305,011 research outputs found
Non-locality and Communication Complexity
Quantum information processing is the emerging field that defines and
realizes computing devices that make use of quantum mechanical principles, like
the superposition principle, entanglement, and interference. In this review we
study the information counterpart of computing. The abstract form of the
distributed computing setting is called communication complexity. It studies
the amount of information, in terms of bits or in our case qubits, that two
spatially separated computing devices need to exchange in order to perform some
computational task. Surprisingly, quantum mechanics can be used to obtain
dramatic advantages for such tasks.
We review the area of quantum communication complexity, and show how it
connects the foundational physics questions regarding non-locality with those
of communication complexity studied in theoretical computer science. The first
examples exhibiting the advantage of the use of qubits in distributed
information-processing tasks were based on non-locality tests. However, by now
the field has produced strong and interesting quantum protocols and algorithms
of its own that demonstrate that entanglement, although it cannot be used to
replace communication, can be used to reduce the communication exponentially.
In turn, these new advances yield a new outlook on the foundations of physics,
and could even yield new proposals for experiments that test the foundations of
physics.Comment: Survey paper, 63 pages LaTeX. A reformatted version will appear in
Reviews of Modern Physic
2008 Abstracts Collection -- IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science
This volume contains the proceedings of the 28th international conference on the Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2008), organized under the auspices of the Indian Association for Research in Computing Science (IARCS)
From quantum-codemaking to quantum code-breaking
This is a semi-popular overview of quantum entanglement as an important
physical resource in the field of data security and quantum computing. After a
brief outline of entanglement's key role in philosophical debates about the
meaning of quantum mechanics I describe its current impact on both cryptography
and cryptanalysis. The paper is based on the lecture given at the conference
"Geometric Issues in the Foundations of Science" (Oxford, June 1996) in honor
of Roger Penrose.Comment: 21 pages, LaTeX2e, psfig, multi3.cls, 1 eps figur
Quantum Mechanics with Trajectories: Quantum Trajectories and Adaptive Grids
Although the foundations of the hydrodynamical formulation of quantum
mechanics were laid over 50 years ago, it has only been within the past few
years that viable computational implementations have been developed. One
approach to solving the hydrodynamic equations uses quantum trajectories as the
computational tool. The trajectory equations of motion are described and
methods for implementation are discussed, including fitting of the fields to
gaussian clusters.Comment: Prepared for CiSE, Computing in Science and Engineering IEEE/AIP
special issue on computational chemistr
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
A digital computer is generally believed to be an efficient universal
computing device; that is, it is believed able to simulate any physical
computing device with an increase in computation time of at most a polynomial
factor. This may not be true when quantum mechanics is taken into
consideration. This paper considers factoring integers and finding discrete
logarithms, two problems which are generally thought to be hard on a classical
computer and have been used as the basis of several proposed cryptosystems.
Efficient randomized algorithms are given for these two problems on a
hypothetical quantum computer. These algorithms take a number of steps
polynomial in the input size, e.g., the number of digits of the integer to be
factored.Comment: 28 pages, LaTeX. This is an expanded version of a paper that appeared
in the Proceedings of the 35th Annual Symposium on Foundations of Computer
Science, Santa Fe, NM, Nov. 20--22, 1994. Minor revisions made January, 199
A Faster Distributed Single-Source Shortest Paths Algorithm
We devise new algorithms for the single-source shortest paths (SSSP) problem
with non-negative edge weights in the CONGEST model of distributed computing.
While close-to-optimal solutions, in terms of the number of rounds spent by the
algorithm, have recently been developed for computing SSSP approximately, the
fastest known exact algorithms are still far away from matching the lower bound
of rounds by Peleg and Rubinovich [SIAM
Journal on Computing 2000], where is the number of nodes in the network
and is its diameter. The state of the art is Elkin's randomized algorithm
[STOC 2017] that performs rounds. We
significantly improve upon this upper bound with our two new randomized
algorithms for polynomially bounded integer edge weights, the first performing
rounds and the second performing rounds. Our bounds also compare favorably to the
independent result by Ghaffari and Li [STOC 2018]. As side results, we obtain a
-approximation -round algorithm for directed SSSP and a new work/depth trade-off for exact
SSSP on directed graphs in the PRAM model.Comment: Presented at the the 59th Annual IEEE Symposium on Foundations of
Computer Science (FOCS 2018
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