysis. We focus on the average two-port resistance at the transition from the nonpercolating to the directed percolating phase and calculate the corresponding resistance exponent $\phi$ to two-loop order. Moreover, we determine the backbone dimension $D_B$ of directed percolation clusters to two-loop order. We obtain a scaling relation for $D_B$ that is in agreement with well known scaling arguments.Comment: 4 page

Robots that can adapt like animals

As robots leave the controlled environments of factories to autonomously function in more complex, natural environments, they will have to respond to the inevitable fact that they will become damaged. However, while animals can quickly adapt to a wide variety of injuries, current robots cannot "think outside the box" to find a compensatory behavior when damaged: they are limited to their pre-specified self-sensing abilities, can diagnose only anticipated failure modes, and require a pre-programmed contingency plan for every type of potential damage, an impracticality for complex robots. Here we introduce an intelligent trial and error algorithm that allows robots to adapt to damage in less than two minutes, without requiring self-diagnosis or pre-specified contingency plans. Before deployment, a robot exploits a novel algorithm to create a detailed map of the space of high-performing behaviors: This map represents the robot's intuitions about what behaviors it can perform and their value. If the robot is damaged, it uses these intuitions to guide a trial-and-error learning algorithm that conducts intelligent experiments to rapidly discover a compensatory behavior that works in spite of the damage. Experiments reveal successful adaptations for a legged robot injured in five different ways, including damaged, broken, and missing legs, and for a robotic arm with joints broken in 14 different ways. This new technique will enable more robust, effective, autonomous robots, and suggests principles that animals may use to adapt to injury

Unboundedness and downward closures of higher-order pushdown automata

We show the diagonal problem for higher-order pushdown automata (HOPDA), and hence the simultaneous unboundedness problem, is decidable. From recent work by Zetzsche this means that we can construct the downward closure of the set of words accepted by a given HOPDA. This also means we can construct the downward closure of the Parikh image of a HOPDA. Both of these consequences play an important role in verifying concurrent higher-order programs expressed as HOPDA or safe higher-order recursion schemes

Why do people fail to turn good intentions into action? : The role of executive control processes in the translation of healthy eating intentions into action in young Scottish adults

Non peer reviewedPublisher PD

Breast cancer risk reduction:is it feasible to initiate a randomised controlled trial of a lifestyle intervention programme (ActWell) within a national breast screening programme?

BackgroundBreast cancer is the most commonly diagnosed cancer and the second cause of cancer deaths amongst women in the UK. The incidence of the disease is increasing and is highest in women from least deprived areas. It is estimated that around 42% of the disease in post-menopausal women could be prevented by increased physical activity and reductions in alcohol intake and body fatness. Breast cancer control endeavours focus on national screening programmes but these do not include communications or interventions for risk reductionThis study aimed to assess the feasibility of delivery, indicative effects and acceptability of a lifestyle intervention programme initiated within the NHS Scottish Breast Screening Programme (NHSSBSP).MethodsA 1:1 randomised controlled trial (RCT) of the 3 month ActWell programme (focussing on body weight, physical activity and alcohol) versus usual care conducted in two NHSSBSP sites between June 2013 and January 2014. Feasibility assessments included recruitment, retention, and fidelity to protocol. Indicative outcomes were measured at baseline and 3 month follow-up (body weight, waist circumference, eating and alcohol habits and physical activity. At study end, a questionnaire assessed participant satisfaction and qualitative interviews elicited women¿s, coaches and radiographers¿ experiences. Statistical analysis used Chi squared tests for comparisons in proportions and paired t tests for comparisons of means. Linear regression analyses were performed, adjusted for baseline values, with group allocation as a fixed effectResultsA pre-set recruitment target of 80 women was achieved within 12 weeks and 65 (81%) participants (29 intervention, 36 control) completed 3 month assessments. Mean age was 58¿±¿5.6 years, mean BMI was 29.2¿±¿7.0 kg/m2 and many (44%) reported a family history of breast cancer.The primary analysis (baseline body weight adjusted) showed a significant between group difference favouring the intervention group of 2.04 kg (95%CI ¿3.24 kg to ¿0.85 kg). Significant, favourable between group differences were also detected for BMI, waist circumference, physical activity and sitting time. Women rated the programme highly and 70% said they would recommend it to others.ConclusionsRecruitment, retention, indicative results and participant acceptability support the development of a definitive RCT to measure long term effects.Trial registrationThe trial was registered with Current Controlled Trials (ISRCTN56223933)

Athletic Cardiac Adaptation in Males Is a Consequence of Elevated Myocyte Mass.

Cardiac remodeling occurs in response to regular athletic training, and the degree of remodeling is associated with fitness. Understanding the myocardial structural changes in athlete's heart is important to develop tools that differentiate athletic from cardiomyopathic change. We hypothesized that athletic left ventricular hypertrophy is a consequence of increased myocardial cellular rather than extracellular mass as measured by cardiovascular magnetic resonance.Forty-five males (30 athletes and 15 sedentary age-matched healthy controls) underwent comprehensive cardiovascular magnetic resonance studies, including native and postcontrast T1 mapping for extracellular volume calculation. In addition, the 30 athletes performed a maximal exercise test to assess aerobic capacity and anaerobic threshold. Participants were grouped by athleticism: untrained, low performance, and high performance (O2max 60 mL/kg per min, respectively). In athletes, indexed cellular mass was greater in high- than low-performance athletes 60.7±7.5 versus 48.6±6.3 g/m(2); P<0.001), whereas extracellular mass was constant (16.3±2.2 versus 15.3±2.2 g/m(2); P=0.20). Indexed left ventricular end-diastolic volume and mass correlated with O2max (r=0.45, P=0.01; r=0.55, P=0.002) and differed significantly by group (P=0.01; P<0.001, respectively). Extracellular volume had an inverse correlation with O2max (r=-0.53, P=0.003 and left ventricular mass index (r=-0.44, P=0.02).Increasing left ventricular mass in athlete's heart occurs because of an expansion of the cellular compartment while the extracellular volume becomes relatively smaller: a difference which becomes more marked as left ventricular mass increases. Athletic remodeling, both on a macroscopic and cellular level, is associated with the degree of an individual's fitness. Cardiovascular magnetic resonance ECV quantification may have a future role in differentiating athlete's heart from change secondary to cardiomyopathy

The relationships between internal and external threat and right-wing attitudes: A three-wave longitudinal study

The interplay between threat and right-wing attitudes has received much research attention, but its longitudinal relationship has hardly been investigated. In this study, we investigated the longitudinal relationships between internal and external threat and right-wing attitudes using a cross-lagged design at three different time points in a large nationally representative sample (N = 800). We found evidence for bidirectional relationships. Higher levels of external threat were related to higher levels of Right-Wing Authoritarianism and to both the egalitarianism and dominance dimensions of Social Dominance Orientation at a later point in time. Conversely, higher levels of RWA were also related to increased perception of external threat later in time. Internal threat did not yield significant direct or indirect longitudinal relationships with right-wing attitudes. Theoretical and practical implications of these longitudinal effects are discussed