585 research outputs found
A new construction for a QMA complete 3-local Hamiltonian
We present a new way of encoding a quantum computation into a 3-local
Hamiltonian. Our construction is novel in that it does not include any terms
that induce legal-illegal clock transitions. Therefore, the weights of the
terms in the Hamiltonian do not scale with the size of the problem as in
previous constructions. This improves the construction by Kempe and Regev, who
were the first to prove that 3-local Hamiltonian is complete for the complexity
class QMA, the quantum analogue of NP.
Quantum k-SAT, a restricted version of the local Hamiltonian problem using
only projector terms, was introduced by Bravyi as an analogue of the classical
k-SAT problem. Bravyi proved that quantum 4-SAT is complete for the class QMA
with one-sided error (QMA_1) and that quantum 2-SAT is in P. We give an
encoding of a quantum circuit into a quantum 4-SAT Hamiltonian using only
3-local terms. As an intermediate step to this 3-local construction, we show
that quantum 3-SAT for particles with dimensions 3x2x2 (a qutrit and two
qubits) is QMA_1 complete. The complexity of quantum 3-SAT with qubits remains
an open question.Comment: 11 pages, 4 figure
Not So SuperDense Coding - Deterministic Dense Coding with Partially Entangled States
The utilization of a -level partially entangled state, shared by two
parties wishing to communicate classical information without errors over a
noiseless quantum channel, is discussed. We analytically construct
deterministic dense coding schemes for certain classes of non-maximally
entangled states, and numerically obtain schemes in the general case. We study
the dependency of the information capacity of such schemes on the partially
entangled state shared by the two parties. Surprisingly, for it is
possible to have deterministic dense coding with less than one ebit. In this
case the number of alphabet letters that can be communicated by a single
particle, is between and 2d. In general we show that the alphabet size
grows in "steps" with the possible values . We also find
that states with less entanglement can have greater communication capacity than
other more entangled states.Comment: 6 pages, 2 figures, submitted to Phys. Rev.
The Influence of 5% KOH Immersion for Seaweed as Raw Materials for Air Freshener Gel
The effect of submersion KOH 5% for seaweed as raw materials products air freshener gel has been studied. Seaweed in Indonesia has a big potentially and it is commonly used in food products, beverages, pharmaceuticals and cosmetics. This research aims to use seaweed as a feedstock gel air freshener. Soaking seaweed with KOH was conducted to determine the nature of the water content and gel strength of the gel air freshener products generated given the scent of oranges and cloves. KOH concentration used was 5%. The results showed the water content of seaweed with KOH soaked lower than without KOH, whereas the gel strength with marinated seaweed KOH higher than without KOH. The results of organoleptic test, in this case the sense of smell, the air freshener gel product indicates that the product that uses citrus scent perfuming/lemon, panelists preferred more than the product is scented gel air freshener clove oil
Deterministic and Probabilistic Binary Search in Graphs
We consider the following natural generalization of Binary Search: in a given
undirected, positively weighted graph, one vertex is a target. The algorithm's
task is to identify the target by adaptively querying vertices. In response to
querying a node , the algorithm learns either that is the target, or is
given an edge out of that lies on a shortest path from to the target.
We study this problem in a general noisy model in which each query
independently receives a correct answer with probability (a
known constant), and an (adversarial) incorrect one with probability .
Our main positive result is that when (i.e., all answers are
correct), queries are always sufficient. For general , we give an
(almost information-theoretically optimal) algorithm that uses, in expectation,
no more than queries, and identifies the target correctly with probability at
leas . Here, denotes the
entropy. The first bound is achieved by the algorithm that iteratively queries
a 1-median of the nodes not ruled out yet; the second bound by careful repeated
invocations of a multiplicative weights algorithm.
