Parallelism for Quantum Computation with Qudits

Robust quantum computation with d-level quantum systems (qudits) poses two requirements: fast, parallel quantum gates and high fidelity two-qudit gates. We first describe how to implement parallel single qudit operations. It is by now well known that any single-qudit unitary can be decomposed into a sequence of Givens rotations on two-dimensional subspaces of the qudit state space. Using a coupling graph to represent physically allowed couplings between pairs of qudit states, we then show that the logical depth of the parallel gate sequence is equal to the height of an associated tree. The implementation of a given unitary can then optimize the tradeoff between gate time and resources used. These ideas are illustrated for qudits encoded in the ground hyperfine states of the atomic alkalies $^{87}$Rb and $^{133}$Cs. Second, we provide a protocol for implementing parallelized non-local two-qudit gates using the assistance of entangled qubit pairs. Because the entangled qubits can be prepared non-deterministically, this offers the possibility of high fidelity two-qudit gates.Comment: 9 pages, 3 figure

Group finding in the stellar halo using M-giants in 2MASS: An extended view of the Pisces Overdensity?

A density based hierarchical group-finding algorithm is used to identify stellar halo structures in a catalog of M-giants from the Two Micron All Sky Survey (2MASS). The intrinsic brightness of M-giant stars means that this catalog probes deep into the halo where substructures are expected to be abundant and easy to detect. Our analysis reveals 16 structures at high Galactic latitude (greater than 15 degree), of which 10 have been previously identified. Among the six new structures two could plausibly be due to masks applied to the data, one is associated with a strong extinction region and one is probably a part of the Monoceros ring. Another one originates at low latitudes, suggesting some contamination from disk stars, but also shows protrusions extending to high latitudes, implying that it could be a real feature in the stellar halo. The last remaining structure is free from the defects discussed above and hence is very likely a satellite remnant. Although the extinction in the direction of the structure is very low, the structure does match a low temperature feature in the dust maps. While this casts some doubt on its origin, the low temperature feature could plausibly be due to real dust in the structure itself. The angular position and distance of this structure encompass the Pisces overdensity traced by RR Lyraes in Stripe 82 of the Sloan Digital Sky Survey (SDSS). However, the 2MASS M-giants indicate that the structure is much more extended than what is visible with the SDSS, with the point of peak density lying just outside Stripe 82. The morphology of the structure is more like a cloud than a stream and reminiscent of that seen in simulations of satellites disrupting along highly eccentric orbits.Comment: Accepted for publication in Ap

3D stellar kinematics at the Galactic center: measuring the nuclear star cluster spatial density profile, black hole mass, and distance

We present 3D kinematic observations of stars within the central 0.5 pc of the Milky Way nuclear star cluster using adaptive optics imaging and spectroscopy from the Keck telescopes. Recent observations have shown that the cluster has a shallower surface density profile than expected for a dynamically relaxed cusp, leading to important implications for its formation and evolution. However, the true three dimensional profile of the cluster is unknown due to the difficulty in de-projecting the stellar number counts. Here, we use spherical Jeans modeling of individual proper motions and radial velocities to constrain for the first time, the de-projected spatial density profile, cluster velocity anisotropy, black hole mass ($M_\mathrm{BH}$), and distance to the Galactic center ($R_0$) simultaneously. We find that the inner stellar density profile of the late-type stars, $\rho(r)\propto r^{-\gamma}$ to have a power law slope $\gamma=0.05_{-0.60}^{+0.29}$, much more shallow than the frequently assumed Bahcall $\&$ Wolf slope of $\gamma=7/4$. The measured slope will significantly affect dynamical predictions involving the cluster, such as the dynamical friction time scale. The cluster core must be larger than 0.5 pc, which disfavors some scenarios for its origin. Our measurement of $M_\mathrm{BH}=5.76_{-1.26}^{+1.76}\times10^6$ $M_\odot$ and $R_0=8.92_{-0.55}^{+0.58}$ kpc is consistent with that derived from stellar orbits within 1$^{\prime\prime}$ of Sgr A*. When combined with the orbit of S0-2, the uncertainty on $R_0$ is reduced by 30% ($8.46_{-0.38}^{+0.42}$ kpc). We suggest that the MW NSC can be used in the future in combination with stellar orbits to significantly improve constraints on $R_0$.Comment: 7 pages, 3 figures, 2 tables, ApJL accepte

Angular Alignment Testing of Laser Mirror Mounts Under Temperature Cycling

A number of commercial and custom-built laser mirror mounts were tested for angular alignment sensitivity during temperature cycling from room temperature (20 C) to 40 C. A Nd:YAG laser beam was reflected off a mirror that was held by the mount under test and was directed to a position-sensitive detector. Horizontal and vertical movement of the reflected beam was recorded, and the angular movement, as a function of temperature (coefficient of thermal tilt (CTT)) was calculated from these data. In addition, the amount of hysteresis in the movement after cycling from room temperature to 40 C and back was determined. All commercial mounts showed greater angular movement than the simpler National Aeronautics and Space Administration Lidar Atmospheric Sensing Experiment (NASA LASE) custom mirror mounts

