1,861 research outputs found
Quantum complexities of ordered searching, sorting, and element distinctness
We consider the quantum complexities of the following three problems:
searching an ordered list, sorting an un-ordered list, and deciding whether the
numbers in a list are all distinct. Letting N be the number of elements in the
input list, we prove a lower bound of \frac{1}{\pi}(\ln(N)-1) accesses to the
list elements for ordered searching, a lower bound of \Omega(N\log{N}) binary
comparisons for sorting, and a lower bound of \Omega(\sqrt{N}\log{N}) binary
comparisons for element distinctness. The previously best known lower bounds
are {1/12}\log_2(N) - O(1) due to Ambainis, \Omega(N), and \Omega(\sqrt{N}),
respectively. Our proofs are based on a weighted all-pairs inner product
argument.
In addition to our lower bound results, we give a quantum algorithm for
ordered searching using roughly 0.631 \log_2(N) oracle accesses. Our algorithm
uses a quantum routine for traversing through a binary search tree faster than
classically, and it is of a nature very different from a faster algorithm due
to Farhi, Goldstone, Gutmann, and Sipser.Comment: This new version contains new results. To appear at ICALP '01. Some
of the results have previously been presented at QIP '01. This paper subsumes
the papers quant-ph/0009091 and quant-ph/000903
Using of small-scale quantum computers in cryptography with many-qubit entangled states
We propose a new cryptographic protocol. It is suggested to encode
information in ordinary binary form into many-qubit entangled states with the
help of a quantum computer. A state of qubits (realized, e.g., with photons) is
transmitted through a quantum channel to the addressee, who applies a quantum
computer tuned to realize the inverse unitary transformation decoding of the
message. Different ways of eavesdropping are considered, and an estimate of the
time needed for determining the secret unitary transformation is given. It is
shown that using even small quantum computers can serve as a basis for very
efficient cryptographic protocols. For a suggested cryptographic protocol, the
time scale on which communication can be considered secure is exponential in
the number of qubits in the entangled states and in the number of gates used to
construct the quantum network
Quantum state transfer and entanglement distribution among distant nodes in a quantum network
We propose a scheme to utilize photons for ideal quantum transmission between
atoms located at spatially-separated nodes of a quantum network. The
transmission protocol employs special laser pulses which excite an atom inside
an optical cavity at the sending node so that its state is mapped into a
time-symmetric photon wavepacket that will enter a cavity at the receiving node
and be absorbed by an atom there with unit probability. Implementation of our
scheme would enable reliable transfer or sharing of entanglement among
spatially distant atoms.Comment: 4 pages, 3 postscript figure
Quantum Cryptography Based on the Time--Energy Uncertainty Relation
A new cryptosystem based on the fundamental time--energy uncertainty relation
is proposed. Such a cryptosystem can be implemented with both correlated photon
pairs and single photon states.Comment: 5 pages, LaTex, no figure
Scaling Property of the global string in the radiation dominated universe
We investigate the evolution of the global string network in the radiation
dominated universe by use of numerical simulations in 3+1 dimensions. We find
that the global string network settles down to the scaling regime where the
energy density of global strings, , is given by with the string tension per unit length and the scaling parameter,
, irrespective of the cosmic time. We also find that the
loop distribution function can be fitted with that predicted by the so-called
one scale model. Concretely, the number density, , of the loop with
the length, , is given by
where and is related with the Nambu-Goldstone(NG)
boson radiation power from global strings, , as with
. Therefore, the loop production function also scales and
the typical scale of produced loops is nearly the horizon distance. Thus, the
evolution of the global string network in the radiation dominated universe can
be well described by the one scale model in contrast with that of the local
string network.Comment: 18 pages, 9 figures, to appear in Phys. Rev.
