Physical Optimization of Quantum Error Correction Circuits

Quantum error correcting codes have been developed to protect a quantum computer from decoherence due to a noisy environment. In this paper, we present two methods for optimizing the physical implementation of such error correction schemes. First, we discuss an optimal quantum circuit implementation of the smallest error-correcting code (the three bit code). Quantum circuits are physically implemented by serial pulses, i.e. by switching on and off external parameters in the Hamiltonian one after another. In contrast to this, we introduce a new parallel switching method that allows faster gate operation by switching all external parameters simultaneously. These two methods are applied to electron spins in coupled quantum dots subject to a Heisenberg coupling H=J(t) S_1*S_2 which can generate the universal quantum gate `square-root-of-swap'. Using parallel pulses, the encoding for three-bit quantum error correction in a Heisenberg system can be accelerated by a factor of about two. We point out that parallel switching has potential applications for arbitrary quantum computer architectures.Comment: 13 pages, 6 figure

奥付

This paper demonstrates the application of a numerical continuation method to dynamic piecewise aeroelastic systems. The aeroelastic system is initially converted into a state space form and then into a set of equations which solve the system as the motion moves between different linear zones in a free-play motion. Once an initial condition is found that satisfies these sets of equations, a continuation method is used to find all other possible solutions of the same period for a variation in any parameter. This process can then be repeated for different order systems, allowing the limit cycle behaviour of the whole system to be built up. The solutions found using this method have been shown to be the same as those found using a more traditional Runge-Kutta type of approach with a considerable time saving and added flexibility through multiple parameter variation

Implementation of a Deutsch-like quantum algorithm utilizing entanglement at the two-qubit level, on an NMR quantum information processor

We describe the experimental implementation of a recently proposed quantum algorithm involving quantum entanglement at the level of two qubits using NMR. The algorithm solves a generalisation of the Deutsch problem and distinguishes between even and odd functions using fewer function calls than is possible classically. The manipulation of entangled states of the two qubits is essential here, unlike the Deutsch-Jozsa algorithm and the Grover's search algorithm for two bits.Comment: 4 pages, two eps figure

Decoherence of geometric phase gates

We consider the effects of certain forms of decoherence applied to both adiabatic and non-adiabatic geometric phase quantum gates. For a single qubit we illustrate path-dependent sensitivity to anisotropic noise and for two qubits we quantify the loss of entanglement as a function of decoherence.Comment: 4 pages, 3 figure

Structure determination of PF3 adsorption on Cu(100) using X-ray standing waves

The local structure of the Cu(100)c(4x2)-PF3 adsorption phase has been investigated through the use of normal-incidence X-ray standing waves (NIXSW), monitored by P 1s and F 1s photoemission, together with P K-edge near-edge X-ray absorption fine structure (NEXAFS). NEXAFS shows the molecule to be oriented with its C3v symmetry axis essentially perpendicular to the surface, while the P NIXSW data show the molecule to be adsorbed in atop sites 2.37±0.04 Å above the surface, this distance corresponding to the Cu-P nearest-neighbour distance in the absence of any surface relaxation. F NIXSW indicates a surprisingly small height difference of the P and F atoms above the surface 0.44±0.06 Å, compared with the value expected for an undistorted gas-phase geometry of 0.77 Å, implying significant increases in the F-P-F bond angles. In addition, however, the F NIXSW data indicate that the molecules have a well-defined azimuthal orientation with a molecular mirror plane aligned in a substrate mirror plane, and with a small (5-10°) tilt of the molecule in this plane such that the two symmetrically-equivalent F atoms in each molecule are tilted down towards the surface

Universal quantum computation and simulation using any entangling Hamiltonian and local unitaries

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? We provide an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling n-qubit Hamiltonian and local unitaries. It follows that universal quantum computation can be performed using any entangling interaction and local unitary operations.Comment: Added references to NMR refocusing and to earlier work by Leung et al and Jones and Knil

Quantum phase gate with a selective interaction

We present a proposal for implementing quantum phase gates using selective interactions. We analize selectivity and the possibility to implement these gates in two particular systems, namely, trapped ions and Cavity QED.Comment: Four pages of TEX file and two EPS figures. Submitted for publicatio

