1,592 research outputs found
Virtual Parallel Computing and a Search Algorithm using Matrix Product States
We propose a form of parallel computing on classical computers that is based
on matrix product states. The virtual parallelization is accomplished by
representing bits with matrices and by evolving these matrices from an initial
product state that encodes multiple inputs. Matrix evolution follows from the
sequential application of gates, as in a logical circuit. The action by
classical probabilistic one-bit and deterministic two-bit gates such as NAND
are implemented in terms of matrix operations and, as opposed to quantum
computing, it is possible to copy bits. We present a way to explore this method
of computation to solve search problems and count the number of solutions. We
argue that if the classical computational cost of testing solutions (witnesses)
requires less than local two-bit gates acting on bits, the search
problem can be fully solved in subexponential time. Therefore, for this
restricted type of search problem, the virtual parallelization scheme is faster
than Grover's quantum algorithmComment: 4 pages, 1 figure (published version
Parallel local search for solving Constraint Problems on the Cell Broadband Engine (Preliminary Results)
We explore the use of the Cell Broadband Engine (Cell/BE for short) for
combinatorial optimization applications: we present a parallel version of a
constraint-based local search algorithm that has been implemented on a
multiprocessor BladeCenter machine with twin Cell/BE processors (total of 16
SPUs per blade). This algorithm was chosen because it fits very well the
Cell/BE architecture and requires neither shared memory nor communication
between processors, while retaining a compact memory footprint. We study the
performance on several large optimization benchmarks and show that this
achieves mostly linear time speedups, even sometimes super-linear. This is
possible because the parallel implementation might explore simultaneously
different parts of the search space and therefore converge faster towards the
best sub-space and thus towards a solution. Besides getting speedups, the
resulting times exhibit a much smaller variance, which benefits applications
where a timely reply is critical
Quantum Proofs
Quantum information and computation provide a fascinating twist on the notion
of proofs in computational complexity theory. For instance, one may consider a
quantum computational analogue of the complexity class \class{NP}, known as
QMA, in which a quantum state plays the role of a proof (also called a
certificate or witness), and is checked by a polynomial-time quantum
computation. For some problems, the fact that a quantum proof state could be a
superposition over exponentially many classical states appears to offer
computational advantages over classical proof strings. In the interactive proof
system setting, one may consider a verifier and one or more provers that
exchange and process quantum information rather than classical information
during an interaction for a given input string, giving rise to quantum
complexity classes such as QIP, QSZK, and QMIP* that represent natural quantum
analogues of IP, SZK, and MIP. While quantum interactive proof systems inherit
some properties from their classical counterparts, they also possess distinct
and uniquely quantum features that lead to an interesting landscape of
complexity classes based on variants of this model.
In this survey we provide an overview of many of the known results concerning
quantum proofs, computational models based on this concept, and properties of
the complexity classes they define. In particular, we discuss non-interactive
proofs and the complexity class QMA, single-prover quantum interactive proof
systems and the complexity class QIP, statistical zero-knowledge quantum
interactive proof systems and the complexity class \class{QSZK}, and
multiprover interactive proof systems and the complexity classes QMIP, QMIP*,
and MIP*.Comment: Survey published by NOW publisher
Optimal Communication Structures for Concurrent Computing
This research focuses on communicative solvers that run concurrently and exchange information to improve performance. This “team of solvers” enables individual algorithms to communicate information regarding their progress and intermediate solutions, and allows them to synchronize memory structures with more “successful” counterparts. The result is that fewer nodes spend computational resources on “struggling” processes. The research is focused on optimization of communication structures that maximize algorithmic efficiency using the theoretical framework of Markov chains. Existing research addressing communication between the cooperative solvers on parallel systems lacks generality: Most studies consider a limited number of communication topologies and strategies, while the evaluation of different configurations is mostly limited to empirical testing. Currently, there is no theoretical framework for tuning communication between cooperative solvers to match the underlying hardware and software. Our goal is to provide such functionality by mapping solvers’ dynamics to Markov processes, and formulating the automatic tuning of communication as a well-defined optimization problem with an objective to maximize solvers’ performance metrics
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