Diabatic quantum and classical annealing of the Sherrington-Kirkpatrick model

Quantum annealing is a contender to solve combinatorial optimization problems based on quantum dynamics. While significant efforts have been undertaken to investigate the quality of the solutions and the required runtimes, much less attention has been paid to understanding the dynamics of quantum annealing and the process leading to the solution during the sweep itself. In this comprehensive study, we investigate various aspects of the quantum annealing dynamics using different approaches. We perform quantum annealing, simulated quantum annealing, and classical annealing on several hundred instances of the Sherrington-Kirkpatrick model with intermediate system sizes up to 22 spins using numerical simulations. We observe qualitative differences between the quantum and classical methods, in particular at intermediate times, where a peak in the fidelity, also known as diabatic bump, appears for hard instances. Furthermore, we investigate the two-point correlation functions, which feature differences at intermediate times as well. At short times, however, the methods are similar again, which can be explained by relating the short-time expansion of quantum annealing to a high-temperature expansion, thus allowing in principle to find the classical solution already at short times, albeit at prohibitive sampling cost.Comment: revised version: 22 pages, 11 figure

Hydrodynamic Chromatography Coupled with Single Particle-Inductively Coupled Plasma Mass Spectrometry for Investigating Nanoparticles Agglomerates

Studying the environmental fate of engineered or natural colloids requires efficient methods for measuring their size and quantifying them in the environment. For example, an ideal method should maintain its correctness, accuracy, reproducibility, and robustness when applied to samples contained in complex matrixes and distinguish the target particles from the natural colloidal background signals. Since it is expected that a large portion of nanoparticles will form homo- or heteroagglomerates when released into environmental media, it is necessary to differentiate agglomerates from primary particles. At present, most sizing techniques do not fulfill these requirements. In this study, we used online coupling of two promising complementary sizing techniques: hydrodynamic chromatography (HDC) and single-particle ICPMS analysis to analyze gold nanoparticles agglomerated under controlled conditions. We used the single-particle mode of the ICPMS detector to detect single particles eluted from an HDC-column and determine a mass and an effective diameter for each particle using a double calibration approach. The average agglomerate relative density and fractal dimension were calculated using these data and used to follow the morphological evolution of agglomerates over time during the agglomeration process. The results demonstrate the ability of HDC coupled to single-particle analysis to identify and characterize nanoparticle homoagglomerates and is a very promising technique for the analysis of colloids in complex media