Limitations of Quantum Simulation Examined by Simulating a Pairing Hamiltonian using Nuclear Magnetic Resonance

Quantum simulation uses a well-known quantum system to predict the behavior of another quantum system. Certain limitations in this technique arise, however, when applied to specific problems, as we demonstrate with a theoretical and experimental study of an algorithm to find the low-lying spectrum of a Hamiltonian. While the number of elementary quantum gates does scale polynomially with the size of the system, it increases inversely to the desired error bound $\epsilon$. Making such simulations robust to decoherence using fault-tolerance constructs requires an additional factor of $1/ \epsilon$ gates. These constraints are illustrated by using a three qubit nuclear magnetic resonance system to simulate a pairing Hamiltonian, following the algorithm proposed by Wu, Byrd, and Lidar.Comment: 6 pages, 2 eps figure

Widespread late Cenozoic increase in erosion rates across the interior of eastern Tibet constrained by detrital low-temperature thermochronometry

New detrital low-temperature thermochronometry provides estimates of long-term erosion rates and the timing of initiation of river incision from across the interior of the Tibetan Plateau. We use the erosion history of this region to evaluate proposed models of orogenic development as well as regional climatic events. Erosion histories of the externally drained portion of the east-central Tibetan Plateau are recorded in modern river sands from major rivers across a transect that spans >750 km and covers a region with no published thermochronometric ages. Individual grains from eight catchments were analyzed for apatite (U-Th)/He and fission track thermochronometry. A wide distribution in ages that, in most cases, spans the entire Cenozoic and Late Mesozoic eras requires a long period of slow or no erosion with a relative increase in erosion rate toward the present. We apply a recently developed methodology for inversion of detrital thermochronometric data for three specified erosion scenarios: constant erosion rate, two-stage erosion history, and three-stage erosion history. Modeling results suggest that rates increase by at least an order of magnitude between 11 and 4 Ma following a period of slow erosion across the studied catchments. Synchroneity in accelerated erosion across the whole of the Tibetan Plateau rather than a spatial or temporal progression challenges the widely held notion that the plateau evolved as a steep, northward-propagating topographic front, or that south to north precipitation gradients exert a primary control on erosion rates. Instead, we suggest that accelerated river incision late in the orogen's history relates to regional-scale uplift that occurred in concert with eastern expansion of the plateau

Sierra Nevada river incision from apatite ^4He/^3He thermochronometry

Published erosion rates suggest that acceleration of river incision beginning some time before 3 Ma initiated formation of the deep river canyons in the southern Sierra Nevada. Such acceleration signals a change in erosional efficacy but its initial timing is poorly constrained. Increased erosional efficacy caused by elevation gain is predicted by scenarios such as block faulting, mantle lithosphere removal, and passage of a slab window. The timing and magnitude of elevation gain may be used to distinguish between competing mechanisms. As in many landscapes, the small magnitude ( < 1.5 km) and antiquity of river incision in the Sierra Nevada make the timing of landscape evolution and its relation to tectonic scenarios inaccessible by most methods. Until recently, we have lacked the potential to 'see' erosional events that exhume leas than several kilometers and that occur over several to several tens of millions of years

Class-based probability estimation using a semantic hierarchy

This article concerns the estimation of a particular kind of probability, namely, the probability of a noun sense appearing as a particular argument of a predicate. In order to overcome the accompanying sparse-data problem, the proposal here is to define the probabilities in terms of senses from a semantic hierarchy and exploit the fact that the senses can be grouped into classes consisting of semantically similar senses. There is a particular focus on the problem of how to determine a suitable class for a given sense, or, alternatively, how to determine a suitable level of generalization in the hierarchy. A procedure is developed that uses a chi-square test to determine a suitable level of generalization. In order to test the performance of the estimation method, a pseudo-disambiguation task is used, together with two alternative estimation methods. Each method uses a different generalization procedure; the first alternative uses the minimum description length principle, and the second uses Resnik's measure of selectional preference. In addition, the performance of our method is investigated using both the standard Pearson chi-square statistic and the log-likelihood chi-square statistic

