Related papers: Quantum anholonomy with topology change
The purpose of this paper is to introduce a version of singular homology based on smooth mappings of manifolds with corners. Although variants of such a theory exists in the literature, we felt that certain points were not adequately…
Entangled quantum networks provide great flexibilities and scalabilities for quantum information processing or quantum Internet. Most of results are focused on the nonlocalities of quantum networks. Our goal in this work is to explore new…
We define a notion of quantum automorphism group of Graph C*-algebras for finite, connected graphs. Under the assumption that the underlying graph does not have any multiple edge or loop, the quantum automorphism group of underlying…
We introduce a new model for investigating spectral properties of quantum graphs, a quantum circulant graph. Circulant graphs are the Cayley graphs of cyclic groups. Quantum circulant graphs with standard vertex conditions maintain…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
We study a set of scattering matrices of quantum graphs containing minimal number of passbands, i.e., maximal number of zero elements. The cases of even and odd vertex degree are considered. Using a solution of inverse scattering problem,…
We develop a unified quantum framework for subgraph counting in graphs. We encode a graph on $N$ vertices into a quantum state on $2\lceil \log_2 N \rceil$ working qubits and $2$ ancilla qubits using its adjacency list, with worst-case gate…
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…
The study of quantum evolution on graphs for diversified topologies is beneficial to modeling various realistic systems. A systematic method, the dimerized decomposition, is proposed to analyze the dynamics on an arbitrary network. By…
Quantum network is a set of nodes connected with channels, through which the nodes communicate photons and classical information. Classical structural complexity of a quantum network may be defined through its physical structure, i.e.…
These notes review a description of quantum mechanics in terms of the topology of spaces, basing on the axioms of Topological Quantum Field Theory and path integral formalism. In this description quantum states and operators are encoded by…
We show that the space of chains of smooth maps from spheres into a fixed compact oriented manifold has a natural structure of a transversal $d$-algebra. We construct a structure of transversal 1-category on the space of chains of maps from…
Topological phases of noninteracting particles are distinguished by global properties of their band structure and eigenfunctions in momentum space. On the other hand, group theory as conventionally applied to solid-state physics focuses…
Gibbs states of an infinite system of interacting quantum particles are considered. Each particle moves on a compact Riemannian manifold and is attached to a vertex of a graph (one particle per vertex). Two kinds of graphs are studied: (a)…
In this paper, we will present some ideas to use 3D topology for quantum computing. Topological quantum computing in the usual sense works with an encoding of information as knotted quantum states of topological phases of matter, thus being…
We explore the tunneling behavior of a quantum particle on a finite graph, in the presence of an asymptotically large potential. Surprisingly the behavior is governed by the local symmetry of the graph around the wells.
When two or more subsystems of a quantum system interact with each other they can become entangled. In this case the individual subsystems can no longer be described as pure quantum states. For systems with only 2 subsystems this…
We study a simple one-dimensional quantum system on a circle with n scale free point interactions. The spectrum of this system is discrete and expressible as a solution of an explicit secular equation. However, its statistical properties…
We propose a new classification scheme for quantum entanglement based on topological links. This is done by identifying a non-rigid ring to a particle, attributing the act of cutting and removing a ring to the operation of tracing out the…
We give a scheme for interpreting shaded tangles as quantum circuits, with the property that if two shaded tangles are ambient isotopic, their corresponding computational effects are identical. We analyze 11 known quantum procedures in this…