Read-only-memory-based quantum computation: Experimental explorations using nuclear magnetic resonance and future prospects

Read-only-memory-based (ROM-based) quantum computation (QC) is an alternative to oracle-based QC. It has the advantages of being less magical, and being more suited to implementing space-efficient computation (i.e., computation using the minimum number of writable qubits). Here we consider a number of small (one- and two-qubit) quantum algorithms illustrating different aspects of ROM-based QC. They are: (a) a one-qubit algorithm to solve the Deutsch problem; (b) a one-qubit binary multiplication algorithm; (c) a two-qubit controlled binary multiplication algorithm; and (d) a two-qubit ROM-based version of the Deutsch-Jozsa algorithm. For each algorithm we present experimental verification using nuclear magnetic resonance ensemble QC. The average fidelities for the implementation were in the ranges 0.9-0.97 for the one-qubit algorithms, and 0.84-0.94 for the two-qubit algorithms. We conclude with a discussion of future prospects for ROM-based quantum computation. We propose a four-qubit algorithm, using Grover's iterate, for solving a miniature real-world problem relating to the lengths of paths in a network.

Simulations of thermal Bose fields in the classical limit

We demonstrate that the time-dependent projected Gross-Pitaevskii equation (GPE) derived earlier [M. J. Davis, R. J. Ballagh, and K. Burnett, J. Phys. B 34, 4487 (2001)] can represent the highly occupied modes of a homogeneous, partially-condensed Bose gas. Contrary to the often held belief that the GPE is valid only at zero temperature, we find that this equation will evolve randomized initial wave functions to a state describing thermal equilibrium. In the case of small interaction strengths or low temperatures, our numerical results can be compared to the predictions of Bogoliubov theory and its perturbative extensions. This demonstrates the validity of the GPE in these limits and allows us to assign a temperature to the simulations unambiguously. However, the GPE method is nonperturbative, and we believe it can be used to describe the thermal properties of a Bose gas even when Bogoliubov theory fails. We suggest a different technique to measure the temperature of our simulations in these circumstances. Using this approach we determine the dependence of the condensate fraction and specific heat on temperature for several interaction strengths, and observe the appearance of vortex networks. Interesting behavior near the critical point is observed and discussed.

Magnetic-field-induced superconductivity in layered organic molecular crystals with localized magnetic moments

l-(BETS)2FeCl4 undergoes transitions from an antiferromagnetic insulator to a metal and then to a superconductor as a magnetic field is increased. We use a Hubbard-Kondo model to clarify the role of the Fe31 magnetic ions in these phase transitions. In the high-field regime, the magnetic field acting on the electron spins is compensated by the exchange field He due to the magnetic ions. We show how He can be extracted from the observed splitting of the Shubnikov–de Haas frequencies. We predict the field range for field-induced superconductivity in other materials.

Numerical investigations of flow and energy fields near a thermoacoustic couple

The flow field and the energy transport near thermoacoustic couples are simulated using a 2D full Navier-Stokes solver. The thermoacoustic couple plate is maintained at a constant temperature; plate lengths, which are short and long compared with the particle displacement lengths of the acoustic standing waves, are tested. Also investigated are the effects of plate spacing and the amplitude of the standing wave. Results are examined in the form of energy vectors, particle paths, and overall entropy generation rates. These show that a net heat-pumping effect appears only near the edges of thermoacoustic couple plates, within about a particle displacement distance from the ends. A heat-pumping effect can be seen even on the shortest plates tested when the plate spacing exceeds the thermal penetration depth. It is observed that energy dissipation near the plate increases quadratically as the plate spacing is reduced. The results also indicate that there may be a larger scale vortical motion outside the plates which disappears as the plate spacing is reduced. (C) 2002 Acoustical Society of America.

Axial mixing in rotating drums using magnetic resonance imaging using bran as a model for solid state fermentations

Magnetic resonance imaging (MRI) is an easily automated, reliable technique to investigate axial mixing within rotating drums. Moist bran can be clearly differentiated from dry bran using MRI allowing a non-segregating tracer for axial mixing. For a 20-cm diameter drum, the axial dispersion coefficient in the particle bed was 0.51 cm s(-2). Axial dispersion is scale-dependent.

Nitrate in soil humic acids revealed by N-14 nuclear magnetic resonance spectroscopy

Ecosystem management such as plant residue retention and prescribed burning can significantly affect soil organic matter (SOM) composition and, thereby, the closely associated carbon (C) and nitrogen (N) cycling processes, which underpin terrestrial ecosystem productivity and sustainability. Humic acid (HA) is an important SOM component and its chemical composition has attracted much attention. Here we report the first application of N-14 nuclear magnetic resonance (NMR) spectroscopy to soil HA study, revealing the surprising existence of nitrate-N and ammonia-N in the HAs. This newly discovered HA nitrate-N, though in a relatively low concentrations, is closely related to soil N availability and responsive to plant residue management regimes in contrasting forest ecosystems. The HA nitrate-N may be a useful and sensitive biochemical indicator of SOM quality in response to different ecosystem management regimes.

Behaviour of caregivers to protect their infants from exposure to the sun in Queensland, Australia.