Even for , we show several hardness results for the problem of
determining whether a target can be found using queries. Our upper bound of
implies a quasipolynomial-time algorithm for undirected connected
graphs; we show that this is best-possible under the Strong Exponential Time
Hypothesis (SETH). Furthermore, for directed graphs, or for undirected graphs
with non-uniform node querying costs, the problem is PSPACE-complete. For a
semi-adaptive version, in which one may query nodes each in rounds, we
show membership in in the polynomial hierarchy, and hardness
for
An O(n^3)-Time Algorithm for Tree Edit Distance
The {\em edit distance} between two ordered trees with vertex labels is the
minimum cost of transforming one tree into the other by a sequence of
elementary operations consisting of deleting and relabeling existing nodes, as
well as inserting new nodes. In this paper, we present a worst-case
-time algorithm for this problem, improving the previous best
-time algorithm~\cite{Klein}. Our result requires a novel
adaptive strategy for deciding how a dynamic program divides into subproblems
(which is interesting in its own right), together with a deeper understanding
of the previous algorithms for the problem. We also prove the optimality of our
algorithm among the family of \emph{decomposition strategy} algorithms--which
also includes the previous fastest algorithms--by tightening the known lower
bound of ~\cite{Touzet} to , matching our
algorithm's running time. Furthermore, we obtain matching upper and lower
bounds of when the two trees have
different sizes and~, where .Comment: 10 pages, 5 figures, 5 .tex files where TED.tex is the main on
Efficient Dynamic Approximate Distance Oracles for Vertex-Labeled Planar Graphs
Let be a graph where each vertex is associated with a label. A
Vertex-Labeled Approximate Distance Oracle is a data structure that, given a
vertex and a label , returns a -approximation of
the distance from to the closest vertex with label in . Such
an oracle is dynamic if it also supports label changes. In this paper we
present three different dynamic approximate vertex-labeled distance oracles for
planar graphs, all with polylogarithmic query and update times, and nearly
linear space requirements
Linear-Space Approximate Distance Oracles for Planar, Bounded-Genus, and Minor-Free Graphs
A (1 + eps)-approximate distance oracle for a graph is a data structure that
supports approximate point-to-point shortest-path-distance queries. The most
relevant measures for a distance-oracle construction are: space, query time,
and preprocessing time. There are strong distance-oracle constructions known
for planar graphs (Thorup, JACM'04) and, subsequently, minor-excluded graphs
(Abraham and Gavoille, PODC'06). However, these require Omega(eps^{-1} n lg n)
space for n-node graphs. We argue that a very low space requirement is
essential. Since modern computer architectures involve hierarchical memory
(caches, primary memory, secondary memory), a high memory requirement in effect
may greatly increase the actual running time. Moreover, we would like data
structures that can be deployed on small mobile devices, such as handhelds,
which have relatively small primary memory. In this paper, for planar graphs,
bounded-genus graphs, and minor-excluded graphs we give distance-oracle
constructions that require only O(n) space. The big O hides only a fixed
constant, independent of \epsilon and independent of genus or size of an
excluded minor. The preprocessing times for our distance oracle are also faster
than those for the previously known constructions. For planar graphs, the
preprocessing time is O(n lg^2 n). However, our constructions have slower query
times. For planar graphs, the query time is O(eps^{-2} lg^2 n). For our
linear-space results, we can in fact ensure, for any delta > 0, that the space
required is only 1 + delta times the space required just to represent the graph
itself
Fixed Point and Aperiodic Tilings
An aperiodic tile set was first constructed by R.Berger while proving the
undecidability of the domino problem. It turned out that aperiodic tile sets
appear in many topics ranging from logic (the Entscheidungsproblem) to physics
(quasicrystals) We present a new construction of an aperiodic tile set that is
based on Kleene's fixed-point construction instead of geometric arguments. This
construction is similar to J. von Neumann self-reproducing automata; similar
ideas were also used by P. Gacs in the context of error-correcting
computations. The flexibility of this construction allows us to construct a
"robust" aperiodic tile set that does not have periodic (or close to periodic)
tilings even if we allow some (sparse enough) tiling errors. This property was
not known for any of the existing aperiodic tile sets.Comment: v5: technical revision (positions of figures are shifted
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