Related papers: Circuits via topoi
We develop a sound and complete graphical theory for discrete linear time-invariant dynamical systems. The graphical syntax, as in previous work, is closely related to the classical notion of signal flow diagrams, differently from previous…
Topological protection allows robust transport of localized phenomena such as quantum information, solitons, and dislocations. The transport can be either dissipative or non-dissipative. Here, we experimentally demonstrate and theoretically…
Transitivity, the existence of periodic points and positive topological entropy can be used to characterize complexity in dynamical systems. It is known that for graphs that are not trees, for every $\varepsilon>0,$ there exist (complicate)…
Topological phase transitions track changes in topological properties of a system and occur in real materials as well as quantum engineered systems, all of which differ greatly in terms of dimensionality, symmetries, interactions, and…
Visibility algorithms are a family of geometric and ordering criteria by which a real-valued time series of N data is mapped into a graph of N nodes. This graph has been shown to often inherit in its topology non-trivial properties of the…
This paper addresses the problem of designing universal quantum circuits to transform $k$ uses of a $d$-dimensional unitary input-operation into a unitary output-operation in a probabilistic heralded manner. Three classes of protocols are…
The paper introduces and studies differentially positive systems, that is, systems whose linearization along an arbitrary trajectory is positive. A generalization of Perron Frobenius theory is developed in this differential framework to…
Circuit discovery and activation steering in transformers have developed as separate research threads, yet both operate on the same representational space. Are they two views of the same underlying structure? We show they follow a single…
We introduce a general diagrammatic theory of digital circuits, based on connections between monoidal categories and graph rewriting. The main achievement of the paper is conceptual, filling a foundational gap in reasoning syntactically and…
Concepts from the Ergodic Theory are used to describe the existence of non-transitive maps in attractors of phase synchronous chaotic systems. It is shown that for a class of phase-coherent systems, e.g. the sinusoidally forced Chua's…
A major problem in the consistent-histories approach to quantum theory is contending with the potentially large number of consistent sets of history propositions. One possibility is to find a scheme in which a unique set is selected in some…
Higher-order quantum theory is an extension of quantum theory where one introduces transformations whose input and output are transformations, thus generalizing the notion of channels and quantum operations. The generalization then goes…
We present a braided circuit topology framework for investigating topology and structural phase transitions in aggregates of semiflexible polymers. In the conventional approach to circuit topology, which specifically applies to single…
We study the topology of circularly ordered sets. While the algebraic notion is classical, the general topological theory has received comparatively little attention. In this work we provide a self-contained topological exposition and…
The theory of time-dependent quantum transport addresses the question: How do electrons flow through a junction under the influence of an external perturbation as time goes by? In this paper, we invert this question and search for a…
We introduce the calculus of Classical Transitions (CT), which extends the research line on the relationship between linear logic and processes to labelled transitions. The key twist from previous work is registering parallelism in typing…
We consider the current fluctuations in a mesoscopic circuit consisting of nodes connected by arbitrary connectors, in a setup with multiple normal or superconducting terminals. In the limit of weak superconducting proximity effect,…
We prove special cases of a general conjecture: If an invertible field theory admits a projectively topological boundary theory, then it has finite order in the abelian group of invertible field theories. One can substitute `gapped' for…
Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces---so-called ``topological semantics''. The first is classical higher-order logic, with…
We show that the concept of topological order, introduced to describe ordered quantum systems which cannot be classified by broken symmetries, also applies to classical systems. Starting from a specific example, we show how to use pure…