Related papers: Quantum Causal Graph Dynamics
We define what it means for a joint probability distribution to be compatible with a set of independent causal mechanisms, at a qualitative level -- or, more precisely, with a directed hypergraph ${\mathcal{A}}$, which is the qualitative…
The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several…
In this paper, we analyze the applicability of the Causal Identification algorithm to causal time series graphs with latent confounders. Since these graphs extend over infinitely many time steps, deciding whether causal effects across…
This paper introduces a new framework for recovering causal graphs from observational data, leveraging the observation that the distribution of an effect, conditioned on its causes, remains invariant to changes in the prior distribution of…
Visual representations underlie object recognition tasks, but they often contain both robust and non-robust features. Our main observation is that image classifiers may perform poorly on out-of-distribution samples because spurious…
Probabilistic cellular automata with deterministic updating are quantum systems. We employ the quantum formalism for an investigation of random probabilistic cellular automata, which start with a probability distribution over initial…
One of the most fundamental open problems in physics is the unification of general relativity and quantum theory to a theory of quantum gravity. An aspect that might become relevant in such a theory is that the dynamical nature of causal…
A new approach to quantum walks is presented. Considering a quantum system undergoing some unitary discrete-time evolution in a directed graph G, we think of the vertices of G as sites that are occupied by the quantum system, whose internal…
Courant theorem provides an upper bound for the number of nodal domains of eigenfunctions of a wide class of Laplacian-type operators. In particular, it holds for generic eigenfunctions of quantum graph. The theorem stipulates that, after…
Quantum computers are expected to revolutionize our ability to process information. The advancement from classical to quantum computing is a product of our advancement from classical to quantum physics -- the more our understanding of the…
We investigate the computational power and unified resource use of hybrid quantum-classical computations, such as teleportation and measurement-based computing. We introduce a physically causal and local graphical calculus for quantum…
Intervention theories of causality define a relationship as causal if appropriately specified interventions to manipulate a putative cause tend to produce changes in the putative effect. Interventionist causal theories are commonly…
Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph,…
Recently, several claims have been made that certain fundamental problems of distributed computing, including Leader Election and Distributed Consensus, begin to admit feasible and efficient solutions when the model of distributed…
Unitarity of the global evolution is an extremely stringent condition on finite state models in discrete spacetime. Quantum cellular automata, in particular, are tightly constrained. In previous work we proved a simple No-go Theorem which…
Quantum computation with quantum data that can traverse closed timelike curves represents a new physical model of computation. We argue that a model of quantum computation in the presence of closed timelike curves can be formulated which…
Federated Graph Learning (FGL) has emerged as a powerful paradigm for decentralized training of graph neural networks while preserving data privacy. However, existing FGL methods are predominantly designed for static graphs and rely on…
We present a mathematical framework that unifies the quantum causal history formalism from theoretical high energy physics and the directed graph operator framework from the theory of operator algebras. The approach involves completely…
Quantum teleportation plays a key role in modern quantum technologies. Thus, it is of much interest to generate alternative approaches or representations aimed at allowing us a better understanding of the physics involved in the process…
Analyzing the geometry of correlation sets constrained by general causal structures is of paramount importance for foundational and quantum technology research. Addressing this task is generally challenging, prompting the development of…