179,001 research outputs found
Efficient discrete-time simulations of continuous-time quantum query algorithms
The continuous-time query model is a variant of the discrete query model in
which queries can be interleaved with known operations (called "driving
operations") continuously in time. Interesting algorithms have been discovered
in this model, such as an algorithm for evaluating nand trees more efficiently
than any classical algorithm. Subsequent work has shown that there also exists
an efficient algorithm for nand trees in the discrete query model; however,
there is no efficient conversion known for continuous-time query algorithms for
arbitrary problems.
We show that any quantum algorithm in the continuous-time query model whose
total query time is T can be simulated by a quantum algorithm in the discrete
query model that makes O[T log(T) / log(log(T))] queries. This is the first
upper bound that is independent of the driving operations (i.e., it holds even
if the norm of the driving Hamiltonian is very large). A corollary is that any
lower bound of T queries for a problem in the discrete-time query model
immediately carries over to a lower bound of \Omega[T log(log(T))/log (T)] in
the continuous-time query model.Comment: 12 pages, 6 fig
Continuous client-side query evaluation over dynamic linked data
Existing solutions to query dynamic Linked Data sources extend the SPARQL language, and require continuous server processing for each query. Traditional SPARQL endpoints already accept highly expressive queries, so extending these endpoints for time-sensitive queries increases the server cost even further. To make continuous querying over dynamic Linked Data more affordable, we extend the low-cost Triple Pattern Fragments (TPF) interface with support for time-sensitive queries. In this paper, we introduce the TPF Query Streamer that allows clients to evaluate SPARQL queries with continuously updating results. Our experiments indicate that this extension significantly lowers the server complexity, at the expense of an increase in the execution time per query. We prove that by moving the complexity of continuously evaluating queries over dynamic Linked Data to the clients and thus increasing bandwidth usage, the cost at the server side is significantly reduced. Our results show that this solution makes real-time querying more scalable for a large amount of concurrent clients when compared to the alternatives
Gate-efficient discrete simulations of continuous-time quantum query algorithms
We show how to efficiently simulate continuous-time quantum query algorithms
that run in time T in a manner that preserves the query complexity (within a
polylogarithmic factor) while also incurring a small overhead cost in the total
number of gates between queries. By small overhead, we mean T within a factor
that is polylogarithmic in terms of T and a cost measure that reflects the cost
of computing the driving Hamiltonian. This permits any continuous-time quantum
algorithm based on an efficiently computable driving Hamiltonian to be
converted into a gate-efficient algorithm with similar running time.Comment: 28 pages, 2 figure
Qubit Complexity of Continuous Problems
The number of qubits used by a quantum algorithm will be a crucial
computational resource for the foreseeable future. We show how to obtain the
classical query complexity for continuous problems. We then establish a simple
formula for a lower bound on the qubit complexity in terms of the classical
query complexityComment: 6 pages, 2 figure
An Optimal Query Assignment for Wireless Sensor Networks
A trade-off between two QoS requirements of wireless sensor networks: query
waiting time and validity (age) of the data feeding the queries, is
investigated. We propose a Continuous Time Markov Decision Process with a drift
that trades-off between the two QoS requirements by assigning incoming queries
to the wireless sensor network or to the database. To compute an optimal
assignment policy, we argue, by means of non-standard uniformization, a
discrete time Markov decision process, stochastically equivalent to the initial
continuous process. We determine an optimal query assignment policy for the
discrete time process by means of dynamic programming. Next, we assess
numerically the performance of the optimal policy and show that it outperforms
in terms of average assignment costs three other heuristics, commonly used in
practice. Lastly, the optimality of the our model is confirmed also in the case
of real query traffic, where our proposed policy achieves significant cost
savings compared to the heuristics.Comment: 27 pages, 20 figure
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