UK Coal resource for new exploitation technologies. Final report

This focus of this report are the UK coal resources available for exploitation by the new technologies of Underground Coal Gasification, Coalbed Methane production and Carbon Dioxide Sequestration. It also briefly considers the potential for further underground and opencast mining and the extraction of methane from working and closed mines. The potential for mining was mainly considered because it has a bearing on the scope for the new exploitation technologies rather than to identify resources or potential mine development areas. The report covers the UK landward area and nearshore areas, although information on the extent of underground mining was not available for the nearshore areas. This work was carried out by the British Geological Survey, with the assistance of Wardell Armstrong and Imperial College, London. It represents a summary of the results of the Study of the UK Coal Resource for New Exploitation Technologies Project, carried out for the DTI Cleaner Coal Technology Programme (Contract No. C/01/00301/00/00) under the management of Future Energy Solutions (Agreement No. C/01/00301/00/00). Coalbed methane production can be subdivided into three categories: Methane drained from working mines, known as Coal Mine Methane (CMM), has been exploited in the UK since at least the 1950s. Currently all working mines except Daw Mill and Ellington drain methane. It is used to generate electricity at Harworth, Tower and Thoresby collieries and in boilers at Welbeck, Kellingley and Ricall/Whitemoor collieries. There is potential to increase the exploitation of CMM in the UK but this is mainly a question of economics. There is also an environmental case for further utilisation, as methane is an important greenhouse gas, 23 times more powerful than carbon dioxide on a mass basis. Methane drained from abandoned mines, known as Abandoned Mine Methane (AMM), is a methane-rich gas that is obtained from abandoned mines by applying suction to the workings. The fuel gas component consists primarily of methane desorbed from seams surrounding the mined seam(s). These unmined seams have been de-stressed and fractured by the collapse of overlying and underlying strata into the void left by the extracted seam(s). Currently AMM is being exploited at sites in North Staffordshire (Silverdale Colliery), the East Midlands (Bentinck, Shirebrook and Markham collieries) and Yorkshire (Hickleton, Monk Bretton and Wheldale collieries). The methane-rich gas is used for electricity generation or supplied to local industry for use in boilers and kilns. Over the last few years, the fledgling UK AMM industry has started to ascend a learning curve. However, it has suffered a major setback since the wholesale price of electricity fell under the New Electricity Trading Arrangements and AMM does not currently qualify as renewable energy in the UK. Coalbed methane produced via boreholes from virgin coal seams, known as Virgin Coalbed Methane (VCBM), has been the subject of significant exploration effort in Lancashire, North Wales, South Wales and Scotland. The best production of gas and water from a single well is understood to be from the project at Airth, north of Falkirk in Scotland. However, this is not economic at present. The main reason for the slow development of VCBM in the UK is perceived to be the widespread low permeability of UK coal seams, although little work has been carried out in the UK on coal permeability, or to truly identify the reasons for the lack of success. This must be overcome before the otherwise significant resource bases in the Clackmannan Syncline, Canonbie, Cumbria, South Lancashire, North Wales, North Staffordshire and South Wales coalfields can be exploited. A technological breakthrough is required to overcome the likely widespread low permeability in the UK Carboniferous coal seams. Otherwise, at best, production will probably be limited to niche opportunities in areas where high seam permeability exists. The criteria used to define and map the location of VCBM resources are as follows: • Coal seams greater than 0.4 m in thickness at depths >200 m • Seam gas content >1m3/tonne • 500 metres or more horizontal separation from underground coal workings • Vertical separation of 150m above and 40 m below a previously worked seam Vertical separation of >100 m from major unconformities of these areas is thought to be about ,900 x 109 m3 (about 29 years of UK natural gas consumption). he main criteria sed for the delineation and mapping of resource areas with potential for UCG were: eparation from underground coal workings and current omic and environmental grounds as described later in this report. he establishment of these criteria do not rule out UCG projects in shallower or thinner seams, if • Vertical separation of >100 m from major aquifers, and • Areas with a CMM resource (current underground coal mining licences) were excluded. Note that the presence of a CBM resource does not imply permeability in the coal seams or that the resource can be recovered economically now or at any time in the future. Using these criteria resource areas were defined and represented on the maps. The total VCBM resource 2 Underground coal gasification (UCG) is the process whereby the injection of oxygen and steam/water via a borehole results in the partial in-situ combustion of coal to produce a combustible gas mixture consisting of CO2, CH4, H2 and CO, the proportions depending on temperature, pressure conditions and the reactant gases injected. This product gas is then extracted via a producing well for use as an energy source. All previous trials of this technology in the UK took place in the 1950’s or before, e.g. Durham (1912), Newman Spinney (1949-1956) and Bayton (c.1955), although this country is well placed for UCG, with large reserves of indigenous coal both onshore and offshore. T u • Seams of 2 m thickness or greater • Seams at depths between 600 and 1200 m from the surface • 500 m or more horizontal and vertical scoal mining licences, and • Greater than 100 m from major aquifers While seams outside these depth and thicknesses criteria are known to support UCG, the criteria were chosen for this generic study on econ T local site specific factors support it. Mapping of the potential UCG resource has identified large areas suitable for UCG, particularly in Eastern England, Midland Valley of Scotland, North Wales, Cheshire Basin, South Lancashire, Canonbie, the Midlands and Warwickshire. Potential also exists in other coalfields but on a smaller scale; this is often limited by the extent of former underground coal mining activities. The total area where coals are suitable for gasification is approximately 2.8 x 109m2. Where the criteria for UCG are met, the minimum volume of coal available for gasification, calculated assuming only one 2 m thick seam meets the criteria across each area, is app63 roximately 5,698 x 10 m (~7 Btonnes). Using an verage of the total thickness of coals that meet the criteria across each area gives a more realistic source figure of 12,911 x 106m3 (~17 Btonnes). pass the expensive step of parating the CO2 from flue gases. If the main objective, however, is CO2 sequestration rather than ethane production then separation of the flue gases may be worthwhile. O2 on coal seams, is would render them unminable and ungasifiable (because the CO2 would be released). Any future ining of such coals would require re-capture and sequestration of the stored CO . ion, providing that other issues, such as low seam permeability, can be vercome. Large areas where coal is below 1,200 m occur in the UK, particularly in the Cheshire asin and Eastern England. In summary • and its potential application in the UK cannot be assessed. However, there are vast areas of coal at depths below 1,200 m that are possibly too deep for mining and in situ gasification