Exposure to the sun by infants has been demonstrated to increase the risk of the development of melanoma and other skin cancers later in life. A cohort of 508 women who delivered healthy Caucasian babies were followed up at 1 year to determine their knowledge, attitudes and practices regarding sun protection towards themselves and their child. In addition, the 1-year-old infants were assessed by a trained nurse for the number of nevi they had on their skin. Results indicate caregivers reported a high level of sun-protection practices towards their child, with 93% of the caregivers reporting usually or always placing the child in the shade when going outside. Further, 81% of the caregivers reported usually or always placing a hat on the child, while 64% reported usually or always applying sunscreen to the child's exposed skin. Interestingly, only 61% of the caregivers reported that they stayed in the shade to reduce sun exposure and only 42% wore a hat when out in the sun. Mother's own personal sun-protection methods predicted the method of sun protection that she would most likely use for the child. While children appear to be reasonably protected from the sun, they are influenced by their mother's own behaviors.

Conditional simulation of random fields by successive residuals

This paper presents a new approach to the LU decomposition method for the simulation of stationary and ergodic random fields. The approach overcomes the size limitations of LU and is suitable for any size simulation. The proposed approach can facilitate fast updating of generated realizations with new data, when appropriate, without repeating the full simulation process. Based on a novel column partitioning of the L matrix, expressed in terms of successive conditional covariance matrices, the approach presented here demonstrates that LU simulation is equivalent to the successive solution of kriging residual estimates plus random terms. Consequently, it can be used for the LU decomposition of matrices of any size. The simulation approach is termed conditional simulation by successive residuals as at each step, a small set (group) of random variables is simulated with a LU decomposition of a matrix of updated conditional covariance of residuals. The simulated group is then used to estimate residuals without the need to solve large systems of equations.

Repeated three-dimensional magnetic resonance imaging of atherosclerosis development in innominate arteries of low-density lipoprotein receptor-knockout mice

Background-In vivo methods to evaluate the size and composition of atherosclerotic lesions in animal models of atherosclerosis would assist in the testing of antiatherosclerotic drugs. We have developed an MRI method of detecting atherosclerotic plaque in the major vessels at the base of the heart in low-density lipoprotein (LDL) receptor-knockout (LDLR-/-) mice on a high-fat diet. Methods and Results-Three-dimensional fast spin-echo magnetic resonance images were acquired at 7 T by use of cardiac and respiratory triggering, with approximate to140-mum isotropic resolution, over 30 minutes. Comparison of normal and fat-suppressed images from female LDLR-/- mice I week before and 8 and 12 weeks after the transfer to a high-fat diet allowed visualization and quantification of plaque development in the innominate artery in vivo. Plaque mean cross-sectional area was significantly greater at week 12 in the LDLR-/- mice (0.14+/-0.086 mm(2) [mean+/-SD]) than in wild-type control mice on a normal diet (0.017+/-0.031 mm(2), p

Rapid field calculations for the effect of ferromagnetic material in MRI magnet design

Magnetic resonance imaging (MRI) magnets have very stringent constraints on the homogeneity of the static magnetic field that they generate over desired imaging regions. The magnet system also preferably generates very little stray field external to its structure, so that ease of siting and safety are assured. This work concentrates on deriving, means of rapidly computing the effect of 'cold' and 'warm' ferromagnetic material in or around the superconducting magnet system, so as to facilitate the automated design of hybrid material MR magnets. A complete scheme for the direct calculation of the spherical harmonics of the magnetic field generated by a circular ring of ferromagnetic material is derived under the conditions of arbitrary external magnetizing fields. The magnetic field produced by the superconducting coils in the system is computed using previously developed methods. The final, hybrid algorithm is fast enough for use in large-scale optimization methods. The resultant fields from a practical example of a 4 T, clinical MRI magnet containing both superconducting coils and magnetic material are presented.

A mathematical model of concentrate solids content for the wet drum magnetic separator

Low concentrate density from wet drum magnetic separators in dense medium circuits can cause operating difficulties due to inability to obtain the required circulating medium density and, indirectly, high medium solids losses. The literature is almost silent on the processes controlling concentrate density. However, the common name for the region through which concentrate is discharged-the squeeze pan gap-implies that some extrusion process is thought to be at work. There is no model of magnetics recovery in a wet drum magnetic separator, which includes as inputs all significant machine and operating variables. A series of trials, in both factorial experiments and in single variable experiments, was done using a purpose built rig which featured a small industrial scale (700 mm lip length, 900 turn diameter) wet drum magnetic separator. A substantial data set of 191 trials was generated in this work. The results of the factorial experiments were used to identify the variables having a significant effect on magnetics recovery. It is proposed, based both on the experimental observations of the present work and on observations reported in the literature, that the process controlling magnetic separator concentrate density is one of drainage. Such a process should be able to be defined by an initial moisture, a drainage rate and a drainage time, the latter being defined by the volumetric flowrate and the volume within the drainage zone. The magnetics can be characterised by an experimentally derived ultimate drainage moisture. A model based on these concepts and containing adjustable parameters was developed. This model was then fitted to a randomly chosen 80% of the data, and validated by application to the remaining 20%. The model is shown to be a good fit to data over concentrate solids content values from 40% solids to 80% solids and for both magnetite and ferrosilicon feeds. (C) 2003 Elsevier Science B.V. All rights reserved.