Quantum Probabilistic Subroutines and Problems in Number Theory

We present a quantum version of the classical probabilistic algorithms $\grave{a}$ la Rabin. The quantum algorithm is based on the essential use of Grover's operator for the quantum search of a database and of Shor's Fourier transform for extracting the periodicity of a function, and their combined use in the counting algorithm originally introduced by Brassard et al. One of the main features of our quantum probabilistic algorithm is its full unitarity and reversibility, which would make its use possible as part of larger and more complicated networks in quantum computers. As an example of this we describe polynomial time algorithms for studying some important problems in number theory, such as the test of the primality of an integer, the so called 'prime number theorem' and Hardy and Littlewood's conjecture about the asymptotic number of representations of an even integer as a sum of two primes.Comment: 9 pages, RevTex, revised version, accepted for publication on PRA: improvement in use of memory space for quantum primality test algorithm further clarified and typos in the notation correcte

A field investigation into the effects of a kelp forest (Macrocystis pyrifera) on coastal hydrodynamics and transport

Macrocystis pyrifera (Giant Kelp) forests form important habitats in temperate coastal regions. Hydrodynamics control the transport of nutrients, food particles, larvae and spores at scales ranging from boundary layers around individual blades to entire kelp forests. Our measurements include vertical profiles of current and temperature, and concurrent wave measurements, at a number of different locations in and around a kelp forest at Santa Cruz, California. We find that flow at the site is dominated by variations at diurnal and semidiurnal frequencies. A vertically sheared across-shore flow, consistent with flow driven by an across-shore density gradient, is thought to be important for exchange between the kelp forest and the surrounding coastal ocean. Within the kelp forest, currents are reduced by a factor that correlates with surface canopy coverage, higher frequency internal waves are damped, and onshore transport due to waves (Stokes drift) is estimated to be similar in magnitude to that due to currents. Richardson numbers within the kelp forest are higher than those outside the kelp forest and indicate that the water column within the kelp forest is usually stable to turbulence generation by mean velocity shear

Reducing the communication complexity with quantum entanglement

We propose a probabilistic two-party communication complexity scenario with a prior nonmaximally entangled state, which results in less communication than that is required with only classical random correlations. A simple all-optical implementation of this protocol is presented and demonstrates our conclusion.Comment: 4 Pages, 2 Figure

Palaeontology, the biogeohistory of Victoria

The broad-scale distribution of fossils within Victoria is controlled by general global patterns in the biological evolution of life on Earth, the local development and environmental evolution of habitats, and the occurrence of geological processes conducive to the preservation of fossil floras and faunas. Early Palaeozoic fossils are mostly marine in origin because of the predominance of marine sedimentary rocks in Victoria and because life on land was not significant during most of this time interval. Middle Palaeozoic sequences have both terrestrial and marine fossil records. Within Victoria, marine rocks are only very minor components of strata deposited during the late Palaeozoic, so that few marine fossils are known from this time period. A similar situation existed during most of the Mesozoic except towards the end of this era when marine conditions began to prevail in the Bass Strait region. During long intervals in the Cainozoic, large areas of Victoria were flooded by shallow-marine seas, particularly in the southern basins of Bass Strait, as well as in the northwest of the State (Murray Basin). Cainozoic sediments contain an extraordinary range of animal and plant fossils. During the Quaternary, the landscape of Victoria became, and continues to be, dominated by continental environments including, at times, extensive freshwater lake systems. Fossil floras and faunas from sediments deposited in these lake systems and from other continental sediments, as well as from Quaternary sediments deposited in marginal marine environments, collectively record a history of rapid fluctuations in climate and sea level.<br /

A switchable controlled-NOT gate in a spin-chain NMR quantum computer

A method of switching a controlled-NOT gate in a solid-stae NMR quantum computer is presented. Qubits of I=1/2 nuclear spins are placed periodically along a quantum spin chain (1-D antiferromagnet) having a singlet ground state with a finite spin gap to the lowest excited state caused by some quantum effect. Irradiation of a microwave tuned to the spin gap energy excites a packet of triplet magnons at a specific part of the chain where control and target qubits are involved. The packet switches on the Suhl-Nakamura interaction between the qubits, which serves as a controlled NOT gate. The qubit initialization is achieved by a qubit initializer consisting of semiconducting sheets attached to the spin chain, where spin polarizations created by the optical pumping method in the semiconductors are transferred to the spin chain. The scheme allows us to separate the initialization process from the computation, so that one can optimize the computation part without being restricted by the initialization scheme, which provides us with a wide selection of materials for a quantum computer.Comment: 8 pages, 5 figure

