1,597 research outputs found
Distributed Computability in Byzantine Asynchronous Systems
In this work, we extend the topology-based approach for characterizing
computability in asynchronous crash-failure distributed systems to asynchronous
Byzantine systems. We give the first theorem with necessary and sufficient
conditions to solve arbitrary tasks in asynchronous Byzantine systems where an
adversary chooses faulty processes. In our adversarial formulation, outputs of
non-faulty processes are constrained in terms of inputs of non-faulty processes
only. For colorless tasks, an important subclass of distributed problems, the
general result reduces to an elegant model that effectively captures the
relation between the number of processes, the number of failures, as well as
the topological structure of the task's simplicial complexes.Comment: Will appear at the Proceedings of the 46th Annual Symposium on the
Theory of Computing, STOC 201
Property Testing of LP-Type Problems
Given query access to a set of constraints S, we wish to quickly check if some objective function ? subject to these constraints is at most a given value k. We approach this problem using the framework of property testing where our goal is to distinguish the case ?(S) ? k from the case that at least an ? fraction of the constraints in S need to be removed for ?(S) ? k to hold. We restrict our attention to the case where (S,?) are LP-Type problems which is a rich family of combinatorial optimization problems with an inherent geometric structure. By utilizing a simple sampling procedure which has been used previously to study these problems, we are able to create property testers for any LP-Type problem whose query complexities are independent of the number of constraints. To the best of our knowledge, this is the first work that connects the area of LP-Type problems and property testing in a systematic way. Among our results are property testers for a variety of LP-Type problems that are new and also problems that have been studied previously such as a tight upper bound on the query complexity of testing clusterability with one cluster considered by Alon, Dar, Parnas, and Ron (FOCS 2000). We also supply a corresponding tight lower bound for this problem and other LP-Type problems using geometric constructions
Good approximate quantum LDPC codes from spacetime circuit Hamiltonians
We study approximate quantum low-density parity-check (QLDPC) codes, which
are approximate quantum error-correcting codes specified as the ground space of
a frustration-free local Hamiltonian, whose terms do not necessarily commute.
Such codes generalize stabilizer QLDPC codes, which are exact quantum
error-correcting codes with sparse, low-weight stabilizer generators (i.e. each
stabilizer generator acts on a few qubits, and each qubit participates in a few
stabilizer generators). Our investigation is motivated by an important question
in Hamiltonian complexity and quantum coding theory: do stabilizer QLDPC codes
with constant rate, linear distance, and constant-weight stabilizers exist?
We show that obtaining such optimal scaling of parameters (modulo
polylogarithmic corrections) is possible if we go beyond stabilizer codes: we
prove the existence of a family of approximate QLDPC
codes that encode logical qubits into physical
qubits with distance and approximation infidelity
. The code space is
stabilized by a set of 10-local noncommuting projectors, with each physical
qubit only participating in projectors. We
prove the existence of an efficient encoding map, and we show that arbitrary
Pauli errors can be locally detected by circuits of polylogarithmic depth.
Finally, we show that the spectral gap of the code Hamiltonian is
by analyzing a spacetime circuit-to-Hamiltonian
construction for a bitonic sorting network architecture that is spatially local
in dimensions.Comment: 51 pages, 13 figure
Geometric, Feature-based and Graph-based Approaches for the Structural Analysis of Protein Binding Sites : Novel Methods and Computational Analysis
In this thesis, protein binding sites are considered. To enable the extraction of information from the space of protein binding sites, these binding sites must be mapped onto a mathematical space. This can be done by mapping binding sites onto vectors, graphs or point clouds. To finally enable a structure on the mathematical space, a distance measure is required, which is introduced in this thesis. This distance measure eventually can be used to extract information by means of data mining techniques
Deterministic Replacement Path Covering
In this article, we provide a unified and simplified approach to derandomize
central results in the area of fault-tolerant graph algorithms. Given a graph
, a vertex pair , and a set of edge faults , a replacement path is an - shortest path in
. For integer parameters , a replacement path covering
(RPC) is a collection of subgraphs of , denoted by
, such that for every set of at
most faults (i.e., ) and every replacement path of at
most edges, there exists a subgraph that
contains all the edges of and does not contain any of the edges of . The
covering value of the RPC is then defined to be the number
of subgraphs in .
We present efficient deterministic constructions of -RPCs whose
covering values almost match the randomized ones, for a wide range of
parameters. Our time and value bounds improve considerably over the previous
construction of Parter (DISC 2019). We also provide an almost matching lower
bound for the value of these coverings. A key application of our above
deterministic constructions is the derandomization of the algebraic
construction of the distance sensitivity oracle by Weimann and Yuster (FOCS
2010). The preprocessing and query time of the our deterministic algorithm
nearly match the randomized bounds. This resolves the open problem of Alon,
Chechik and Cohen (ICALP 2019)
A generic framework for median graph computation based on a recursive embedding approach
The median graph has been shown to be a good choice to obtain a representative of a set of graphs. However, its computation is a complex problem. Recently, graph embedding into vector spaces has been proposed to obtain approximations of the median graph. The problem with such an approach is how to go from a point in the vector space back to a graph in the graph space. The main contribution of this paper is the generalization of this previous method, proposing a generic recursive procedure that permits to recover the graph corresponding to a point in the vector space, introducing only the amount of approximation inherent to the use of graph matching algorithms. In order to evaluate the proposed method, we compare it with the set median and with the other state-of-the-art embedding-based methods for the median graph computation. The experiments are carried out using four different databases (one semi-artificial and three containing real-world data). Results show that with the proposed approach we can obtain better medians, in terms of the sum of distances to the training graphs, than with the previous existing methods. © 2011 Elsevier Inc. All rights reserved.This work has been supported by the Spanish research programmes Consolider Ingenio 2010 CSD2007-00018, TIN2006-15694-C02-02 and TIN2008-04998 and the fellowship RYC-2009-05031.Peer Reviewe
A succinct solution to Rmap alignment
Peer reviewe
Density-matrix simulation of small surface codes under current and projected experimental noise
We present a full density-matrix simulation of the quantum memory and
computing performance of the distance-3 logical qubit Surface-17, following a
recently proposed quantum circuit and using experimental error parameters for
transmon qubits in a planar circuit QED architecture. We use this simulation to
optimize components of the QEC scheme (e.g., trading off stabilizer measurement
infidelity for reduced cycle time) and to investigate the benefits of feedback
harnessing the fundamental asymmetry of relaxation-dominated error in the
constituent transmons. A lower-order approximate calculation extends these
predictions to the distance- Surface-49. These results clearly indicate
error rates below the fault-tolerance threshold of surface code, and the
potential for Surface-17 to perform beyond the break-even point of quantum
memory. At state-of-the-art qubit relaxation times and readout speeds,
Surface-49 could surpass the break-even point of computation.Comment: 10 pages + 8 pages appendix, 12 figure
- …