Optimizing embedding-related quantum annealing parameters for reducing hardware bias

Quantum annealers have been designed to propose near-optimal solutions to NP-hard optimization problems. However, the accuracy of current annealers such as the ones of D-Wave Systems, Inc., is limited by environmental noise and hardware biases. One way to deal with these imperfections and to improve the quality of the annealing results is to apply a variety of pre-processing techniques such as spin reversal (SR), anneal offsets (AO), or chain weights (CW). Maximizing the effectiveness of these techniques involves performing optimizations over a large number of parameters, which would be too costly if needed to be done for each new problem instance. In this work, we show that the aforementioned parameter optimization can be done for an entire class of problems, given each instance uses a previously chosen fixed embedding. Specifically, in the training phase, we fix an embedding E of a complete graph onto the hardware of the annealer, and then run an optimization algorithm to tune the following set of parameter values: the set of bits to be flipped for SR, the specific qubit offsets for AO, and the distribution of chain weights, optimized over a set of training graphs randomly chosen from that class, where the graphs are embedded onto the hardware using E. In the testing phase, we estimate how well the parameters computed during the training phase work on a random selection of other graphs from that class. We investigate graph instances of varying densities for the Maximum Clique, Maximum Cut, and Graph Partitioning problems. Our results indicate that, compared to their default behavior, substantial improvements of the annealing results can be achieved by using the optimized parameters for SR, AO, and CW

Comparing Three Generations of D-Wave Quantum Annealers for Minor Embedded Combinatorial Optimization Problems

Quantum annealing is a novel type of analog computation that aims to use quantum mechanical fluctuations to search for optimal solutions of Ising problems. Quantum annealing in the Transverse Ising model, implemented on D-Wave QPUs, are available as cloud computing resources. In this article we report concise benchmarks across three generations of D-Wave quantum annealers, consisting of four different devices, for the NP-Hard combinatorial optimization problems unweighted maximum clique and unweighted maximum cut on random graphs. The Ising, or equivalently QUBO, formulation of these problems do not require auxiliary variables for order reduction, and their overall structure and weights are not highly complex, which makes these problems simple test cases to understand the sampling capability of current D-Wave quantum annealers. All-to-all minor embeddings of size $52$, with relatively uniform chain lengths, are used for a direct comparison across the Chimera, Pegasus, and Zephyr device topologies. A grid search over annealing times and the minor embedding chain strengths is performed in order to determine the level of reasonable performance for each device and problem type. Experiment metrics that are reported are approximation ratios for non-broken chain samples and chain break proportions. How fairly the quantum annealers sample optimal maximum cliques, for instances which contain multiple maximum cliques, is also quantified using entropy of the measured ground state distributions. The newest generation of quantum annealing hardware, which has a Zephyr hardware connectivity, performed the best overall with respect to approximation ratios and chain break frequencies

Why and when is pausing beneficial in quantum annealing?

Recent empirical results using quantum annealing hardware have shown that mid anneal pausing has a surprisingly beneficial impact on the probability of finding the ground state for of a variety of problems. A theoretical explanation of this phenomenon has thus far been lacking. Here we provide an analysis of pausing using a master equation framework, and derive conditions for the strategy to result in a success probability enhancement. The conditions, which we identify through numerical simulations and then prove to be sufficient, require that relative to the pause duration the relaxation rate is large and decreasing right after crossing the minimum gap, small and decreasing at the end of the anneal, and is also cumulatively small over this interval, in the sense that the system does not thermally equilibrate. This establishes that the observed success probability enhancement can be attributed to incomplete quantum relaxation, i.e., is a form of beneficial non-equilibrium coupling to the environment.Comment: 20 pages, 11 figure

Extended Ensemble Monte Carlo

``Extended Ensemble Monte Carlo''is a generic term that indicates a set of algorithms which are now popular in a variety of fields in physics and statistical information processing. Exchange Monte Carlo (Metropolis-Coupled Chain, Parallel Tempering), Simulated Tempering (Expanded Ensemble Monte Carlo), and Multicanonical Monte Carlo (Adaptive Umbrella Sampling) are typical members of this family. Here we give a cross-disciplinary survey of these algorithms with special emphasis on the great flexibility of the underlying idea. In Sec.2, we discuss the background of Extended Ensemble Monte Carlo. In Sec.3, 4 and 5, three types of the algorithms, i.e., Exchange Monte Carlo, Simulated Tempering, Multicanonical Monte Carlo are introduced. In Sec.6, we give an introduction to Replica Monte Carlo algorithm by Swendsen and Wang. Strategies for the construction of special-purpose extended ensembles are discussed in Sec.7. We stress that an extension is not necessary restricted to the space of energy or temperature. Even unphysical (unrealizable) configurations can be included in the ensemble, if the resultant fast mixing of the Markov chain offsets the increasing cost of the sampling procedure. Multivariate (multi-component) extensions are also useful in many examples. In Sec.8, we give a survey on extended ensembles with a state space whose dimensionality is dynamically varying. In the appendix, we discuss advantages and disadvantages of three types of extended ensemble algorithms.Comment: Major revision that includes addition of concrete examples, references, improved introduction to Multicanonical MC, change in the order of the sections, and a number of small but important corrections. 49 pages, no figure