Quantum phase transitions and thermodynamic properties in highly anisotropic magnets

The systems exhibiting quantum phase transitions (QPT) are investigated within the Ising model in the transverse field and Heisenberg model with easy-plane single-site anisotropy. Near QPT a correspondence between parameters of these models and of quantum phi^4 model is established. A scaling analysis is performed for the ground-state properties. The influence of the external longitudinal magnetic field on the ground-state properties is investigated, and the corresponding magnetic susceptibility is calculated. Finite-temperature properties are considered with the use of the scaling analysis for the effective classical model proposed by Sachdev. Analytical results for the ordering temperature and temperature dependences of the magnetization and energy gap are obtained in the case of a small ground-state moment. The forms of dependences of observable quantities on the bare splitting (or magnetic field) and renormalized splitting turn out to be different. A comparison with numerical calculations and experimental data on systems demonstrating magnetic and structural transitions (e.g., into singlet state) is performed.Comment: 46 pages, RevTeX, 6 figure

ATP synthase: from single molecule to human bioenergetics

ATP synthase (FoF1) consists of an ATP-driven motor (F1) and a H+-driven motor (Fo), which rotate in opposite directions. FoF1 reconstituted into a lipid membrane is capable of ATP synthesis driven by H+ flux. As the basic structures of F1 (α3β3γδε) and Fo (ab2c10) are ubiquitous, stable thermophilic FoF1 (TFoF1) has been used to elucidate molecular mechanisms, while human F1Fo (HF1Fo) has been used to study biomedical significance. Among F1s, only thermophilic F1 (TF1) can be analyzed simultaneously by reconstitution, crystallography, mutagenesis and nanotechnology for torque-driven ATP synthesis using elastic coupling mechanisms. In contrast to the single operon of TFoF1, HFoF1 is encoded by both nuclear DNA with introns and mitochondrial DNA. The regulatory mechanism, tissue specificity and physiopathology of HFoF1 were elucidated by proteomics, RNA interference, cytoplasts and transgenic mice. The ATP synthesized daily by HFoF1 is in the order of tens of kilograms, and is primarily controlled by the brain in response to fluctuations in activity

Dynamics of Local Search Trajectory in Traveling Salesman Problem

This paper investigates dynamics of a local search trajectory generated by running the Or-opt heuristic on the traveling salesman problem. This study evaluates the dynamics of the local search heuristic by estimating the correlation dimension for the search trajectory, and finds that the local heuristic search process exhibits the transition from high-dimensional stochastic to low-dimensional chaotic behavior. The detection of dynamical complexity for a heuristic search process has both practical as well as theoretical relevance. The revealed dynamics may cast new light on design and analysis of heuristics and result in the potential for improved search process.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45818/1/10732_2005_Article_3604.pd

Dimethyl fumarate in patients admitted to hospital with COVID-19 (RECOVERY): a randomised, controlled, open-label, platform trial

Dimethyl fumarate (DMF) inhibits inflammasome-mediated inflammation and has been proposed as a treatment for patients hospitalised with COVID-19. This randomised, controlled, open-label platform trial (Randomised Evaluation of COVID-19 Therapy [RECOVERY]), is assessing multiple treatments in patients hospitalised for COVID-19 (NCT04381936, ISRCTN50189673). In this assessment of DMF performed at 27 UK hospitals, adults were randomly allocated (1:1) to either usual standard of care alone or usual standard of care plus DMF. The primary outcome was clinical status on day 5 measured on a seven-point ordinal scale. Secondary outcomes were time to sustained improvement in clinical status, time to discharge, day 5 peripheral blood oxygenation, day 5 C-reactive protein, and improvement in day 10 clinical status. Between 2 March 2021 and 18 November 2021, 713 patients were enroled in the DMF evaluation, of whom 356 were randomly allocated to receive usual care plus DMF, and 357 to usual care alone. 95% of patients received corticosteroids as part of routine care. There was no evidence of a beneficial effect of DMF on clinical status at day 5 (common odds ratio of unfavourable outcome 1.12; 95% CI 0.86-1.47; p = 0.40). There was no significant effect of DMF on any secondary outcome