Resource Requirements for Fault-Tolerant Quantum Simulation: The Transverse Ising Model Ground State

We estimate the resource requirements, the total number of physical qubits and computational time, required to compute the ground state energy of a 1-D quantum Transverse Ising Model (TIM) of N spin-1/2 particles, as a function of the system size and the numerical precision. This estimate is based on analyzing the impact of fault-tolerant quantum error correction in the context of the Quantum Logic Array (QLA) architecture. Our results show that due to the exponential scaling of the computational time with the desired precision of the energy, significant amount of error correciton is required to implement the TIM problem. Comparison of our results to the resource requirements for a fault-tolerant implementation of Shor's quantum factoring algorithm reveals that the required logical qubit reliability is similar for both the TIM problem and the factoring problem.Comment: 19 pages, 8 figure

Impacts of the Extended-Weight Coal Haul Road System

The Extended-Weight Coal Haul Road System, created by the Kentucky Legislature in 1986, consists of all roads which carry over 50,000 tons of coal in a calendar year. Trucks hauling coal on this system are authorized to exceed normal weight limits through the payment of an annual decal fee. A research study was initiated in July of 1992 to analyze the impacts of the extended-weight system. Analyses in this report are based on the following: historical data on coal production and transportation: data from coal decal applications; interviews of legislators. transportation officials. coal company representatives. and coal trucking representatives: newspaper articles; vehicle classification data: analyses of pavement costs: pavement rideability data; and accident data. Primary conclusions include: I) The extended-weight 5)\u27Stem has apparently been somewhat successful in accomplishing the objective of enhancing the competitiveness and economic viability of the Kentucky coal industry; 2) Overall accident rates did not increase as a result of implementation of the extended-weight system. but the fatal accident injury rates were significantly higher on the extended-weight system and for trucks operating with the coal decal; 3) Advance-warning flashers have been evaluated and recommended as a means of reducing intersection accidents involving heavy/coal trucks; 4) The coal-decal fee structure results in a net annual loss in Road Fund revenue of approximately S2 million; 5) Forty percent of revenue from decal fees are allocated to counties even though county-maintained roads comprise only eight percent of the extended-weight system; 6) Heavier weights of coal-decal trucks add approximately $9 million annually to the pavement overlay costs; 7) Road users throughout the state are subsidizing the movement of Kentucky coal by participating in the cost of maintaining and improving tile highway system; and 8) Possibly reflecting the increased funding of extended-weight roads., the rideability index. has risen to a level above the statewide average. The primary recommendation was that the extended-weight system should evolve into a comprehensive trucking network. A Resource and Commodity Highway System was evaluated as a separate study and found to be a feasible and desirable means of providing a trucking highway network that is fully compatible with the dimensions and characteristics of large trucks

Benzylic C-H functionalisation by [Et3SiH + KOtBu] leads to radical rearrangements in o-tolylaryl ethers, amines

Reaction of Et 3SiH+KO tBu with diaryl ethers, sulfides and amines that feature an ortho alkyl group leads to rearrangement products. The rearrangements arise from formation of benzyl radicals, likely formed through hydrogen atom abstraction by triethylsilyl radicals. The rearrangements involve cyclisation of the benzyl radical onto the partner arene, which, from computation, is the rate determining step. In the case of diaryl ethers, Truce-Smiles rearrangements arise from radical cyclisations to form 5-membered rings, but for diarylamines, cyclisations to form dihydroacridines are observed. (Figure presented.)

Laser ablation loading of a surface-electrode ion trap

We demonstrate loading by laser ablation of $^{88}$Sr$^+$ ions into a mm-scale surface-electrode ion trap. The laser used for ablation is a pulsed, frequency-tripled Nd:YAG with pulse energies of 1-10 mJ and durations of 3-5 ns. An additional laser is not required to photoionize the ablated material. The efficiency and lifetime of several candidate materials for the laser ablation target are characterized by measuring the trapped ion fluorescence signal for a number of consecutive loads. Additionally, laser ablation is used to load traps with a trap depth (40 meV) below where electron impact ionization loading is typically successful ($\gtrsim$ 500 meV).Comment: 4 pages, 4 figure