Quantum State Transfer on a Class of Circulant Graphs

We study the existence of quantum state transfer on non-integral circulant graphs. We find that continuous time quantum walks on quantum networks based on certain circulant graphs with $2^k$ $\left(k\in\mathbb{Z}\right)$ vertices exhibit pretty good state transfer when there is no external dynamic control over the system. We generalize few previously known results on pretty good state transfer on circulant graphs, and this way we re-discover all integral circulant graphs on $2^k$ vertices exhibiting perfect state transfer.Comment: arXiv admin note: text overlap with arXiv:1705.0885

State transfer in strongly regular graphs with an edge perturbation

Quantum walks, an important tool in quantum computing, have been very successfully investigated using techniques in algebraic graph theory. We are motivated by the study of state transfer in continuous-time quantum walks, which is understood to be a rare and interesting phenomenon. We consider a perturbation on an edge $uv$ of a graph where we add a weight $\beta$ to the edge and a loop of weight $\gamma$ to each of $u$ and $v$. We characterize when for this perturbation results in strongly cospectral vertices $u$ and $v$. Applying this to strongly regular graphs, we give infinite families of strongly regular graphs where some perturbation results in perfect state transfer. Further, we show that, for every strongly regular graph, there is some perturbation which results in pretty good state transfer. We also show for any strongly regular graph $X$ and edge $e \in E(X)$, that $\phi(X\setminus e)$ does not depend on the choice of $e$.Comment: 25 page

Perfect quantum state transfer in weighted paths with potentials (loops) using orthogonal polynomials

A simple method for transmitting quantum states within a quantum computer is via a quantum spin chain---that is, a path on $n$ vertices. Unweighted paths are of limited use, and so a natural generalization is to consider weighted paths; this has been further generalized to allow for loops (\emph{potentials} in the physics literature). We study the particularly important situation of perfect state transfer with respect to the corresponding adjacency matrix or Laplacian through the use of orthogonal polynomials. Low-dimensional examples are given in detail. Our main result is that PST with respect to the Laplacian matrix cannot occur for weighted paths on $n\geq 3$ vertices nor can it occur for certain symmetric weighted trees. The methods used lead us to a conjecture directly linking the rationality of the weights of weighted paths on $n>3$ vertices, with or without loops, with the capacity for PST between the end vertices with respect to the adjacency matrix.Comment: 16 pages; some minor updates from previous versio

An Infinite Family of Circulant Graphs with Perfect State Transfer in Discrete Quantum Walks

We study perfect state transfer in Kendon's model of discrete quantum walks. In particular, we give a characterization of perfect state transfer purely in terms of the graph spectra, and construct an infinite family of $4$-regular circulant graphs that admit perfect state transfer. Prior to our work, the only known infinite families of examples were variants of cycles and diamond chains

Detecting Token Systems on Ethereum

We propose and compare two approaches to identify smart contracts as token systems by analyzing their public bytecode. The first approach symbolically executes the code in order to detect token systems by their characteristic behavior of updating internal accounts. The second approach serves as a comparison base and exploits the common interface of ERC-20, the most popular token standard. We present quantitative results for the Ethereum blockchain, and validate the effectiveness of both approaches using a set of curated token systems as ground truth. We observe 100% recall for the second approach. Recall rates of 89% (with well explainable missed detections) indicate that the first approach may also be able to identify "hidden" or undocumented token systems that intentionally do not implement the standard. One possible application of the proposed methods is to facilitate regulator' tasks of monitoring and policing the use of token systems and their underlying platforms

Pretty good quantum state transfer in asymmetric graphs via potential

We construct infinite families of graphs in which pretty good state transfer can be induced by adding a potential to the nodes of the graph (i.e. adding a number to a diagonal entry of the adjacency matrix). Indeed, we show that given any graph with a pair of cospectral nodes, a simple modification of the graph, along with a suitable potential, yields pretty good state transfer (i.e. asymptotically perfect state transfer) between the nodes. This generalizes previous work, concerning graphs with an involution, to asymmetric graphs.Comment: 15 page

Strongly Cospectral Vertices

Two vertices $a$ and $b$ in a graph $X$ are cospectral if the vertex-deleted subgraphs $X\setminus a$ and $X\setminus b$ have the same characteristic polynomial. In this paper we investigate a strengthening of this relation on vertices, that arises in investigations of continuous quantum walks. Suppose the vectors $e_a$ for $a$ in $V(X)$ are the standard basis for $\mathbb{R}^{V(X)}$. We say that $a$ and $b$ are strongly cospectral if, for each eigenspace $U$ of $A(X)$, the orthogonal projections of $e_a$ and $e_b$ are either equal or differ only in sign. We develop the basic theory of this concept and provide constructions of graphs with pairs of strongly cospectral vertices. Given a continuous quantum walk on on a graph, each vertex determines a curve in complex projective space. We derive results that show tht the closer these curves are, the more "similar" the corresponding vertices are.Comment: 30 page

Comparative Analysis of Distributed and Parallel File Systems' Internal Techniques

A file system optimization is the most common task in the file system field. Usually, it is seen as the key file system problem. Moreover, it is possible to state that optimization is dominant in commercial development. A problem of a new file system architecture development arises more frequently in academia. End-user can treat file system performance as the key problem of file system evolving as technology. Such understanding arises from common treatment of persistent memory as slow subsystem. As a result, problem of improving performance of data processing treats as a problem of file system performance optimization. However, evolution of physical technologies of persistent data storage requires significant changing of concepts and approaches of file systems' internal techniques. Generally speaking, only trying to improve the file system efficiency cannot resolve all issue of file systems as technological direction. Moreover, it can impede evolution of file system technology at whole. It is impossible to satisfy end-user's expectations by means of file systems optimization only. New persistent storage technologies can question about file systems necessity at whole without suggestion of revolutionary new file system's approaches. However, file system contains paradigm of information structuring that is very important for end-user as a human being. It needs to distinguish the two classes of tasks: (1) optimization task; (2) task of elaboration a new architecture vision or paradigm. But, frequently, project goal degenerates into optimization task which is meant really elaboration of a new paradigm. End-user expectations are complex and contradictory set of requirements. Only optimization tasks cannot resolve the all current needs of end-user in the file system field. End-user's expectations require resolving tasks of a new architecture vision or paradigm elaboration

Pretty Good State Transfer of Multiple Qubit States on Paths

We discuss pretty good state transfer of multiple qubit states and provide a model for considering state transfer of arbitrary states on unmodulated XX-type spin chains. We then provide families of paths and initial states for which we can determine whether there is pretty good state transfer based on the eigenvalue support of the initial state.Comment: 17 page

Quantum consciousness in warm, wet, and noisy brain

The emergence of quantum consciousness stems from dynamic flows of hydrogen ions in brain liquid. This liquid contains vast areas of the fourth phase of water with hexagonal packing of its molecules, the so-called exclusion zone (EZ) of water. The hydrogen ion motion on such hexagonal lattices shows as the hopping of the ions forward and the holes (vacant places) backward, caused by the Grotthuss mechanism. By supporting this motion using external infrasound sources, one may achieve the appearance of the superfluid state of the EZ water. Flows of the hydrogen ions are described by the modified Navier-Stokes equation. It, along with the continuity equation, yields the nonlinear Schrodinger equation, which describes the quantum effects of these flows, such as the tunneling at long distances or the interference on gap junctions.Comment: 20 pages, 11 figure