Completeness of the classical 2D Ising model and universal quantum computation

We prove that the 2D Ising model is complete in the sense that the partition function of any classical q-state spin model (on an arbitrary graph) can be expressed as a special instance of the partition function of a 2D Ising model with complex inhomogeneous couplings and external fields. In the case where the original model is an Ising or Potts-type model, we find that the corresponding 2D square lattice requires only polynomially more spins w.r.t the original one, and we give a constructive method to map such models to the 2D Ising model. For more general models the overhead in system size may be exponential. The results are established by connecting classical spin models with measurement-based quantum computation and invoking the universality of the 2D cluster states.Comment: 4 pages, 1 figure. Minor change

Analysis of a continuous-variable quadripartite cluster state from a single optical parametric oscillator

We examine the feasibility of generating continuous-variable multipartite entanglement in an intra-cavity quadruply concurrent downconversion scheme that has been proposed for the generation of cluster states by Menicucci \textit{et al.} [Physical Review Letters \textbf{101}, 130501 (2008)]. By calculating optimized versions of the van Loock-Furusawa correlations we demonstrate genuine quadripartite entanglement and investigate the degree of entanglement present. Above the oscillation threshold the basic cluster state geometry under consideration suffers from phase diffusion. We alleviate this problem by incorporating a small injected signal into our analysis. Finally, we investigate squeezed joint operators. While the squeezed joint operators approach zero in the undepleted regime, we find that this is not the case when we consider the full interaction Hamiltonian and the presence of a cavity. In fact, we find that the decay of these operators is minimal in a cavity, and even depletion alone inhibits cluster state formation.Comment: 26 pages, 12 figure

State-dependent, addressable subwavelength lattices with cold atoms

We discuss how adiabatic potentials can be used to create addressable lattices on a subwavelength scale, which can be used as a tool for local operations and readout within a lattice substructure, while taking advantage of the faster timescales and higher energy and temperature scales determined by the shorter lattice spacing. For alkaline-earth-like atoms with non-zero nuclear spin, these potentials can be made state dependent, for which we give specific examples with $^{171}$Yb atoms. We discuss in detail the limitations in generating the lattice potentials, in particular non-adiabatic losses, and show that the loss rates can always be made exponentially small by increasing the laser power.Comment: replaced with the published version. 23 pages, 11 figure

Direct evaluation of pure graph state entanglement

We address the question of quantifying entanglement in pure graph states. Evaluation of multipartite entanglement measures is extremely hard for most pure quantum states. In this paper we demonstrate how solving one problem in graph theory, namely the identification of maximum independent set, allows us to evaluate three multipartite entanglement measures for pure graph states. We construct the minimal linear decomposition into product states for a large group of pure graph states, allowing us to evaluate the Schmidt measure. Furthermore we show that computation of distance-like measures such as relative entropy of entanglement and geometric measure becomes tractable for these states by explicit construction of closest separable and closest product states respectively. We show how these separable states can be described using stabiliser formalism as well as PEPs-like construction. Finally we discuss the way in which introducing noise to the system can optimally destroy entanglement.Comment: 23 pages, 9 figure

Single-parameter non-adiabatic quantized charge pumping

Controlled charge pumping in an AlGaAs/GaAs gated nanowire by single-parameter modulation is studied experimentally and theoretically. Transfer of integral multiples of the elementary charge per modulation cycle is clearly demonstrated. A simple theoretical model shows that such a quantized current can be generated via loading and unloading of a dynamic quasi-bound state. It demonstrates that non-adiabatic blockade of unwanted tunnel events can obliterate the requirement of having at least two phase-shifted periodic signals to realize quantized pumping. The simple configuration without multiple pumping signals might find wide application in metrological experiments and quantum electronics.Comment: 4 pages, 4 figure

Age-Depth Stratigraphy of Pine Island Glacier Inferred from Airborne Radar and Ice-Core Chronology

Understanding the contribution of the West Antarctic Ice Sheet (WAIS) to past and future sea level has been a major scientific priority over the last three decades. In recent years, observed thinning and ice‐flow acceleration of the marine‐based Pine Island Glacier has highlighted that understanding dynamic changes is critical to predicting the long‐term stability of the WAIS. However, relatively little is known about the evolution of the catchment during the Holocene. Internal Reflecting Horizons (IRHs) provide a cumulative record of accumulation, basal melt and ice dynamics that, if dated, can be used to constrain ice‐flow models. Here, we use airborne radars to trace four spatially‐extensive IRHs deposited in the late Quaternary across the Pine Island Glacier catchment. We use the WAIS Divide ice‐core chronology to assign ages to three IRHs: 4.72 ± 0.28, 6.94 ± 0.31, and 16.50 ± 0.79 ka. We use a 1‐D model, constrained by observational and modelled accumulation rates, to produce an independent validation of our ice‐core‐derived ages and provide an age estimate for our shallowest IRH (2.31‐2.92 ka). We find that our upper three IRHs correspond to three large peaks in sulphate concentrations in the WAIS Divide ice‐core record and hypothesise that the origin of these spatially‐extensive IRHs is from past volcanic activity. The clear correspondence between our IRHs and the ones previously identified over the Weddell Sea Sector, altogether representing ∼20% of the WAIS, indicates that a unique set of stratigraphic markers spanning the Holocene exists over a large part of West Antarctica

A targeted drilling and dating campaign to identify Stone Age archaeological sites before excavation in west coast southern Africa

Here we present the results of a targeted drilling campaign that facilitated a geochronological study with coarse sampling resolution inside a new cave site, Simons Cave, on the west coast of southern Africa. A combination of radiocarbon (14C) dating and optically stimulated luminescence (OSL) dating was used as a range-finder. Results confirmed preservation of Holocene and late Pleistocene sediments up to 133 ± 35 ka, overlapping with the ages of Middle Stone Age (MSA) occupations of the broader west coast region. A subsequent, systematic test- excavation at the site then embarked on a second geochronological study with a higher sampling resolution. Ultimately, the comparative study confirmed the potential of Simons Cave as a new site for the exploration of hominin occupation through the later Pleistocene and Holocene, yet raised several issues concerning the direct comparability of information deriving from drilled sediment cores and actual archaeological excavation

Decay of Entanglement for Solid-State Qubits

We investigate the time evolution of entanglement under various models of decoherence: A general heuristic model based on local relaxation and dephasing times, and two microscopic models describing decoherence of electron spin qubits in quantum dots due to the hyperfine interaction with the nuclei. For each of the decoherence models, we investigate and compare how long the entanglement can be detected. We also introduce filtered witness operators, which extend the available detection time, and investigate this detection time for various multipartite entangled states. By comparing the time required for detection with the time required for generation and manipulation of entanglement, we estimate for a range of different entangled states how many qubits can be entangled in a one-dimensional array of electron spin qubits.Comment: 12 pages, 5 figure