2,619 research outputs found
Adapt Or Die: Polynomial Lower Bounds For Non-Adaptive Dynamic Data Structures
In this paper, we study the role non-adaptivity plays in maintaining dynamic data structures. Roughly speaking, a data structure is non-adaptive if the memory locations it reads and/or writes when processing a query or update depend only on the query or update and not on the contents of previously read cells. We study such non-adaptive data structures in the cell probe model. The cell probe model is one of the least restrictive lower bound models and in particular, cell probe lower bounds apply to data structures developed in the popular word-RAM model. Unfortunately, this generality comes at a high cost: the highest lower bound proved for any data structure problem is only polylogarithmic (if allowed adaptivity). Our main result is to demonstrate that one can in fact obtain polynomial cell probe lower bounds for non-adaptive data structures. To shed more light on the seemingly inherent polylogarithmic lower bound barrier, we study several different notions of non-adaptivity and identify key properties that must be dealt with if we are to prove polynomial lower bounds without restrictions on the data structures. Finally, our results also unveil an interesting connection between data structures and depth-2 circuits. This allows us to translate conjectured hard data structure problems into good candidates for high circuit lower bounds; in particular, in the area of linear circuits for linear operators. Building on lower bound proofs for data structures in slightly more restrictive models, we also present a number of properties of linear operators which we believe are worth investigating in the realm of circuit lower bounds
08381 Abstracts Collection -- Computational Complexity of Discrete Problems
From the 14th of September to the 19th of September, the Dagstuhl Seminar
08381 ``Computational Complexity of Discrete Problems\u27\u27 was held in Schloss Dagstuhl - Leibniz Center for Informatics.
During the seminar, several participants presented their current
research, and ongoing work as well as open problems were discussed.
Abstracts of the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this report. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
Mathematical open problems in Projected Entangled Pair States
Projected Entangled Pair States (PEPS) are used in practice as an efficient
parametrization of the set of ground states of quantum many body systems. The
aim of this paper is to present, for a broad mathematical audience, some
mathematical questions about PEPS.Comment: Notes associated to the Santal\'o Lecture 2017, Universidad
Complutense de Madrid (UCM), minor typos correcte
The Quantum PCP Conjecture
The classical PCP theorem is arguably the most important achievement of
classical complexity theory in the past quarter century. In recent years,
researchers in quantum computational complexity have tried to identify
approaches and develop tools that address the question: does a quantum version
of the PCP theorem hold? The story of this study starts with classical
complexity and takes unexpected turns providing fascinating vistas on the
foundations of quantum mechanics, the global nature of entanglement and its
topological properties, quantum error correction, information theory, and much
more; it raises questions that touch upon some of the most fundamental issues
at the heart of our understanding of quantum mechanics. At this point, the jury
is still out as to whether or not such a theorem holds. This survey aims to
provide a snapshot of the status in this ongoing story, tailored to a general
theory-of-CS audience.Comment: 45 pages, 4 figures, an enhanced version of the SIGACT guest column
from Volume 44 Issue 2, June 201
Tensor network states in time-bin quantum optics
The current shift in the quantum optics community towards large-size
experiments -- with many modes and photons -- necessitates new classical
simulation techniques that go beyond the usual phase space formulation of
quantum mechanics. To address this pressing demand we formulate linear quantum
optics in the language of tensor network states. As a toy model, we extensively
analyze the quantum and classical correlations of time-bin interference in a
single fiber loop. We then generalize our results to more complex time-bin
quantum setups and identify different classes of architectures for
high-complexity and low-overhead boson sampling experiments
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