Related papers: Universal Analog Computation: Fra\"iss\'e Limits o…
Foundational models of computation often abstract away physical hardware limitations. However, in extreme environments like In-Network Computing (INC), these limitations become inviolable laws, creating an acute trilemma among communication…
A cellular automaton is a deterministic and exactly computable dynamical system which mimics certain fundamental aspects of physical dynamics such as spatial locality and finite entropy. CA systems can be constructed which have additional…
Temporal logics are an obvious high-level descriptive companion formalism to dynamical systems which model behavior as deterministic evolution of state over time. A wide variety of distinct temporal logics applicable to dynamical systems…
We review here the recent success in quantum annealing, i.e., optimization of the cost or energy functions of complex systems utilizing quantum fluctuations. The concept is introduced in successive steps through the studies of mapping of…
Previous efforts on reconfigurable analog circuits mostly focused on specialized analog circuits, produced through careful co-design, or on highly reconfigurable, but relatively resource inefficient, accelerators that implement analog…
Coalgebras generalize various kinds of dynamical systems occuring in mathematics and computer science. Examples of systems that can be modeled as coalgebras include automata and Markov chains. We will present a coalgebraic representation of…
Several machine learning models are defined for inputs of any size, such as graphs with different numbers of nodes and point clouds containing varying numbers of points. The universality properties of such any-dimensional models remain…
With distributed computing and mobile applications, synchronizing diverging replicas of data structures is a more and more common problem. We use algebraic methods to reason about filesystem operations, and introduce a simplified definition…
Implementing a qubit quantum computer in continuous-variable systems conventionally requires the engineering of specific interactions according to the encoding basis states. In this work, we present a unified formalism to conduct universal…
This article presents a general description of dynamical systems using the language of enriched functors and enriched natural transformations. This framework is essential to establish the equivalence of three descriptions of dynamics -- a…
Computation plays a key role in predicting and analyzing natural phenomena. There are two fundamental barriers to our ability to computationally understand the long-term behavior of a dynamical system that describes a natural process. The…
The increasing difficulty in continued development of digital electronic logic has led to a renewed interest in alternative approaches. Oscillatory computing is one such approach that leverages alternative physical systems and computation…
The model of open quantum systems is adopted to describe the non-local dynamical behaviour of qubits processed by entangling gates. The analysis gets to the conclusion that a distinction between evaluation steps and task-oriented computing…
An extension of the Dirac procedure for the quantization of constrained systems is necessary to address certain issues that are left open in Dirac's original proposal. These issues play an important role especially in the context of…
Digitalisation is one of the main drivers of most economic sectors nowadays and the digital twin, as a reification of digitalisation for complex systems has attracted much attention from both academics and industry. There have been studies…
Nonlinear computation is essential for a wide range of information processing tasks, yet implementing nonlinear functions using optical systems remains a challenge due to the weak and power-intensive nature of optical nonlinearities.…
Standard quantum mechanics is viewed as a limit of a cut system with artificially restricted dimension of a Hilbert space. Exact spectrum of cut momentum and coordinate operators is derived and the limiting transition to the infinite…
We propose a formalization of generic algorithms that includes analog algorithms. This is achieved by reformulating and extending the framework of abstract state machines to include continuous-time models of computation. We prove that every…
We define a class of dynamical maps on the quasi-local algebra of a quantum spin system, which are quantum analogues of probabilistic cellular automata. We develop criteria for such a system to be ergodic, i.e., to possess a unique…
In this paper, we review recent work published over the last 3 years under the umbrella of Neuromorphic engineering to analyze what are the common features among such systems. We see that there is no clear consensus but each system has one…