Practical engineering of hard spin-glass instances

Recent technological developments in the field of experimental quantum annealing have made prototypical annealing optimizers with hundreds of qubits commercially available. The experimental demonstration of a quantum speedup for optimization problems has since then become a coveted, albeit elusive goal. Recent studies have shown that the so far inconclusive results, regarding a quantum enhancement, may have been partly due to the benchmark problems used being unsuitable. In particular, these problems had inherently too simple a structure, allowing for both traditional resources and quantum annealers to solve them with no special efforts. The need therefore has arisen for the generation of harder benchmarks which would hopefully possess the discriminative power to separate classical scaling of performance with size from quantum. We introduce here a practical technique for the engineering of extremely hard spin-glass Ising-type problem instances that does not require "cherry picking" from large ensembles of randomly generated instances. We accomplish this by treating the generation of hard optimization problems itself as an optimization problem, for which we offer a heuristic algorithm that solves it. We demonstrate the genuine thermal hardness of our generated instances by examining them thermodynamically and analyzing their energy landscapes, as well as by testing the performance of various state-of-the-art algorithms on them. We argue that a proper characterization of the generated instances offers a practical, efficient way to properly benchmark experimental quantum annealers, as well as any other optimization algorithm.

Energy estimation of cosmic rays with the Engineering Radio Array of the Pierre Auger Observatory

The Auger Engineering Radio Array (AERA) is part of the Pierre Auger Observatory and is used to detect the radio emission of cosmic-ray air showers. These observations are compared to the data of the surface detector stations of the Observatory, which provide well-calibrated information on the cosmic-ray energies and arrival directions. The response of the radio stations in the 30-80 MHz regime has been thoroughly calibrated to enable the reconstruction of the incoming electric field. For the latter, the energy deposit per area is determined from the radio pulses at each observer position and is interpolated using a two-dimensional function that takes into account signal asymmetries due to interference between the geomagnetic and charge-excess emission components. The spatial integral over the signal distribution gives a direct measurement of the energy transferred from the primary cosmic ray into radio emission in the AERA frequency range. We measure 15.8 MeV of radiation energy for a 1 EeV air shower arriving perpendicularly to the geomagnetic field. This radiation energy-corrected for geometrical effects-is used as a cosmic-ray energy estimator. Performing an absolute energy calibration against the surface-detector information, we observe that this radio-energy estimator scales quadratically with the cosmic-ray energy as expected for coherent emission. We find an energy resolution of the radio reconstruction of 22% for the data set and 17% for a high-quality subset containing only events with at least five radio stations with signal.