Related papers: Orthogonal Representation of Graphs
Physics is a model of nature able to both describe and predict the results of measurements made with respect to reference systems. These reference systems, in turn, are themselves physical and thus subject to the laws of physics. The…
Numerical stochastic integration is a powerful tool for the investigation of quantum dynamics in interacting many body systems. As with all numerical integration of differential equations, the initial conditions of the system being…
We investigate the relationship between two properties of quantum transformations often studied in popular subtheories of quantum theory: covariance of the Wigner representation of the theory and the existence of a transformation…
Transformers are increasingly employed for graph data, demonstrating competitive performance in diverse tasks. To incorporate graph information into these models, it is essential to enhance node and edge features with positional encodings.…
A quantum version of the action principle in a simple covariant dynamical theory of two relativistic particles is formulated. The central object of this new formulation of quantum theory is a stationary eigenvalue of the quantum action.…
Quantum theory, despite its remarkable success, struggles to represent certain experimental data, particularly those involving integer functions and deterministic relations between quantum jumps. We address this limitation by proposing a…
Existing algorithms for the optimal control of quantum observables are based on locally optimal steps in the space of control fields, or as in the case of genetic algorithms, operate on the basis of heuristics that do not explicitly take…
Quantum contextual sets have been recognized as resources for universal quantum computation, quantum steering and quantum communication. Therefore, we focus on engineering the sets that support those resources and on determining their…
We introduce orbital graphs and discuss some of their basic properties. Then we focus on their usefulness for search algorithms for permutation groups, including finding the intersection of groups and the stabilizer of sets in a group.
Quantum tomography is a procedure to determine the quantum state of a physical system, or equivalently, to estimate the expectation value of any operator. It consists in appropriately averaging the outcomes of the measurement results of…
This brief survey analyzes the epistemological implications about the role of observer in the interpretations of Quantum Mechanics. As we know, the goal of most interpretations of quantum mechanics is to avoid the apparent intrusion of the…
Local observation is an important problem both for the foundations of a quantum theory of gravity and for applications to quantum-cosmological problems such as eternal inflation. While gauge invariant local observables can't be defined, it…
Bargmann invariants, a class of gauge-invariant quantities arising from the overlaps of quantum state vectors, provide a profound and unifying framework for understanding the geometric structure of quantum mechanics. This survey offers a…
Many seemingly paradoxical effects are known in the predictions for outcomes of intermediate measurements made on pre- and post-selected quantum systems. Despite appearances, these effects do not demonstrate the impossibility of a…
Uncertainty relations involving complementary observables are one of the cornerstones of quantum mechanics. Aside from their fundamental significance, they play an important role in practical applications, such as detection of quantum…
In this work, we propose novel families of positional encodings tailored to graph neural networks obtained with quantum computers. These encodings leverage the long-range correlations inherent in quantum systems that arise from mapping the…
A probabilistic propositional logic, endowed with an epistemic component for asserting (non-)compatibility of diagonizable and bounded observables, is presented and illustrated for reasoning about the random results of projective…
We undertake a study of the notion of a quantum graph over arbitrary finite-dimensional $C^*$-algebras $B$ equipped with arbitrary faithful states. Quantum graphs are realised principally as either certain operators on $L^2(B)$, the quantum…
Graph-based linear scaling electronic structure theory for quantum-mechanical molecular dynamics simulations is adapted to the most recent shadow potential formulations of extended Lagrangian Born-Oppenheimer molecular dynamics, including…
We develop the theory of quantum (a.k.a. noncommutative) relations and quantum (a.k.a. noncommutative) graphs in the finite-dimensional covariant setting, where all systems (finite-dimensional $C^*$-algebras) carry an action of a compact…