Current Understanding of Structure–Processing–Property Relationships in BaTiO₃–Bi(M)O₃ Dielectrics

As part of a continued push for high permittivity dielectrics suitable for use at elevated operating temperatures and/or large electric fields, modifications of BaTiO3 with Bi(M)O3, where M represents a net-trivalent B-site occupied by one or more species, have received a great deal of recent attention. Materials in this composition family exhibit weakly coupled relaxor behavior that is not only remarkably stable at high temperatures and under large electric fields, but is also quite similar across various identities of M. Moderate levels of Bi content (as much as 50 mol%) appear to be crucial to the stability of the dielectric response. In addition, the presence of significant Bi reduces the processing temperatures required for densification and increases the required oxygen content in processing atmospheres relative to traditional X7R-type BaTiO3-based dielectrics. Although detailed understanding of the structure–processing–property relationships in this class of materials is still in its infancy, this article reviews the current state of understanding of the mechanisms underlying the high and stable values of both relative permittivity and resistivity that are characteristic of BaTiO3-Bi(M)O3 dielectrics as well as the processing challenges and opportunities associated with these materials

The three-dimensional structure of Saturn's E ring

Saturn's diffuse E ring consists of many tiny (micron and sub-micron) grains of water ice distributed between the orbits of Mimas and Titan. Various gravitational and non-gravitational forces perturb these particles' orbits, causing the ring's local particle density to vary noticeably with distance from the planet, height above the ring-plane, hour angle and time. Using remote-sensing data obtained by the Cassini spacecraft in 2005 and 2006, we investigate the E-ring's three-dimensional structure during a time when the Sun illuminated the rings from the south at high elevation angles (> 15 degrees). These observations show that the ring's vertical thickness grows with distance from Enceladus' orbit and its peak brightness density shifts from south to north of Saturn's equator plane with increasing distance from the planet. These data also reveal a localized depletion in particle density near Saturn's equatorial plane around Enceladus' semi-major axis. Finally, variations are detected in the radial brightness profile and the vertical thickness of the ring as a function of longitude relative to the Sun. Possible physical mechanisms and processes that may be responsible for some of these structures include solar radiation pressure, variations in the ambient plasma, and electromagnetic perturbations associated with Saturn's shadow.Comment: 42 Pages, 13 Figures, modified to include minor proof correction