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Quantum walks on graphs are ubiquitous in quantum computing finding a myriad of applications. Likewise, random walks on graphs are a fundamental building block for a large number of algorithms with diverse applications. While the…

One of the key ways in which quantum mechanics differs from relativity is that it requires a fixed background reference frame for spacetime. In fact, this appears to be one of the main conceptual obstacles to uniting the two theories.…

Our starting point is a particular `canvas' aimed to `draw' theories of physics, which has symmetric monoidal categories as its mathematical backbone. In this paper we consider the conceptual foundations for this canvas, and how these can…

We generalize the quantum random walk protocol for a particle in a one-dimensional chain, by using several types of biased quantum coins, arranged in aperiodic sequences, in a manner that leads to a rich variety of possible wave function…

We consider a quantum system that is being continuously monitored, giving rise to a measurement signal. From such a stream of data, information needs to be inferred about the underlying system's dynamics. Here we focus on hypothesis testing…

The probabilistic interpretation of quantum mechanics has been a point of discussion since the earliest days of the theory. The development of quantum technologies transfer these discussions from philosophical interest to practical…

It is known that the classical framework of causal models is not general enough to allow for causal reasoning about quantum systems. While the framework has been generalized in a variety of different ways to the quantum case, much of this…

In this paper, we use a categorical and functorial set up to model the syntax and inference of logics with algebraic signature, extending previous works on algebraisation of logics. The main feature of this work is that structurality, or…

The semantics of assignment and mutual exclusion in concurrent and multi-core/multi-processor systems is presented with attention to low level architectural features in an attempt to make the presentation realistic. Recursive functions on…

We introduce a concept of a quantum wide sense stationary process taking values in a C*-algebra and expected in a sub-algebra. The power spectrum of such a process is defined, in analogy to classical theory, as a positive measure on…

A novel approach to automated learning of syntactic rules governing natural languages is proposed, based on using probabilities assigned to sentences (and potentially longer word sequences) by transformer neural network language models to…

Synchronous languages are now a standard industry tool for critical embedded systems. Designers write high-level specifications by composing streams of values using block diagrams. These languages have been extended with Bayesian reasoning…

We elaborate on the notion of generalized tomograms, both in the classical and quantum domains. We construct a scheme of star-products of thick tomographic symbols and obtain in explicit form the kernels of classical and quantum generalized…

Random point patterns are ubiquitous in nature, and statistical models such as point processes, i.e., algorithms that generate stochastic collections of points, are commonly used to simulate and interpret them. We propose an application of…

Traces and their extension called combined traces (comtraces) are two formal models used in the analysis and verification of concurrent systems. Both models are based on concepts originating in the theory of formal languages, and they are…

These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…

We investigate an entangled deformation of the deterministic quantum cloning process, called enscription, that can be applied to (certain) sets of distinct quantum states which are not necessarily orthogonal, called texts. Some basic…

We study a connection between the algebraic probability and classical stochastic processes described by master equations. Introducing a definition of a state which has not been used for quantum cases, the classical stochastic processes can…

"What is an algorithm?" is a fundamental question of computer science. Gurevich's behavioural theory of sequential algorithms (aka the sequential ASM thesis) gives a partial answer by defining (non-deterministic) sequential algorithms…

A new notion of stochastic germs for quantum processes is introduced and a characterisation of the stochastic differentials for positive definite (PD) processes is found in terms of their germs for arbitrary Ito algebra. A representation…