Related papers: Labeled Causets in Discrete Quantum Gravity
We define a discrete-time, coined quantum walk on weighted graphs that is inspired by Szegedy's quantum walk. Using this, we prove that many lackadaisical quantum walks, where each vertex has $l$ integer self-loops, can be generalized to a…
Causal nonseparability refers to processes where events take place in a coherent superposition of different causal orders. These may be the key resource for experimental violations of causal inequalities and have been recently identified as…
A causal set C can describe a discrete spacetime, but this discrete spacetime is not quantum, because C is endowed with Boolean logic, as it does not allow cycles. In a quasi-ordered set Q, cycles are allowed. In this paper, we consider a…
The quantum extreme reservoir computation (QERC) is a versatile quantum neural network model that combines the concepts of extreme machine learning with quantum reservoir computation. Key to QERC is the generation of a complex quantum…
The basic framework for this article is the causal set approach to discrete quantum gravity (DQG). Let $Q_n$ be the collection of causal sets with cardinality not greater than $n$ and let $K_n$ be the standard Hilbert space of…
Causal reasoning is essential to science, yet quantum theory challenges it. Quantum correlations violating Bell inequalities defy satisfactory causal explanations within the framework of classical causal models. What is more, a theory…
We propose a manifestly covariant framework for causal set dynamics. The framework is based on a structure, dubbed covtree, which is a partial order on certain sets of finite, unlabeled causal sets. We show that every infinite path in…
Quantum circuit complexity is a fundamental concept whose importance permeates quantum information, computation, many-body physics and high-energy physics. While extensively studied in closed systems, its characterization and behaviors in…
The class of problems in causal inference which seeks to isolate causal correlations solely from observational data even without interventions has come to the forefront of machine learning, neuroscience and social sciences. As new large…
We demonstrate by explicit calculation of the DeWitt-like measure in two-dimensional quantum Regge gravity that it is highly non-local and that the average values of link lengths $l, <l^n>$, do not exist for sufficient high powers of $n$.…
We prove an equivalence transformation between the correlation measure functions of the causally-unbiased quantum gravity space and the causally-biased standard space. The theory of quantum gravity fuses the dynamic (nonfixed) causal…
There has been a recent surge of interest within the field of quantum foundations regarding incorporating ideas from general relativity and quantum gravity. However, many quantum information tools remain agnostic to the underlying…
Causal sets are locally finite, partially ordered sets (posets), which are considered as discrete models of spacetimes. On the one hand, causal sets corresponding to a spacetime manifold are commonly generated with a random process called…
Uncertainty quantification (UQ) is essential for deploying machine learning models in safety-critical physical systems, yet classical Bayesian approaches incur substantial computational overhead. We establish a formal connection between…
Quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister, a system of qubits, representing a…
Identification of causal structures and quantification of direct information flows in complex systems is a challenging yet important task, with practical applications in many fields. Data generated by dynamical processes or large-scale…
For any finite poset we define a generating polynomial counting upsets, downsets, and their intersection. We investigate the behaviour of this polynomial with respect to poset operations, show that it distinguishes series-parallel posets,…
Identifying the causal structures between two statistically correlated events has been widely investigated in many fields of science. While some of the well-studied classical methods are carefully generalized to quantum version of causal…
I develop Rafael D. Sorkin's proposal that a partially ordered process of the birth of spacetime atoms in causal set quantum gravity provides an objective physical correlate of our perception of time passing. I argue that one cannot have a…
This paper presents a framework for Quantum causal modeling based on the interpretation of causality as a relation between an observer's probability assignments to hypothetical or counterfactual experiments. The framework is based on the…