1,150 research outputs found
Finding flows in the one-way measurement model
The one-way measurement model is a framework for universal quantum
computation, in which algorithms are partially described by a graph G of
entanglement relations on a collection of qubits. A sufficient condition for an
algorithm to perform a unitary embedding between two Hilbert spaces is for the
graph G, together with input/output vertices I, O \subset V(G), to have a flow
in the sense introduced by Danos and Kashefi [quant-ph/0506062]. For the
special case of |I| = |O|, using a graph-theoretic characterization, I show
that such flows are unique when they exist. This leads to an efficient
algorithm for finding flows, by a reduction to solved problems in graph theory.Comment: 8 pages, 3 figures: somewhat condensed and updated version, to appear
in PR
Near-equilibrium measurements of nonequilibrium free energy
A central endeavor of thermodynamics is the measurement of free energy
changes. Regrettably, although we can measure the free energy of a system in
thermodynamic equilibrium, typically all we can say about the free energy of a
non-equilibrium ensemble is that it is larger than that of the same system at
equilibrium. Herein, we derive a formally exact expression for the probability
distribution of a driven system, which involves path ensemble averages of the
work over trajectories of the time-reversed system. From this we find a simple
near-equilibrium approximation for the free energy in terms of an excess mean
time-reversed work, which can be experimentally measured on real systems. With
analysis and computer simulation, we demonstrate the accuracy of our
approximations for several simple models.Comment: 5 pages, 3 figure
Optimal path for a quantum teleportation protocol in entangled networks
Bellman's optimality principle has been of enormous importance in the
development of whole branches of applied mathematics, computer science, optimal
control theory, economics, decision making, and classical physics. Examples are
numerous: dynamic programming, Markov chains, stochastic dynamics, calculus of
variations, and the brachistochrone problem. Here we show that Bellman's
optimality principle is violated in a teleportation problem on a quantum
network. This implies that finding the optimal fidelity route for teleporting a
quantum state between two distant nodes on a quantum network with bi-partite
entanglement will be a tough problem and will require further investigation.Comment: 4 pages, 1 figure, RevTeX
Semi-autonomous Intersection Collision Avoidance through Job-shop Scheduling
In this paper, we design a supervisor to prevent vehicle collisions at
intersections. An intersection is modeled as an area containing multiple
conflict points where vehicle paths cross in the future. At every time step,
the supervisor determines whether there will be more than one vehicle in the
vicinity of a conflict point at the same time. If there is, then an impending
collision is detected, and the supervisor overrides the drivers to avoid
collision. A major challenge in the design of a supervisor as opposed to an
autonomous vehicle controller is to verify whether future collisions will occur
based on the current drivers choices. This verification problem is particularly
hard due to the large number of vehicles often involved in intersection
collision, to the multitude of conflict points, and to the vehicles dynamics.
In order to solve the verification problem, we translate the problem to a
job-shop scheduling problem that yields equivalent answers. The job-shop
scheduling problem can, in turn, be transformed into a mixed-integer linear
program when the vehicle dynamics are first-order dynamics, and can thus be
solved by using a commercial solver.Comment: Submitted to Hybrid Systems: Computation and Control (HSCC) 201
Approximating the Minimum Equivalent Digraph
The MEG (minimum equivalent graph) problem is, given a directed graph, to
find a small subset of the edges that maintains all reachability relations
between nodes. The problem is NP-hard. This paper gives an approximation
algorithm with performance guarantee of pi^2/6 ~ 1.64. The algorithm and its
analysis are based on the simple idea of contracting long cycles. (This result
is strengthened slightly in ``On strongly connected digraphs with bounded cycle
length'' (1996).) The analysis applies directly to 2-Exchange, a simple ``local
improvement'' algorithm, showing that its performance guarantee is 1.75.Comment: conference version in ACM-SIAM Symposium on Discrete Algorithms
(1994
Spectral and Dynamical Properties in Classes of Sparse Networks with Mesoscopic Inhomogeneities
We study structure, eigenvalue spectra and diffusion dynamics in a wide class
of networks with subgraphs (modules) at mesoscopic scale. The networks are
grown within the model with three parameters controlling the number of modules,
their internal structure as scale-free and correlated subgraphs, and the
topology of connecting network. Within the exhaustive spectral analysis for
both the adjacency matrix and the normalized Laplacian matrix we identify the
spectral properties which characterize the mesoscopic structure of sparse
cyclic graphs and trees. The minimally connected nodes, clustering, and the
average connectivity affect the central part of the spectrum. The number of
distinct modules leads to an extra peak at the lower part of the Laplacian
spectrum in cyclic graphs. Such a peak does not occur in the case of
topologically distinct tree-subgraphs connected on a tree. Whereas the
associated eigenvectors remain localized on the subgraphs both in trees and
cyclic graphs. We also find a characteristic pattern of periodic localization
along the chains on the tree for the eigenvector components associated with the
largest eigenvalue equal 2 of the Laplacian. We corroborate the results with
simulations of the random walk on several types of networks. Our results for
the distribution of return-time of the walk to the origin (autocorrelator)
agree well with recent analytical solution for trees, and it appear to be
independent on their mesoscopic and global structure. For the cyclic graphs we
find new results with twice larger stretching exponent of the tail of the
distribution, which is virtually independent on the size of cycles. The
modularity and clustering contribute to a power-law decay at short return
times
Flows on Graphs with Random Capacities
We investigate flows on graphs whose links have random capacities. For binary
trees we derive the probability distribution for the maximal flow from the root
to a leaf, and show that for infinite trees it vanishes beyond a certain
threshold that depends on the distribution of capacities. We then examine the
maximal total flux from the root to the leaves. Our methods generalize to
simple graphs with loops, e.g., to hierarchical lattices and to complete
graphs.Comment: 8 pages, 6 figure
Connected component identification and cluster update on GPU
Cluster identification tasks occur in a multitude of contexts in physics and
engineering such as, for instance, cluster algorithms for simulating spin
models, percolation simulations, segmentation problems in image processing, or
network analysis. While it has been shown that graphics processing units (GPUs)
can result in speedups of two to three orders of magnitude as compared to
serial codes on CPUs for the case of local and thus naturally parallelized
problems such as single-spin flip update simulations of spin models, the
situation is considerably more complicated for the non-local problem of cluster
or connected component identification. I discuss the suitability of different
approaches of parallelization of cluster labeling and cluster update algorithms
for calculations on GPU and compare to the performance of serial
implementations.Comment: 15 pages, 14 figures, one table, submitted to PR
Exact bounds for distributed graph colouring
We prove exact bounds on the time complexity of distributed graph colouring.
If we are given a directed path that is properly coloured with colours, by
prior work it is known that we can find a proper 3-colouring in communication rounds. We close the gap between upper and
lower bounds: we show that for infinitely many the time complexity is
precisely communication rounds.Comment: 16 pages, 3 figure
- …