Related papers: Atom graph, partial Boolean algebra and quantum co…
Quantum computing (QC) is a new computational paradigm whose foundations relate to quantum physics. Notable progress has been made, driving the birth of a series of quantum-based algorithms that take advantage of quantum computational…
We address the problem of the construction of quantum walks on Cayley graphs. Our main motivation is the relationship between quantum algorithms and quantum walks. In particular, we discuss the choice of the dimension of the local Hilbert…
Nonlinear modifications of quantum theory are considered potential candidates for the theory of quantum gravity, with the intuitive argument that since Einstein field equations are nonlinear, quantum gravity should be nonlinear as well.…
We prove that for every pair of quantum isomorphic graphs, their block trees and their block graphs are isomorphic, and that such an isomorphism can be chosen so that the corresponding blocks are quantum isomorphic -- in particular,…
Contextuality is a fundamental feature of quantum theory and a necessary resource for quantum computation and communication. It is therefore important to investigate how large contextuality can be in quantum theory. Linear contextuality…
Quantum graphs have recently emerged as models of nonlinear optical, quantum confined systems with exquisite topological sensitivity and the potential for predicting structures with an intrinsic, off-resonance response approaching the…
Recently, quantum contextuality has been proved to be the source of quantum computation's power. That, together with multiple recent contextual experiments, prompts improving the methods of generation of contextual sets and finding their…
We show that families of leafless quantum graphs that are isospectral for the standard Laplacian are finite. We show that the minimum edge length is a spectral invariant. We give an upper bound for the size of isospectral families in terms…
The connection between contextuality and graph theory has led to many developments in the field. In particular, the sets of probability distributions in many contextuality scenarios can be described using well known convex sets from graph…
Contextuality is a key feature of quantum mechanics that provides an important non-classical resource for quantum information and computation. Abramsky and Brandenburger used sheaf theory to give a general treatment of contextuality in…
We introduce a mapping between graphs and pure quantum bipartite states and show that the associated entanglement entropy conveys non-trivial information about the structure of the graph. Our primary goal is to investigate the family of…
We study multi-qubit variational quantum states that can be considered as vertex- and edge-weighted graph. These states are constructed as single-layer variational circuits with $RX$ rotations and $RZZ$ entangling gates, corresponding to…
In 2019, Aterias et al. constructed pairs of quantum isomorphic, non-isomorphic graphs from linear constraint systems. This article deals with quantum automorphisms and quantum isomorphisms of colored versions of those graphs. We show that…
When it isn't possible to tell two distinct experimental procedures apart purely from their input/output statistics, then it seems a plausible hypothesis that the two procedures must be physically identical. We call such a hypothesis…
Quantum $L_\infty$ algebras are a generalization of $L_\infty$ algebras with a scalar product and with operations corresponding to higher genus graphs. We construct a minimal model of a given quantum $L_\infty$ algebra via the homological…
Lie groups and quantum algebras are connected through their common universal enveloping algebra. The adjoint action of Lie group on its algebra is naturally extended to related q-algebra and q-coalgebra. In such a way, quantum structure can…
A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. Searching in this mathematical framework has interested the community since a long time. However, most results consider spatial search…
We describe a cohomological framework for measurement based quantum computation, in which symmetry plays a central role. Therein, the essential information about the computational output is contained in topological invariants, namely…
Violation of a noncontextuality inequality or the phenomenon referred to `quantum contextuality' is a fundamental feature of quantum theory. In this article, we derive a novel family of noncontextuality inequalities along with their…
This paper presents a novel methodology that transforms discrete-time quantum walks into a graph embedding technique, offering a fresh perspective on graph representation methods.Through mathematical manipulations, the approach of this…