Efficient Cluster Algorithm for Spin Glasses in Any Space Dimension

Spin systems with frustration and disorder are notoriously difficult to study both analytically and numerically. While the simulation of ferromagnetic statistical mechanical models benefits greatly from cluster algorithms, these accelerated dynamics methods remain elusive for generic spin-glass-like systems. Here we present a cluster algorithm for Ising spin glasses that works in any space dimension and speeds up thermalization by at least one order of magnitude at temperatures where thermalization is typically difficult. Our isoenergetic cluster moves are based on the Houdayer cluster algorithm for two-dimensional spin glasses and lead to a speedup over conventional state-of-the-art methods that increases with the system size. We illustrate the benefits of the isoenergetic cluster moves in two and three space dimensions, as well as the nonplanar chimera topology found in the D-Wave Inc.~quantum annealing machine.Comment: 5 pages, 4 figure

Best-case performance of quantum annealers on native spin-glass benchmarks: How chaos can affect success probabilities

Recent tests performed on the D-Wave Two quantum annealer have revealed no clear evidence of speedup over conventional silicon-based technologies. Here, we present results from classical parallel-tempering Monte Carlo simulations combined with isoenergetic cluster moves of the archetypal benchmark problem-an Ising spin glass-on the native chip topology. Using realistic uncorrelated noise models for the D-Wave Two quantum annealer, we study the best-case resilience, i.e., the probability that the ground-state configuration is not affected by random fields and random-bond fluctuations found on the chip. We thus compute classical upper-bound success probabilities for different types of disorder used in the benchmarks and predict that an increase in the number of qubits will require either error correction schemes or a drastic reduction of the intrinsic noise found in these devices. We outline strategies to develop robust, as well as hard benchmarks for quantum annealing devices, as well as any other computing paradigm affected by noise.Comment: 8 pages, 5 figure

Generation of Circular Polarization of the Cosmic Microwave Background

The standard cosmological model, which includes only Compton scattering photon interactions at energy scales near recombination, results in zero primordial circular polarization of the cosmic microwave background. In this paper we consider a particular renormalizable and gauge-invariant standard model extension coupling photons to an external vector field via a Chern-Simons term, which arises as a radiative correction if gravitational torsion couples to fermions. We compute the transport equations for polarized photons from a Boltzmann-like equation, showing that such a coupling will source circular polarization of the microwave background. For the particular coupling considered here, the circular polarization effect is always negligible compared to the rotation of the linear polarization orientation, also derived using the same formalism. We note the possibility that limits on microwave background circular polarization may probe other photon interactions and related fundamental effects such as violations of Lorentz invariance.Comment: 20 pages. Revised version includes an explicit calculation of gauge invariance. Text reorganized to improve clarity, and references adde

Seeking Quantum Speedup Through Spin Glasses: The Good, the Bad, and the Ugly

There has been considerable progress in the design and construction of quantum annealing devices. However, a conclusive detection of quantum speedup over traditional silicon-based machines remains elusive, despite multiple careful studies. In this work we outline strategies to design hard tunable benchmark instances based on insights from the study of spin glasses - the archetypal random benchmark problem for novel algorithms and optimization devices. We propose to complement head-to-head scaling studies that compare quantum annealing machines to state-of-the-art classical codes with an approach that compares the performance of different algorithms and/or computing architectures on different classes of computationally hard tunable spin-glass instances. The advantage of such an approach lies in having to only compare the performance hit felt by a given algorithm and/or architecture when the instance complexity is increased. Furthermore, we propose a methodology that might not directly translate into the detection of quantum speedup, but might elucidate whether quantum annealing has a "`quantum advantage" over corresponding classical algorithms like simulated annealing. Our results on a 496 qubit D-Wave Two quantum annealing device are compared to recently-used state-of-the-art thermal simulated annealing codes.Comment: 14 pages, 8 figures, 3 tables, way too many reference

Observation of Muon Neutrino Disappearance with the MINOS Detectors in the NuMI Neutrino Beam

This Letter reports results from the MINOS experiment based on its initial exposure to neutrinos from the Fermilab NuMI beam. The rates and energy spectra of charged current ν_μ interactions are compared in two detectors located along the beam axis at distances of 1 and 735 km. With 1.27×10^(20) 120 GeV protons incident on the NuMI target, 215 events with energies below 30 GeV are observed at the Far Detector, compared to an expectation of 336±14 events. The data are consistent with ν_μ disappearance via oscillations with Δm_(32)^2|=2.74_(-0.26)^(+0.44)×10^(-3)  eV^2 and sin^2(2θ_(23))>0.87 (68% C.L.)

Additional Dimensions to the Study of Funnels in Combinatorial Landscapes

The global structure of travelling salesman's fitness landscapes has recently revealed the presence of multiple `funnels'. This implies that local optima are organised into several clusters, so that a particular local optimum largely belongs to a particular funnel. Such a global structure can increase search difficulty, especially, when the global optimum is located in a deep, narrow funnel. Our study brings more precision (and dimensions) to the notion of funnels with a data-driven approach using Local Optima Networks and the Chained Lin-Kernighan heuristic. We start by exploring the funnel 'floors', characterising them using the notion of communities from complex networks. We then analyse the more complex funnel 'basins'. Since their depth is relevant to search, we visualise them in 3D. Our study, across a set of TSP instances, reveals a multi-funnel structure in most of them. However, the specific topology varies across instances and relates to search difficulty. Finally, including a stronger perturbation into Chained Lin-Kernighan proved to smooth the funnel structure, reducing the number of funnels and enlarging the valley leading to global optima