Tracing Galaxy Formation with Stellar Halos I: Methods

If the favored hierarchical cosmological model is correct, then the Milky Way system should have accreted ~100-200 luminous satellite galaxies in the past \~12 Gyr. We model this process using a hybrid semi-analytic plus N-body approach which distinguishes explicitly between the evolution of light and dark matter in accreted satellites. This distinction is essential to our ability to produce a realistic stellar halo, with mass and density profile much like that of our own Galaxy, and a surviving satellite population that matches the observed number counts and structural parameter distributions of the satellite galaxies of the Milky Way. Our model stellar halos have density profiles which typically drop off with radius faster than those of the dark matter. They are assembled from the inside out, with the majority of mass (~80%) coming from the \~15 most massive accretion events. The satellites that contribute to the stellar halo have median accretion times of ~9 Gyr in the past, while surviving satellite systems have median accretion times of ~5 Gyr in the past. This implies that stars associated with the inner halo should be quite different chemically from stars in surviving satellites and also from stars in the outer halo or those liberated in recent disruption events. We briefly discuss the expected spatial structure and phase space structure for halos formed in this manner. Searches for this type of structure offer a direct test of whether cosmology is indeed hierarchical on small scales.Comment: 22 pages, 16 figures, submitted to Ap

Quantum circuits with uniformly controlled one-qubit gates

Uniformly controlled one-qubit gates are quantum gates which can be represented as direct sums of two-dimensional unitary operators acting on a single qubit. We present a quantum gate array which implements any n-qubit gate of this type using at most 2^{n-1} - 1 controlled-NOT gates, 2^{n-1} one-qubit gates and a single diagonal n-qubit gate. The circuit is based on the so-called quantum multiplexor, for which we provide a modified construction. We illustrate the versatility of these gates by applying them to the decomposition of a general n-qubit gate and a local state preparation procedure. Moreover, we study their implementation using only nearest-neighbor gates. We give upper bounds for the one-qubit and controlled-NOT gate counts for all the aforementioned applications. In all four cases, the proposed circuit topologies either improve on or achieve the previously reported upper bounds for the gate counts. Thus, they provide the most efficient method for general gate decompositions currently known.Comment: 8 pages, 10 figures. v2 has simpler notation and sharpens some result

Using scenarios to explore UK upland futures

Uplands around the world are facing significant social, economic and environmental changes, and decision-makers need to better understand what the future may hold if they are to adapt and maintain upland goods and services. This paper draws together all major research comprising eight studies that have used scenarios to describe possible futures for UK uplands. The paper evaluates which scenarios are perceived by stakeholders to be most likely and desirable, and assesses the benefits and drawbacks of the scenario methods used in UK uplands to date. Stakeholders agreed that the most desirable and likely scenario would be a continuation of hill farming (albeit at reduced levels) based on cross-compliance with environmental measures. The least desirable scenario is a withdrawal of government financial support for hill farming. Although this was deemed by stakeholders to be the least likely scenario, the loss of government support warrants close attention due to its potential implications for the local economy. Stakeholders noted that the environmental implications of this scenario are much less clear-cut. As such, there is an urgent need to understand the full implications of this scenario, so that upland stakeholders can adequately prepare, and policy-makers can better evaluate the likely implications of different policy options. The paper concludes that in future, upland scenario research needs to: (1) better integrate in-depth and representative participation from stakeholders during both scenario development and evaluation; and (2) make more effective use of visualisation techniques and simulation models

Hybrid Reactions to Phytotoxic Effects of The Corn Herbicide, Eradicane Extra

Although corn hybrids are primarily evaluated only for yield performance in the Kentucky Hybrid Corn Performance Test, the 1984 test (Poneleit and Evans, 1985) provided a unique opportunity to evaluate hybrid reactions to an unusual hybrid-herbicide interacting Of seven non-virus test locations, four were treated with Eradicane Extra or Eradicane for weed control. At the Princeton location Eradicane Extra, at 8 pints/acre, was used for johnsongrass rhizome suppression and seedling control. In late July, a routine check revealed that numerous plants had unusual appearances that were similar to abnormalities reported earlier as caused by Eptam and Eradicane (Poneleit et aI, 1975). Subsequent observations confirmed the severity of damage at the Princeton test site and reports of similar hybrid reactions from farmer fields prompted the collection of apparent herbicide damage data from the replicated Princeton test. The other performance test sites where Eradicane Extra or Eradicane was applied did not show significant plant abnormalities. Apparently the appearance of phytotoxic effects owing to Eradicane Extra are sporadic and strongly influenced by specific interaction of environmental factors. It was postulated that this injury occurrence in 1984 was the result of excessive rainfall four to six weeks after planting. Dichlormid (safener) is very water soluble and could have been leached away from the corn roots, and thus not available to protect the corn from EPTC