Exact two-qubit universal quantum circuit

We provide an analytic way to implement any arbitrary two-qubit unitary operation, given an entangling two-qubit gate together with local gates. This is shown to provide explicit construction of a universal quantum circuit that exactly simulates arbitrary two-qubit operations in SU(4). Each block in this circuit is given in a closed form solution. We also provide a uniform upper bound of the applications of the given entangling gates, and find that exactly half of all the Controlled-Unitary gates satisfy the same upper bound as the CNOT gate. These results allow for the efficient implementation of operations in SU(4) required for both quantum computation and quantum simulation.Comment: 5 page

Evaluation of Overall Survival (OS) and Event-Free Survival (EFS) of paediatric sarcoma patients at a single institution

Aims: To evaluate OS and EFS of paediatric sarcoma patients with an interest in comparing metastatic cases with non-metastatic cases, and compiling statistics on treatment methods. Methods: Information was obtained from patient notes in the Schiehallion ward. These contained information about diagnosis, treatment, prognostic indicators, and outcomes for each patient. Results: 56 patients, 2001-2008. Osteosarcoma: 11 patients, 7♂, 4♀; age range: 4-16; = 10; OS = 64%, EFS = 55%; Primary site of disease: Femur (47%), Tibia (41%), Humerus (5.5%), Scapula (5.5%), Other (1%); Metastatic Rate = 27% (OS = 0%). Ewing’s sarcoma: 24 patients, 10♂, 14♀; age range: 1-16, = 12; OS = 71%, EFS = 58%; Primary site of disease: Pelvis (29%), Femur (22%), Paraspinal (16%), Chest Wall (10%), Tibia (10%), Other (13%); Metastatic Rate = 21% (OS = 40%; EFS = 40%); Alveolar rhabdomyosarcoma: 10 patients; OS= 80%, EFS = 60%; Metastatic Rate = 20% (OS = 100%; EFS = 100%). Embryonal rhabdomyosarcoma: 11 patients; OS = 73%, EFS = 73%; Metastatic Rate = 0%. Conclusions: Our results reflect access to an experienced and innovative paediatric sarcoma service with close links to a national Sarcoma MDT. The data falls in line with other studies in terms of age of onset, location of primary tumour, metastatic rate, site of metastases, and prognosis for all cancer types. Limb salvage surgery is greatly favoured over amputation for both osteosarcoma and Ewing’s sarcoma. Females have a more favourable prognosis in osteosarcoma and a slightly poorer prognosis in Ewing’s sarcoma. Yorkhill’s overall survival rates are currently better than the UK-wide statistic for three of the four tumours examined.</p

Anisotropic Local Stress and Particle Hopping in a Deeply Supercooled Liquid

The origin of the microscopic motions that lead to stress relaxation in deeply supercooled liquid remains unclear. We show that in such a liquid the stress relaxation is locally anisotropic which can serve as the driving force for the hopping of the system on its free energy surface. However, not all hopping are equally effective in relaxing the local stress, suggesting that diffusion can decouple from viscosity even at local level. On the other hand, orientational relaxation is found to be always coupled to stress relaxation.Comment: 4 pages, 3 figure

Computer Simulation Study of the Phase Behavior and Structural Relaxation in a Gel-Former Modeled by Three Body Interactions

We report a computer simulation study of a model gel-former obtained by modifying the three-body interactions of the Stillinger-Weber potential for silicon. This modification reduces the average coordination number and consequently shifts the liquid-gas phase coexistence curve to low densities, thus facilitating the formation of gels without phase separation. At low temperatures and densities, the structure of the system is characterized by the presence of long linear chains interconnected by a small number of three coordinated junctions at random locations. At small wave-vectors the static structure factor shows a non-monotonic dependence on temperature, a behavior which is due to the competition between the percolation transition of the particles and the stiffening of the formed chains. We compare in detail the relaxation dynamics of the system as obtained from molecular dynamics with the one obtained from Monte Carlo dynamics. We find that the bond correlation function displays stretched exponential behavior at moderately low temperatures and densities, but exponential relaxation at low temperatures. The bond lifetime shows an Arrhenius behavior, independent of the microscopic dynamics. For the molecular dynamics at low temperatures, the mean squared displacement and the (coherent and incoherent) intermediate scattering function display at intermediate times a dynamics with ballistic character and we show that this leads to compressed exponential relaxation. For the Monte Carlo dynamics we find always an exponential or stretched exponential relaxation. Thus we conclude that the compressed exponential relaxation observed in experiments is due to the out-of-equilibrium dynamics

Energy landscape of a Lennard-Jones liquid: Statistics of stationary points

Molecular dynamics simulations are used to generate an ensemble of saddles of the potential energy of a Lennard-Jones liquid. Classifying all extrema by their potential energy u and number of unstable directions k, a well defined relation k(u) is revealed. The degree of instability of typical stationary points vanishes at a threshold potential energy, which lies above the energy of the lowest glassy minima of the system. The energies of the inherent states, as obtained by the Stillinger-Weber method, approach the threshold energy at a temperature close to the mode-coupling transition temperature Tc.Comment: 4 RevTeX pages, 6 eps figures. Revised versio

Alignments of the Dominant Galaxies in Poor Clusters

We have examined the orientations of brightest cluster galaxies (BCGs) in poor MKW and AWM clusters and find that, like their counterparts in richer Abell clusters, poor cluster BCGs exhibit a strong propensity to be aligned with the principal axes of their host clusters as well as the surrounding distribution of nearby (< 20/h Mpc) Abell clusters. The processes responsible for dominant galaxy alignments are therefore independent of cluster richness. We argue that these alignments most likely arise from anisotropic infall of material into clusters along large-scale filaments.Comment: 8 pages, 5 figure

Liquid Limits: The Glass Transition and Liquid-Gas Spinodal Boundaries of Metastable Liquids

The liquid-gas spinodal and the glass transition define ultimate boundaries beyond which substances cannot exist as (stable or metastable) liquids. The relation between these limits is analyzed {\it via} computer simulations of a model liquid. The results obtained indicate that the liquid - gas spinodal and the glass transition lines intersect at a finite temperature, implying a glass - gas mechanical instability locus at low temperatures. The glass transition lines obtained by thermodynamic and dynamic criteria agree very well with each other.Comment: 5 pages, 4 figures, to appear in Phys. Rev. Let

Impurity mediated mechanism of photorefractive effect in BaTiO<SUB>3</SUB>: a combination of Sangster and piezoelectric effects

An impurity mediated mechanism of photorefractive effect in BaTiO3 is proposed. The photoinduced changes in the relative concentration of Fe3+ in BaTiO3 results in an electro-optic coupling through a combination of the Sangster and piezoelectric effects. This is based on the examination of the extensive results on the EPR of Fe3+ in the BaTiO3 lattice. This model explains the improved photorefractive behavior of BaTiO3 on doping with Co2+