2,286 research outputs found
Adiabatic quantum computation and quantum phase transitions
We analyze the ground state entanglement in a quantum adiabatic evolution
algorithm designed to solve the NP-complete Exact Cover problem. The entropy of
entanglement seems to obey linear and universal scaling at the point where the
mass gap becomes small, suggesting that the system passes near a quantum phase
transition. Such a large scaling of entanglement suggests that the effective
connectivity of the system diverges as the number of qubits goes to infinity
and that this algorithm cannot be efficiently simulated by classical means. On
the other hand, entanglement in Grover's algorithm is bounded by a constant.Comment: 5 pages, 4 figures, accepted for publication in PR
Grover's Quantum Search Algorithm and Diophantine Approximation
In a fundamental paper [Phys. Rev. Lett. 78, 325 (1997)] Grover showed how a
quantum computer can find a single marked object in a database of size N by
using only O(N^{1/2}) queries of the oracle that identifies the object. His
result was generalized to the case of finding one object in a subset of marked
elements. We consider the following computational problem: A subset of marked
elements is given whose number of elements is either M or K, M<K, our task is
to determine which is the case. We show how to solve this problem with a high
probability of success using only iterations of Grover's basic step (and no
other algorithm). Let m be the required number of iterations; we prove that
under certain restrictions on the sizes of M and K the estimation m <
(2N^{1/2})/(K^{1/2}-M^{1/2}) obtains. This bound sharpens previous results and
is known to be optimal up to a constant factor. Our method involves
simultaneous Diophantine approximations, so that Grover's algorithm is
conceptualized as an orbit of an ergodic automorphism of the torus. We comment
on situations where the algorithm may be slow, and note the similarity between
these cases and the problem of small divisors in classical mechanics.Comment: 8 pages, revtex, Title change
Approximate quantum counting on an NMR ensemble quantum computer
We demonstrate the implementation of a quantum algorithm for estimating the
number of matching items in a search operation using a two qubit nuclear
magnetic resonance (NMR) quantum computer.Comment: 4 pages LaTeX/RevTex including 4 figures (3 LaTeX, 1 PostScript).
Submitted to Physical Review Letter
Implementation of quantum search algorithm using classical Fourier optics
We report on an experiment on Grover's quantum search algorithm showing that
{\em classical waves} can search a -item database as efficiently as quantum
mechanics can. The transverse beam profile of a short laser pulse is processed
iteratively as the pulse bounces back and forth between two mirrors. We
directly observe the sought item being found in iterations, in
the form of a growing intensity peak on this profile. Although the lack of
quantum entanglement limits the {\em size} of our database, our results show
that entanglement is neither necessary for the algorithm itself, nor for its
efficiency.Comment: 4 pages, 3 figures; minor revisions plus extra referenc
The return of the four- and five-dimensional preons
We prove the existence of 3/4-BPS preons in four- and five-dimensional gauged
supergravities by explicitly constructing them as smooth quotients of the AdS_4
and AdS_5 maximally supersymmetric backgrounds, respectively. This result
illustrates how the spacetime topology resurrects a fraction of supersymmetry
previously ruled out by the local analysis of the Killing spinor equations.Comment: 10 pages (a minor imprecision has been corrected
The Majorization Arrow in Quantum Algorithm Design
We apply majorization theory to study the quantum algorithms known so far and
find that there is a majorization principle underlying the way they operate.
Grover's algorithm is a neat instance of this principle where majorization
works step by step until the optimal target state is found. Extensions of this
situation are also found in algorithms based in quantum adiabatic evolution and
the family of quantum phase-estimation algorithms, including Shor's algorithm.
We state that in quantum algorithms the time arrow is a majorization arrow.Comment: REVTEX4.b4 file, 4 color figures (typos corrected.
Spontaneous supercurrent induced by ferromagnetic pi-junctions
We present magnetization measurements of mesoscopic superconducting niobium
loops containing a ferromagnetic (PdNi) pi-junction. The loops are prepared on
top of the active area of a micro Hall-sensor based on high mobility
GaAs/AlGaAs heterostructures. We observe asymmetric switching of the loop
between different magnetization states when reversing the sweep direction of
the magnetic field. This provides evidence for a spontaneous current induced by
the intrinsic phase shift of the pi-junction. In addition, the presence of the
spontaneous current near zero applied field is directly revealed by an increase
of the magnetic moment with decreasing temperature, which results in half
integer flux quantization in the loop at low temperatures.Comment: 4 pages, 4 figure
Quantum phase retrieval of a Rydberg wave packet using a half-cycle pulse
A terahertz half-cycle pulse was used to retrieve information stored as
quantum phase in an -state Rydberg atom data register. The register was
prepared as a wave packet with one state phase-reversed from the others (the
"marked bit"). A half-cycle pulse then drove a significant portion of the
electron probability into the flipped state via multimode interference.Comment: accepted by PR
Entanglement in the interaction between two quantum oscillator systems
The fundamental quantum dynamics of two interacting oscillator systems are
studied in two different scenarios. In one case, both oscillators are assumed
to be linear, whereas in the second case, one oscillator is linear and the
other is a non-linear, angular-momentum oscillator; the second case is, of
course, more complex in terms of energy transfer and dynamics. These two
scenarios have been the subject of much interest over the years, especially in
developing an understanding of modern concepts in quantum optics and quantum
electronics. In this work, however, these two scenarios are utilized to
consider and discuss the salient features of quantum behaviors resulting from
the interactive nature of the two oscillators, i.e., coherence, entanglement,
spontaneous emission, etc., and to apply a measure of entanglement in analyzing
the nature of the interacting systems. ... For the coupled linear and
angular-momentum oscillator system in the fully quantum-mechanical description,
we consider special examples of two, three, four-level angular momentum
systems, demonstrating the explicit appearances of entanglement. We also show
that this entanglement persists even as the coupled angular momentum oscillator
is taken to the limit of a large number of levels, a limit which would go over
to the classical picture for an uncoupled angular momentum oscillator
Maximally Minimal Preons in Four Dimensions
Killing spinors of N=2, D=4 supergravity are examined using the spinorial
geometry method, in which spinors are written as differential forms. By making
use of methods developed in hep-th/0606049 to analyze preons in type IIB
supergravity, we show that there are no simply connected solutions preserving
exactly 3/4 of the supersymmetry.Comment: 18 pages. References added, comments added discussing the possibility
of discrete quotients of AdS(4) preserving 3/4 supersymmetry
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