Heterostructured WO3–TiVO4 thin-film photocatalyst for efficient photoelectrochemical water splitting

This is the final version. Available from Elsevier via the DOI in this record. Data availability: Data associated with this study have not been deposited into a publicly available repository. Data will be made available on request to the corresponding author.Photoelectrochemical water splitting via solar irradiation has garnered significant interest due to its potential in large-scale renewable hydrogen production. Heterostructure materials have emerged as an effective strategy, demonstrating enhanced performance in photoelectrochemical water-splitting applications compared to individual photocatalysts. In this study, to augment the performance of sprayed TiVO4 thin films, a hydrothermally prepared WO3 underlayer was integrated beneath the spray pyrolised TiVO4 film. The consequent heterostructure demonstrated notable enhancements in optical, structural, microstructural attributes, and photocurrent properties. This improvement is attributed to the strategic deposition of WO3 underlayer, forming a heterostructure composite electrode. This led to a marked increase in photocurrent density for the WO3/TiVO4 photoanode, reaching a peak of 740 μA/cm2 at an applied potential of 1.23 V vs RHE, about nine-fold that of standalone TiVO4. Electrochemical impedance spectroscopy revealed a reduced semicircle for the heterostructure, indicating improved charge transfer compared to bare TiVO4. The heterostructure photoelectrode exhibited enhanced charge carrier conductivity at the interface and sustained stability over 3 h. The distinct attributes of heterostructure photoelectrode present significant opportunities for devising highly efficient sunlight-driven water splitting systems.Engineering and Physical Sciences Research Council (EPSRC)Saudi Arabia Culture Bureau in the United Kingdo

Band gap grading strategies for high efficiency kesterite based thin film solar cells