Autonomous three-dimensional formation flight for a swarm of unmanned aerial vehicles
This paper investigates the development of a new guidance algorithm for a formation of unmanned aerial vehicles. Using the new approach of bifurcating potential fields, it is shown that a formation of unmanned aerial vehicles can be successfully controlled such that verifiable autonomous patterns are achieved, with a simple parameter switch allowing for transitions between patterns. The key contribution that this paper presents is in the development of a new bounded bifurcating potential field that avoids saturating the vehicle actuators, which is essential for real or safety-critical applications. To demonstrate this, a guidance and control method is developed, based on a six-degreeof-freedom linearized aircraft model, showing that, in simulation, three-dimensional formation flight for a swarm of unmanned aerial vehicles can be achieved
Evolution of a global string network in a matter dominated universe
We evolve the network of global strings in the matter-dominated universe by
means of numerical simulations. The existence of the scaling solution is
confirmed as in the radiation-dominated universe but the scaling parameter
takes a slightly smaller value, , which is
defined as with the energy density of
global strings and the string tension per unit length. The change of
from the radiation to the matter-dominated universe is consistent with
that obtained by Albrecht and Turok by use of the one-scale model. We also
study the loop distribution function and find that it can be well fitted with
that predicted by the one-scale model, where the number density of
the loop with the length is given by with and . Thus, the evolution of the
global string network in the matter-dominated universe can be well described by
the one-scale model as in the radiation-dominated universe.Comment: 10 pages, 5 figure
Whole genome sequencing of enriched chloroplast DNA using the Illumina GAII platform
<p>Abstract</p> <p>Background</p> <p>Complete chloroplast genome sequences provide a valuable source of molecular markers for studies in molecular ecology and evolution of plants. To obtain complete genome sequences, recent studies have made use of the polymerase chain reaction to amplify overlapping fragments from conserved gene loci. However, this approach is time consuming and can be more difficult to implement where gene organisation differs among plants. An alternative approach is to first isolate chloroplasts and then use the capacity of high-throughput sequencing to obtain complete genome sequences. We report our findings from studies of the latter approach, which used a simple chloroplast isolation procedure, multiply-primed rolling circle amplification of chloroplast DNA, Illumina Genome Analyzer II sequencing, and de novo assembly of paired-end sequence reads.</p> <p>Results</p> <p>A modified rapid chloroplast isolation protocol was used to obtain plant DNA that was enriched for chloroplast DNA, but nevertheless contained nuclear and mitochondrial DNA. Multiply-primed rolling circle amplification of this mixed template produced sufficient quantities of chloroplast DNA, even when the amount of starting material was small, and improved the template quality for Illumina Genome Analyzer II (hereafter Illumina GAII) sequencing. We demonstrate, using independent samples of karaka (<it>Corynocarpus laevigatus</it>), that there is high fidelity in the sequence obtained from this template. Although less than 20% of our sequenced reads could be mapped to chloroplast genome, it was relatively easy to assemble complete chloroplast genome sequences from the mixture of nuclear, mitochondrial and chloroplast reads.</p> <p>Conclusions</p> <p>We report successful whole genome sequencing of chloroplast DNA from karaka, obtained efficiently and with high fidelity.</p
Geometry of the 3-Qubit State, Entanglement and Division Algebras
We present a generalization to 3-qubits of the standard Bloch sphere
representation for a single qubit and of the 7-dimensional sphere
representation for 2 qubits presented in Mosseri {\it et
al.}\cite{Mosseri2001}. The Hilbert space of the 3-qubit system is the
15-dimensional sphere , which allows for a natural (last) Hopf
fibration with as base and as fiber. A striking feature is, as in
the case of 1 and 2 qubits, that the map is entanglement sensitive, and the two
distinct ways of un-entangling 3 qubits are naturally related to the Hopf map.
We define a quantity that measures the degree of entanglement of the 3-qubit
state. Conjectures on the possibility to generalize the construction for higher
qubit states are also discussed.Comment: 12 pages, 2 figures, final versio
Entanglement Creation Using Quantum Interrogation
We present some applications of high efficiency quantum interrogation
("interaction free measurement") for the creation of entangled states of
separate atoms and of separate photons. The quantum interrogation of a quantum
object in a superposition of object-in and object-out leaves the object and
probe in an entangled state. The probe can then be further entangled with other
objects in subsequent quantum interrogations. By then projecting out those
cases were the probe is left in a particular final state, the quantum objects
can themselves be left in various entangled states. In this way we show how to
generate two-, three-, and higher qubit entanglement between atoms and between
photons. The effect of finite efficiency for the quantum interrogation is
delineated for the various schemes.Comment: 7 pages, 13 figures, Submitted to PR
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