Related papers: Computational tameness of classical non-causal mod…
Quantum processes with indefinite causal structure emerge when we wonder which are the most general evolutions, allowed by quantum theory, of a set of local systems which are not assumed to be in any particular causal order. These processes…
This paper argues that the requirement of applicableness of quantum linearity to any physical level from molecules and atoms to the level of macroscopic extensional world, which leads to a main foundational problem in quantum theory…
The causal structure of a unitary transformation is the set of relations of possible influence between any input subsystem and any output subsystem. We study whether such causal structure can be understood in terms of compositional…
Computational analysis of time-course data with an underlying causal structure is needed in a variety of domains, including neural spike trains, stock price movements, and gene expression levels. However, it can be challenging to determine…
A generalization of the action principle of classical mechanics, motivated by the Closed Time Path (CTP) scheme of quantum field theory, is presented to deal with initial condition problems and dissipative forces. The similarities of the…
We study the question of what is computable by Turing machines equipped with time travel into the past; i.e., with Deutschian closed timelike curves (CTCs) having no bound on their width or length. An alternative viewpoint is that we study…
Conformal prediction (CP) transforms any model's output into prediction sets guaranteed to include (cover) the true label. CP requires exchangeability, a relaxation of the i.i.d. assumption, to obtain a valid distribution-free coverage…
Can causal relations be subject to quantum indefiniteness, similar to other physical properties? The process-matrix framework formalises this possibility: valid processes are defined by what local laboratories can implement, without…
In the paper we define three new complexity classes for Turing Machine undecidable problems inspired by the famous Cook/Levin's NP-complete complexity class for intractable problems. These are U-complete (Universal complete), D-complete…
Involving only the measurements of commuting observables - the problem-setting and the corresponding solution - quantum algorithms should be subject to classical logic. This would allow flanking their customary quantum description with a…
There is good evidence that quantum computers are more powerful than classical computers, and that various simple modifications of quantum theory yield computational power that is dramatically greater still. However, these modifications…
We examine various categorical structures that can and cannot be constructed. We show that total computable functions can be mimicked by constructible functors. More generally, whatever can be done by a Turing machine can be constructed by…
Conformal prediction (CP), a distribution-free uncertainty quantification (UQ) framework, reliably provides valid predictive inference for black-box models. CP constructs prediction sets that contain the true output with a specified…
The objective of this article is to formalize the definition of NP problems. We construct a mathematical model of discrete problems as independence systems with weighted elements. We introduce two auxiliary sets that characterize the…
Classical machine learning techniques often struggle with overfitting and unreliable predictions when exposed to novel conditions. Introducing causality into the modelling process offers a promising way to mitigate these challenges by…
Positional encoding is essential for supplementing transformer with positional information of tokens. Existing positional encoding methods demand predefined token/feature order, rendering them unsuitable for real-world data with…
Many results have been recently obtained regarding the power of hypothetical closed time-like curves (CTCs) in quantum computation. Here we show that the one-way model of measurement-based quantum computation encompasses in a natural way…
Existing algorithms for explaining the outputs of image classifiers are based on a variety of approaches and produce explanations that frequently lack formal rigour. On the other hand, logic-based explanations are formally and rigorously…
Deutsch proposed two sorts of models of quantum computers, quantum Turing machines (QTMs) and quantum circuit families (QCFs). In this paper we explore the computational powers of these models and re-examine the claim of the computational…
We use techniques of quantum information theory to analyze the quantum causal histories approach to quantum gravity. We show that while it is consistent to introduce closed timelike curves (CTCs), they cannot generically carry independent…