[eng] The main subject of this work focuses on the development of advanced technological strategies for bandgap profile engineering on Earth-abundant and eco-friendly kesterite thin film solar cells which potentially optimize and enhance the energy power conversion efficiency of solar cell devices. By exposing the contemporneuous world energy consumption hassles and its direct implication with the heating imbalance produced by the current greenhouse gas emissions; it is doubtlessly notified that renewable energy supplies, mainly based on thin film solar cells, and focused on sustainable materials such as ‘kesterite’ (CZTS), could successfully perform in a wide variety of energy application scenarios. This is due to its potential to be deposited on flexible substrates, its aesthetics and selective transparency for integrations in construction and automotive sectors. As well as its use in new concepts of energy portability like the Internet of Things, even enhanced when combined with its nanostructured form as a potential thermoelectric material. However, the actual kesterite thin film solar cell devices hinder the actual energy conversion efficiencies of a single absorber layer PN junction. This fact is primordially demonstrated with a theoretical numerical modeling simulation (SCAPS-1D) of first front graded bandgap profile attempts in CZTSSe. Consequently, the effect of the front sulfurization of CZTSe solar cell with a realistic experimental compositional profile is analyzed and discussed. In light of this, it possibly to demonstrate that the next generation of kesterite (and chalcopyrite) solar cells power energy conversion efficiency improvements could be remarkably enhanced with the development of novel and more strategic methodologies for collecting photon energy. In this way, the graded bandgap profiling in kesterites is proposed as a sustainable strategy to improve the utilization of the solar spectrum, through the generation of quasi-electric internal fields along the thin films, increasing the drift and diffusion lengths of minority charge and finally improving the power conversion efficiency. First of all, by developing a novel and disruptive chalcogenization process for the fabrication of CZTSSe solar cells enabling the generation of a superficial graded compositional profile. Hence, controlling several front-graded bandgap profiles along the CZTSSe absorber thin film layer thickness. Furthermore, by means of generating a rear bandgap graded profile strategy mainly based on the spontaneous cationic substitution during the kesterite (CZTGSe) alloy synthesis, it was possible to reduce the effect of deep defect (SnCu) formation and impose an additional drift (back surface) field within the quasi-neutral region. Additionally, this improves the crystallization quality of the absorber material by generating metallic Ge liquid phase fluxes. Thus, controlling several rear-graded bandgap profiles along the CZTGSe absorber thin layer film thickness. Finally, assembling together the abovementioned strategies in order to simultaneous generate both anionic and cationic compositional grading profiles inside the same kesterite matrix structure. In this way providing for the first time a demonstration of the joint synergy between defect passivation and interface energetics-modification, as a result of applying bandgap grading strategies in kesterite-based thin film solar cells. In the case of this work studied kesterite alloyed material (CZTGSSe), the band energy offset can be independently controlled trough the sulfur (S) and germanium (Ge) contents, which is explained by a double U-Shaped graded bandgap model. Consequently, this Thesis develops advanced material synthesis techniques and surface characterization, which, when integrated with the structural complexity of kesterite (CZTGSSe), allow Nature to reveal several new and disruptive properties of matter, deliberately manipulable when working out of thermodynamic equilibrium conditions. Last but not least, by optimizing the synthesis conditions, an absolute increase in bare energy conversion efficiency is obtained for the champion kesterite-based thin film solar cell device (> 10%) without any antireflective coating (ARC) nor metallic grid.[spa] Los suministros de energía renovable basados en celdas solares de película delgada/fina, y enfocados en materiales sostenibles, tales como la ‘kesterita’ (CZTS), podrían desenvolverse de manera muy exitosa en una amplia variedad de escenarios de aplicaciones energéticas. Esto se debe a su potencial para ser depositadas sobre substratos flexibles, su estética y transparencia selectiva para integraciones en sectores como el de construcción y la automoción. Así como su uso en nuevos conceptos de portabilidad energética, tales como el Internet de las cosas. Las celdas solares actuales de kesterita y de una sola capa absorbente con perfiles de banda prohibida no variables limitan la plenitud en la obtención de mejores eficiencias de conversión energética para una unión PN. Ante esto, esta Tesis demuestra que la eficiencia de conversión energética de la próxima generación de celdas solares de kesterita (y calcopiritas) puede verse potenciada tras desarrollar nuevas metodologías más estratégicas de recolección de energía fotónica. Por tanto, se propone el graduado del perfil el de banda prohibida como una estrategia sostenible para mejorar la utilización del espectro solar, mediante la generación de campos internos cuasi-eléctricos a lo largo de las películas finas, consiguiendo incrementar las longitudes de deriva y difusión de los portadores de carga minoritarios y finalmente aumentar la eficiencia. De esta manera, esta Tesis desarrolla técnicas avanzadas de síntesis y caracterización de superficies, que al integrarse con la complejidad estructural de la kesterita (CZTGSSe), permiten a la Naturaleza revelarnos varias novedosas y disruptivas propiedades de la materia, deliberadamente manipulables cuando se trabaja en condiciones fuera del equilibrio termodinámico. Por último, al optimizar las condiciones de síntesis, se obtiene un notable incremento en la eficiencia absoluta de conversión energética en celdas solares a película delgada basadas en kesterita mayores al 10%, esto sin depositar recubrimiento anti-reflectante (ARC), ni rejilla metálica alguna

Nanoscale Control of Metal Oxideand Carbonaceous Functional Materials

The controlled fabrication of nanometer scale devices is of fundamental concern for numerous technologies, from separations to electronics and catalysis. The complexity of device architectures calls for the development of synthetic methods that independently control each feature: pore dimensions, wall thickness, and any subsequent functional nanomaterial layers (e.g. photoactive electrocatalysts). Precision control over these orthogonal methods can be used to integrate 3D and 1D nanostructures. This dissertation presents the development of techniques useful in fabricating highly controlled nanoscale devices. The growth of single-phase bismuth vanadate (BiVO4) by atomic layer deposition (ALD) is demonstrated for the first time, allowing for the conformal growth of ultrathin BiVO4 on arbitrary substrates. A new tin oxide underlayer (SnO2) was developed to act as a hole-blocking underlayer concomitantly with ultrathin BiVO4 is to fabricate space-efficient photoanodes on a high-aspect ratio 3D substrate, combining the advantages gained by reducing BiVO4 thickness and preserving optical thickness. The heterojunction SnO2/BiVO4 space-efficient photoanode achieved the highest reported applied-bias photon-to-charge efficiency for any photoanode material synthesized via ALD. Lastly, the first demonstration of persistent micelle templates (PMT) with carbonaceous materials is reported, demonstrating independent control over important feature sizes, such as wall thickness and pore size, to adjust the capacity and charge/discharge rates of carbon-based supercapacitors