1,979 research outputs found
Practical implementation of a quantum backtracking algorithm
In previous work, Montanaro presented a method to obtain quantum speedups for
backtracking algorithms, a general meta-algorithm to solve constraint
satisfaction problems (CSPs). In this work, we derive a space efficient
implementation of this method. Assume that we want to solve a CSP with
constraints on variables and that the union of the domains in which these
variables take their value is of cardinality . Then, we show that the
implementation of Montanaro's backtracking algorithm can be done by using data qubits. We detail an implementation of the predicate associated
to the CSP with an additional register of qubits. We explicit our
implementation for graph coloring and SAT problems, and present simulation
results. Finally, we discuss the impact of the usage of static and dynamic
variable ordering heuristics in the quantum setting.Comment: 18 pages, 10 figure
A Tutorial on Clique Problems in Communications and Signal Processing
Since its first use by Euler on the problem of the seven bridges of
K\"onigsberg, graph theory has shown excellent abilities in solving and
unveiling the properties of multiple discrete optimization problems. The study
of the structure of some integer programs reveals equivalence with graph theory
problems making a large body of the literature readily available for solving
and characterizing the complexity of these problems. This tutorial presents a
framework for utilizing a particular graph theory problem, known as the clique
problem, for solving communications and signal processing problems. In
particular, the paper aims to illustrate the structural properties of integer
programs that can be formulated as clique problems through multiple examples in
communications and signal processing. To that end, the first part of the
tutorial provides various optimal and heuristic solutions for the maximum
clique, maximum weight clique, and -clique problems. The tutorial, further,
illustrates the use of the clique formulation through numerous contemporary
examples in communications and signal processing, mainly in maximum access for
non-orthogonal multiple access networks, throughput maximization using index
and instantly decodable network coding, collision-free radio frequency
identification networks, and resource allocation in cloud-radio access
networks. Finally, the tutorial sheds light on the recent advances of such
applications, and provides technical insights on ways of dealing with mixed
discrete-continuous optimization problems
SICStus MT - A Multithreaded Execution Environment for SICStus Prolog
The development of intelligent software agents and other
complex applications which continuously interact with their
environments has been one of the reasons why explicit concurrency has
become a necessity in a modern Prolog system today. Such applications
need to perform several tasks which may be very different with respect
to how they are implemented in Prolog. Performing these tasks
simultaneously is very tedious without language support.
This paper describes the design, implementation and evaluation of a
prototype multithreaded execution environment for SICStus Prolog. The
threads are dynamically managed using a small and compact set of
Prolog primitives implemented in a portable way, requiring almost no
support from the underlying operating system
Demystifying the Information Reconciliation Protocol Cascade
Cascade is an information reconciliation protocol proposed in the context of
secret key agreement in quantum cryptography. This protocol allows removing
discrepancies in two partially correlated sequences that belong to distant
parties, connected through a public noiseless channel. It is highly
interactive, thus requiring a large number of channel communications between
the parties to proceed and, although its efficiency is not optimal, it has
become the de-facto standard for practical implementations of information
reconciliation in quantum key distribution. The aim of this work is to analyze
the performance of Cascade, to discuss its strengths, weaknesses and
optimization possibilities, comparing with some of the modified versions that
have been proposed in the literature. When looking at all design trade-offs, a
new view emerges that allows to put forward a number of guidelines and propose
near optimal parameters for the practical implementation of Cascade improving
performance significantly in comparison with all previous proposals.Comment: 30 pages, 13 figures, 3 table
On the Effect of Quantum Interaction Distance on Quantum Addition Circuits
We investigate the theoretical limits of the effect of the quantum
interaction distance on the speed of exact quantum addition circuits. For this
study, we exploit graph embedding for quantum circuit analysis. We study a
logical mapping of qubits and gates of any -depth quantum adder
circuit for two -qubit registers onto a practical architecture, which limits
interaction distance to the nearest neighbors only and supports only one- and
two-qubit logical gates. Unfortunately, on the chosen -dimensional practical
architecture, we prove that the depth lower bound of any exact quantum addition
circuits is no longer , but . This
result, the first application of graph embedding to quantum circuits and
devices, provides a new tool for compiler development, emphasizes the impact of
quantum computer architecture on performance, and acts as a cautionary note
when evaluating the time performance of quantum algorithms.Comment: accepted for ACM Journal on Emerging Technologies in Computing
System
PhasePack: A Phase Retrieval Library
Phase retrieval deals with the estimation of complex-valued signals solely
from the magnitudes of linear measurements. While there has been a recent
explosion in the development of phase retrieval algorithms, the lack of a
common interface has made it difficult to compare new methods against the
state-of-the-art. The purpose of PhasePack is to create a common software
interface for a wide range of phase retrieval algorithms and to provide a
common testbed using both synthetic data and empirical imaging datasets.
PhasePack is able to benchmark a large number of recent phase retrieval methods
against one another to generate comparisons using a range of different
performance metrics. The software package handles single method testing as well
as multiple method comparisons.
The algorithm implementations in PhasePack differ slightly from their
original descriptions in the literature in order to achieve faster speed and
improved robustness. In particular, PhasePack uses adaptive stepsizes,
line-search methods, and fast eigensolvers to speed up and automate
convergence
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