Related papers: Quantum structures from association schemes
We study continuous-time quantum walks mimicking the quantum search based on Grover's procedure. This allows us to consider structures, that is, databases, with arbitrary topological arrangements of their entries. We show that the…
Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph,…
Association rules mining (ARM) is one of the most important problems in knowledge discovery and data mining. Given a transaction database that has a large number of transactions and items, the task of ARM is to acquire consumption habits of…
The star-triangle relation plays an important role in the realm of exactly solvable models, offering exact results for classical two-dimensional statistical mechanical models. In this article, we construct integrable quantum circuits using…
n [D. de Caen, E.R. van Dam. Fissioned triangular schemes via the cross-ratio, {Europ. J. Combin.}, 22 (2001) 297-301], de Caen and van Dam constructed a fission scheme $\FT(q+1)$ of the triangular scheme on $\PG(1,q)$. This fission scheme…
Classes of self-dual codes and dual-containing codes are constructed. The codes are obtained within group rings and, using an isomorphism between group rings and matrices, equivalent codes are obtained in matrix form. Distances and other…
We formulate three current models of discrete-time quantum walks in a combinatorial way. These walks are shown to be closely related to rotation systems and 1-factorizations of graphs. For two of the models, we compute the traces and total…
The practical utility of a quantum network depends on its ability to establish entanglement between arbitrary node pairs with quality sufficient to execute entanglement enabled tasks. This capability can be assessed globally, through…
We consider the space of probabilities {P(x)}, where the x are coordinates of a configuration space. Under the action of the translation group there is a natural metric over the space of parameters of the group given by the Fisher-Rao…
A fundamental problem in quantum information is to describe efficiently multipartite quantum states. An efficient representation in terms of graphs exists for several families of quantum states (graph, cluster, stabilizer states),…
In this Thesis we examine the interplay between the encoding of information in quantum systems and their geometrical and topological properties. We first study photonic qubit probes of space-time curvature, showing how gauge-independent…
Usually in quantum mechanics the Heisenberg algebra is generated by operators of position and momentum. The algebra is then represented on an Hilbert space of square integrable functions. Alternatively one generates the Heisenberg algebra…
In this paper, we provide two methods of constructing quantum codes from linear codes over finite chain rings. The first one is derived from the Calderbank-Shor-Steane (CSS) construction applied to self-dual codes over finite chain rings.…
We examine mathematical questions around angle (or phase) operator associated with a number operator through a short list of basic requirements. We implement three methods of construction of quantum angle. The first one is based on operator…
Quantum Bayesian Computation (QBC) is an emerging field that levers the computational gains available from quantum computers to provide an exponential speed-up in Bayesian computation. Our paper adds to the literature in two ways. First, we…
A new family of free fermionic quantum spin chains with multispin interactions was recently introduced. Here we show that it is possible to build standard quantum Ising chains -- but with inhomogeneous couplings -- which have the same…
A new method for the construction of Fock-adapted operator Markovian cocycles is outlined, and its use is illustrated by application to a number of examples arising in physics and probability. The construction uses the Trotter-Kato Theorem…
We propose a new architecture for the measurement-based quantum computation model. The new design relies on small composite light-atom primary clusters. These are then assembled into cluster arrays using ancillary light modes and the actual…
We develop a fundamental framework for the quantum mechanics of stochastic systems (QMSS), showing that classical discrete stochastic processes emerge naturally as perturbations of the quantum harmonic oscillator (QHO). By constructing…
One of the traditional ways of introducing bosons and fermions is through creation-annihilation algebras. Historically, these have been associated with emission and absorption processes at the quantum level and are characteristic of the…