Computational Perspective on Recent Advances in Quantum Electronics: From Electron Quantum Optics to Nanoelectronic Devices and Systems

Quantum electronics has significantly evolved over the last decades. Where initially the clear focus was on light-matter interactions, nowadays approaches based on the electron's wave nature have solidified themselves as additional focus areas. This development is largely driven by continuous advances in electron quantum optics, electron based quantum information processing, electronic materials, and nanoelectronic devices and systems. The pace of research in all of these areas is astonishing and is accompanied by substantial theoretical and experimental advancements. What is particularly exciting is the fact that the computational methods, together with broadly available large-scale computing resources, have matured to such a degree so as to be essential enabling technologies themselves. These methods allow to predict, analyze, and design not only individual physical processes but also entire devices and systems, which would otherwise be very challenging or sometimes even out of reach with conventional experimental capabilities. This review is thus a testament to the increasingly towering importance of computational methods for advancing the expanding field of quantum electronics. To that end, computational aspects of a representative selection of recent research in quantum electronics are highlighted where a major focus is on the electron's wave nature. By categorizing the research into concrete technological applications, researchers and engineers will be able to use this review as a source for inspiration regarding problem-specific computational methods.

Computational aspects of relaxation complexity: possibilities and limitations

The relaxation complexity $${{\,\mathrm{rc}\,}}(X)$$ rc ( X ) of the set of integer points X contained in a polyhedron is the smallest number of facets of any polyhedron P such that the integer points in P coincide with X. It is a useful tool to investigate the existence of compact linear descriptions of X. In this article, we derive tight and computable upper bounds on $${{\,\mathrm{rc}\,}}_\mathbb {Q}(X)$$ rc Q ( X ) , a variant of $${{\,\mathrm{rc}\,}}(X)$$ rc ( X ) in which the polyhedra P are required to be rational, and we show that $${{\,\mathrm{rc}\,}}(X)$$ rc ( X ) can be computed in polynomial time if X is 2-dimensional. Further, we investigate computable lower bounds on $${{\,\mathrm{rc}\,}}(X)$$ rc ( X ) with the particular focus on the existence of a finite set $$Y \subseteq \mathbb {Z}^d$$ Y ⊆ Z d such that separating X and $$Y \setminus X$$ Y \ X allows us to deduce $${{\,\mathrm{rc}\,}}(X) \ge k$$ rc ( X ) ≥ k . In particular, we show for some choices of X that no such finite set Y exists to certify the value of $${{\,\mathrm{rc}\,}}(X)$$ rc ( X ) , providing a negative answer to a question by Weltge (2015). We also obtain an explicit formula for $${{\,\mathrm{rc}\,}}(X)$$ rc ( X ) for specific classes of sets X and present the first practically applicable approach to compute $${{\,\mathrm{rc}\,}}(X)$$ rc ( X ) for sets X that admit a finite certificate.

Computational timeline reconstruction of the stories surrounding Trump: Story turbulence, narrative control, and collective chronopathy

Measuring the specific kind, temporal ordering, diversity, and turnover rate of stories surrounding any given subject is essential to developing a complete reckoning of that subject’s historical impact. Here, we use Twitter as a distributed news and opinion aggregation source to identify and track the dynamics of the dominant day-scale stories around Donald Trump, the 45th President of the United States. Working with a data set comprising around 20 billion 1-grams, we first compare each day’s 1-gram and 2-gram usage frequencies to those of a year before, to create day- and week-scale timelines for Trump stories for 2016–2021. We measure Trump’s narrative control, the extent to which stories have been about Trump or put forward by Trump. We then quantify story turbulence and collective chronopathy—the rate at which a population’s stories for a subject seem to change over time. We show that 2017 was the most turbulent overall year for Trump. In 2020, story generation slowed dramatically during the first two major waves of the COVID-19 pandemic, with rapid turnover returning first with the Black Lives Matter protests following George Floyd’s murder and then later by events leading up to and following the 2020 US presidential election, including the storming of the US Capitol six days into 2021. Trump story turnover for 2 months during the COVID-19 pandemic was on par with that of 3 days in September 2017. Our methods may be applied to any well-discussed phenomenon, and have potential to enable the computational aspects of journalism, history, and biography.

A review on instance ranking problems in statistical learning

Ranking problems, also known as preference learning problems, define a widely spread class of statistical learning problems with many applications, including fraud detection, document ranking, medicine, chemistry, credit risk screening, image ranking or media memorability. While there already exist reviews concentrating on specific types of ranking problems like label and object ranking problems, there does not yet seem to exist an overview concentrating on instance ranking problems that both includes developments in distinguishing between different types of instance ranking problems as well as careful discussions about their differences and the applicability of the existing ranking algorithms to them. In instance ranking, one explicitly takes the responses into account with the goal to infer a scoring function which directly maps feature vectors to real-valued ranking scores, in contrast to object ranking problems where the ranks are given as preference information with the goal to learn a permutation. In this article, we systematically review different types of instance ranking problems and the corresponding loss functions resp. goodness criteria. We discuss the difficulties when trying to optimize those criteria. As for a detailed and comprehensive overview of existing machine learning techniques to solve such ranking problems, we systematize existing techniques and recapitulate the corresponding optimization problems in a unified notation. We also discuss to which of the instance ranking problems the respective algorithms are tailored and identify their strengths and limitations. Computational aspects and open research problems are also considered.