6,658 research outputs found
Simulating quantum computation by contracting tensor networks
The treewidth of a graph is a useful combinatorial measure of how close the
graph is to a tree. We prove that a quantum circuit with gates whose
underlying graph has treewidth can be simulated deterministically in
time, which, in particular, is polynomial in if
. Among many implications, we show efficient simulations for
log-depth circuits whose gates apply to nearby qubits only, a natural
constraint satisfied by most physical implementations. We also show that
one-way quantum computation of Raussendorf and Briegel (Physical Review
Letters, 86:5188--5191, 2001), a universal quantum computation scheme with
promising physical implementations, can be efficiently simulated by a
randomized algorithm if its quantum resource is derived from a small-treewidth
graph.Comment: 7 figure
High-Quality Shared-Memory Graph Partitioning
Partitioning graphs into blocks of roughly equal size such that few edges run
between blocks is a frequently needed operation in processing graphs. Recently,
size, variety, and structural complexity of these networks has grown
dramatically. Unfortunately, previous approaches to parallel graph partitioning
have problems in this context since they often show a negative trade-off
between speed and quality. We present an approach to multi-level shared-memory
parallel graph partitioning that guarantees balanced solutions, shows high
speed-ups for a variety of large graphs and yields very good quality
independently of the number of cores used. For example, on 31 cores, our
algorithm partitions our largest test instance into 16 blocks cutting less than
half the number of edges than our main competitor when both algorithms are
given the same amount of time. Important ingredients include parallel label
propagation for both coarsening and improvement, parallel initial partitioning,
a simple yet effective approach to parallel localized local search, and fast
locality preserving hash tables
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Preparing sparse solvers for exascale computing.
Sparse solvers provide essential functionality for a wide variety of scientific applications. Highly parallel sparse solvers are essential for continuing advances in high-fidelity, multi-physics and multi-scale simulations, especially as we target exascale platforms. This paper describes the challenges, strategies and progress of the US Department of Energy Exascale Computing project towards providing sparse solvers for exascale computing platforms. We address the demands of systems with thousands of high-performance node devices where exposing concurrency, hiding latency and creating alternative algorithms become essential. The efforts described here are works in progress, highlighting current success and upcoming challenges. This article is part of a discussion meeting issue 'Numerical algorithms for high-performance computational science'
Optimal Summation and Integration by Deterministic, Randomized, and Quantum Algorithms
We survey old and new results about optimal algorithms for summation of
finite sequences and for integration of functions from Hoelder or Sobolev
spaces. First we discuss optimal deterministic and randomized algorithms. Then
we add a new aspect, which has not been covered before on conferences about
(quasi-) Monte Carlo methods: quantum computation. We give a short introduction
into this setting and present recent results of the authors on optimal quantum
algorithms for summation and integration. We discuss comparisons between the
three settings. The most interesting case for Monte Carlo and quantum
integration is that of moderate smoothness k and large dimension d which, in
fact, occurs in a number of important applied problems. In that case the
deterministic exponent is negligible, so the n^{-1/2} Monte Carlo and the
n^{-1} quantum speedup essentially constitute the entire convergence rate. We
observe that -- there is an exponential speed-up of quantum algorithms over
deterministic (classical) algorithms, if k/d tends to zero; -- there is a
(roughly) quadratic speed-up of quantum algorithms over randomized classical
algorithms, if k/d is small.Comment: 13 pages, contribution to the 4th International Conference on Monte
Carlo and Quasi-Monte Carlo Methods, Hong Kong 200
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