10,277 research outputs found
On the efficiency of Hamiltonian-based quantum computation for low-rank matrices
We present an extension of Adiabatic Quantum Computing (AQC) algorithm for
the unstructured search to the case when the number of marked items is unknown.
The algorithm maintains the optimal Grover speedup and includes a small
counting subroutine.
Our other results include a lower bound on the amount of time needed to
perform a general Hamiltonian-based quantum search, a lower bound on the
evolution time needed to perform a search that is valid in the presence of
control error and a generic upper bound on the minimum eigenvalue gap for
evolutions.
In particular, we demonstrate that quantum speedup for the unstructured
search using AQC type algorithms may only be achieved under very rigid control
precision requirements.Comment: 17 pages, no figures, to appear in JM
Local and global statistical distances are equivalent on pure states
The statistical distance between pure quantum states is obtained by finding a
measurement that is optimal in a sense defined by Wootters. As such, one may
expect that the statistical distance will turn out to be different if the set
of possible measurements is restricted in some way. It nonetheless turns out
that if the restriction is to local operations and classical communication
(LOCC) on any multipartite system, then the statistical distance is the same as
it is without restriction, being equal to the angle between the states in
Hilbert space.Comment: 5 pages, comments welcom
Improved Lower Bounds for Locally Decodable Codes and Private Information Retrieval
We prove new lower bounds for locally decodable codes and private information
retrieval. We show that a 2-query LDC encoding n-bit strings over an l-bit
alphabet, where the decoder only uses b bits of each queried position of the
codeword, needs code length m = exp(Omega(n/(2^b Sum_{i=0}^b {l choose i})))
Similarly, a 2-server PIR scheme with an n-bit database and t-bit queries,
where the user only needs b bits from each of the two l-bit answers, unknown to
the servers, satisfies t = Omega(n/(2^b Sum_{i=0}^b {l choose i})). This
implies that several known PIR schemes are close to optimal. Our results
generalize those of Goldreich et al. who proved roughly the same bounds for
linear LDCs and PIRs. Like earlier work by Kerenidis and de Wolf, our classical
lower bounds are proved using quantum computational techniques. In particular,
we give a tight analysis of how well a 2-input function can be computed from a
quantum superposition of both inputs.Comment: 12 pages LaTeX, To appear in ICALP '0
Neurotransmitter profile of saccadic omnipause neurons in nucleus raphe interpositus
Saccadic omnipause neurons (OPNs) are essential for the generation of saccadic eye movements. In primates OPNs are located near the midline within the nucleus raphe interpositus (rip). In the present study we used several different neuroanatomical methods to investigate the transmitters associated with OPNs in the monkey. Immunolabeling for the calcium-binding protein parvalbumin was employed to mark OPNs in the monkey and define the homologous cell group in cat and human. The use of antibodies against GABA, glycine (GLY), glutamate (GLU), serotonin (5-HT), and tyrosine hydroxylase revealed that the somata of OPNs are GLY immunoreactive, but they are devoid of GABA and 5-HT immunostaining. In situ hybridization with the GAD67 mRNA probe confirmed the negative GABA immunostaining of OPNs. 3H-GLY was injected into a projection field of OPNs, the rostral interstitial nucleus of the medial longitudinal fascicle (riMLF)--the vertical saccadic burst neuron area. This resulted in selective retrograde labeling of the OPNs in rip, while no labeling was found in the superior colliculus, which sends an excitatory projection to the riMLF. The somata and dendrites of putative burst neurons in the riMLF were contacted by numerous GLY- immunoreactive terminals. The quantitative analysis of immunoreactive terminal-like structures contacting OPNs revealed a strong input from GLY- and GABA-positive terminals on somata and dendrites, whereas GLU- positive puncta were mainly confined to the dendrites. Very few 5-HT and catecholaminergic terminals contacted OPN somata. Our findings suggest that OPNs use GLY as a neurotransmitter, and they receive numerous contacts from GABAergic, glycinergic, and glutaminergic afferents, and significantly fewer from monoaminergic inputs.</jats:p
Solution to the Equations of the Moment Expansions
We develop a formula for matching a Taylor series about the origin and an
asymptotic exponential expansion for large values of the coordinate. We test it
on the expansion of the generating functions for the moments and connected
moments of the Hamiltonian operator. In the former case the formula produces
the energies and overlaps for the Rayleigh-Ritz method in the Krylov space. We
choose the harmonic oscillator and a strongly anharmonic oscillator as
illustrative examples for numerical test. Our results reveal some features of
the connected-moments expansion that were overlooked in earlier studies and
applications of the approach
Character of Locally Inequivalent Classes of States and Entropy of Entanglement
In this letter we have established the physical character of pure bipartite
states with the same amount of entanglement in the same Schmidt rank that
either they are local unitarily connected or they are incomparable. There exist
infinite number of deterministically locally inequivalent classes of pure
bipartite states in the same Schmidt rank (starting from three) having same
amount of entanglement. Further, if there exists incomparable states with same
entanglement in higher Schmidt ranks (greater than three), then they should
differ in at least three Schmidt coefficients.Comment: 4 pages, revtex4, no figure, accepted in Physical Review A (rapid
communications
Single-qubit optical quantum fingerprinting
We analyze and demonstrate the feasibility and superiority of linear optical
single-qubit fingerprinting over its classical counterpart. For one-qubit
fingerprinting of two-bit messages, we prepare `tetrahedral' qubit states
experimentally and show that they meet the requirements for quantum
fingerprinting to exceed the classical capability. We prove that shared
entanglement permits 100% reliable quantum fingerprinting, which will
outperform classical fingerprinting even with arbitrary amounts of shared
randomness.Comment: 4 pages, one figur
Classification of the Entangled states L\times N\times N
We presented a general classification scheme for the tripartite entangled system under stochastic local operation and classical
communication. The whole classification procedure consists of two correlated
parts: the simultaneous similarity transformation of a commuting matrix pair
into a canonical form and the study of internal symmetry of parameters in the
canonical form. Based on this scheme, a concrete example of entanglement
classification for a system is given.Comment: 21 pages; published in Phys. Rev.
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