303 research outputs found
Reversibility in the Extended Measurement-based Quantum Computation
When applied on some particular quantum entangled states, measurements are
universal for quantum computing. In particular, despite the fondamental
probabilistic evolution of quantum measurements, any unitary evolution can be
simulated by a measurement-based quantum computer (MBQC). We consider the
extended version of the MBQC where each measurement can occur not only in the
(X,Y)-plane of the Bloch sphere but also in the (X,Z)- and (Y,Z)-planes. The
existence of a gflow in the underlying graph of the computation is a necessary
and sufficient condition for a certain kind of determinism. We extend the
focused gflow (a gflow in a particular normal form) defined for the (X,Y)-plane
to the extended case, and we provide necessary and sufficient conditions for
the existence of such normal forms
Gardner's Minichess Variant is solved
A 5x5 board is the smallest board on which one can set up all kind of chess
pieces as a start position. We consider Gardner's minichess variant in which
all pieces are set as in a standard chessboard (from Rook to King). This game
has roughly 9x10^{18} legal positions and is comparable in this respect with
checkers. We weakly solve this game, that is we prove its game-theoretic value
and give a strategy to draw against best play for White and Black sides. Our
approach requires surprisingly small computing power. We give a human readable
proof. The way the result is obtained is generic and could be generalized to
bigger chess settings or to other games
Graph States, Pivot Minor, and Universality of (X,Z)-measurements
The graph state formalism offers strong connections between quantum
information processing and graph theory. Exploring these connections, first we
show that any graph is a pivot-minor of a planar graph, and even a pivot minor
of a triangular grid. Then, we prove that the application of measurements in
the (X,Z)-plane over graph states represented by triangular grids is a
universal measurement-based model of quantum computation. These two results are
in fact two sides of the same coin, the proof of which is a combination of
graph theoretical and quantum information techniques
Complexity of Graph State Preparation
The graph state formalism is a useful abstraction of entanglement. It is used
in some multipartite purification schemes and it adequately represents
universal resources for measurement-only quantum computation. We focus in this
paper on the complexity of graph state preparation. We consider the number of
ancillary qubits, the size of the primitive operators, and the duration of
preparation. For each lexicographic order over these parameters we give upper
and lower bounds for the complexity of graph state preparation. The first part
motivates our work and introduces basic notions and notations for the study of
graph states. Then we study some graph properties of graph states,
characterizing their minimal degree by local unitary transformations, we
propose an algorithm to reduce the degree of a graph state, and show the
relationship with Sutner sigma-game.
These properties are used in the last part, where algorithms and lower bounds
for each lexicographic order over the considered parameters are presented.Comment: 17 page
Toward Quantum Combinatorial Games
In this paper, we propose a Quantum variation of combinatorial games,
generalizing the Quantum Tic-Tac-Toe proposed by Allan Goff. A combinatorial
game is a two-player game with no chance and no hidden information, such as Go
or Chess. In this paper, we consider the possibility of playing superpositions
of moves in such games. We propose different rulesets depending on when
superposed moves should be played, and prove that all these rulesets may lead
similar games to different outcomes. We then consider Quantum variations of the
game of Nim. We conclude with some discussion on the relative interest of the
different rulesets
Optimal accessing and non-accessing structures for graph protocols
An accessing set in a graph is a subset B of vertices such that there exists
D subset of B, such that each vertex of V\B has an even number of neighbors in
D. In this paper, we introduce new bounds on the minimal size kappa'(G) of an
accessing set, and on the maximal size kappa(G) of a non-accessing set of a
graph G. We show strong connections with perfect codes and give explicitly
kappa(G) and kappa'(G) for several families of graphs. Finally, we show that
the corresponding decision problems are NP-Complete
Online Diagnosis based on Chronicle Recognition of a Coil Winding Machine
This paper falls under the problems of the diagnosis of Discrete Event System (DES) such as coil winding machine. Among the various techniques used for the on-line diagnosis, we are interested in the chronicle recognition and fault tree. The Chronicle can be defined as temporal patterns that represent system possible evolutions of an observed system. Starting from the model of the system to be diagnosed, the proposed method based on the P-time Petri net allows to generate the chronicles necessary to the diagnosis. Finally, to demonstrate the effectiveness and accuracy of the monitoring approach, an application to a coil winding unit is outlined
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