4,455 research outputs found
Hamiltonian and measuring time for analog quantum search
We derive in this study a Hamiltonian to solve with certainty the analog
quantum search problem analogue to the Grover algorithm. The general form of
the initial state is considered. Since the evaluation of the measuring time for
finding the marked state by probability of unity is crucially important in the
problem, especially when the Bohr frequency is high, we then give the exact
formula as a function of all given parameters for the measuring time.Comment: 5 page
Quantum computers can search rapidly by using almost any transformation
A quantum computer has a clear advantage over a classical computer for
exhaustive search. The quantum mechanical algorithm for exhaustive search was
originally derived by using subtle properties of a particular quantum
mechanical operation called the Walsh-Hadamard (W-H) transform. This paper
shows that this algorithm can be implemented by replacing the W-H transform by
almost any quantum mechanical operation. This leads to several new applications
where it improves the number of steps by a square-root. It also broadens the
scope for implementation since it demonstrates quantum mechanical algorithms
that can readily adapt to available technology.Comment: This paper is an adapted version of quant-ph/9711043. It has been
modified to make it more readable for physicists. 9 pages, postscrip
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
Nested quantum search and NP-complete problems
A quantum algorithm is known that solves an unstructured search problem in a
number of iterations of order , where is the dimension of the
search space, whereas any classical algorithm necessarily scales as . It
is shown here that an improved quantum search algorithm can be devised that
exploits the structure of a tree search problem by nesting this standard search
algorithm. The number of iterations required to find the solution of an average
instance of a constraint satisfaction problem scales as , with
a constant depending on the nesting depth and the problem
considered. When applying a single nesting level to a problem with constraints
of size 2 such as the graph coloring problem, this constant is
estimated to be around 0.62 for average instances of maximum difficulty. This
corresponds to a square-root speedup over a classical nested search algorithm,
of which our presented algorithm is the quantum counterpart.Comment: 18 pages RevTeX, 3 Postscript 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
Pressure-Induced Superconductivity in Sc to 74 GPa
Using a diamond anvil cell with nearly hydrostatic helium pressure medium we
have significantly extended the superconducting phase diagram Tc(P) of Sc, the
lightest of all transition metals. We find that superconductivity is induced in
Sc under pressure, Tc increasing monotonically to 8.2 K at 74.2 GPa. The Tc(P)
dependences of the trivalent d-electron metals Sc, Y, La, and Lu are compared
and discussed within a simple s-d charge transfer framework.Comment: to be published in Phys. Rev. B (Brief Reports
Parameter Estimation with Mixed-State Quantum Computation
We present a quantum algorithm to estimate parameters at the quantum
metrology limit using deterministic quantum computation with one bit. When the
interactions occurring in a quantum system are described by a Hamiltonian , we estimate by zooming in on previous estimations and by
implementing an adaptive Bayesian procedure. The final result of the algorithm
is an updated estimation of whose variance has been decreased in
proportion to the time of evolution under H. For the problem of estimating
several parameters, we implement dynamical-decoupling techniques and use the
results of single parameter estimation. The cases of discrete-time evolution
and reference-frame alignment are also discussed within the adaptive approach.Comment: 12 pages. Improved introduction and technical details moved to
Appendi
Extending scientific computing system with structural quantum programming capabilities
We present a basic high-level structures used for developing quantum
programming languages. The presented structures are commonly used in many
existing quantum programming languages and we use quantum pseudo-code based on
QCL quantum programming language to describe them. We also present the
implementation of introduced structures in GNU Octave language for scientific
computing. Procedures used in the implementation are available as a package
quantum-octave, providing a library of functions, which facilitates the
simulation of quantum computing. This package allows also to incorporate
high-level programming concepts into the simulation in GNU Octave and Matlab.
As such it connects features unique for high-level quantum programming
languages, with the full palette of efficient computational routines commonly
available in modern scientific computing systems. To present the major features
of the described package we provide the implementation of selected quantum
algorithms. We also show how quantum errors can be taken into account during
the simulation of quantum algorithms using quantum-octave package. This is
possible thanks to the ability to operate on density matrices
A Quantum Random Walk Search Algorithm
Quantum random walks on graphs have been shown to display many interesting
properties, including exponentially fast hitting times when compared with their
classical counterparts. However, it is still unclear how to use these novel
properties to gain an algorithmic speed-up over classical algorithms. In this
paper, we present a quantum search algorithm based on the quantum random walk
architecture that provides such a speed-up. It will be shown that this
algorithm performs an oracle search on a database of items with
calls to the oracle, yielding a speed-up similar to other quantum
search algorithms. It appears that the quantum random walk formulation has
considerable flexibility, presenting interesting opportunities for development
of other, possibly novel quantum algorithms.Comment: 13 pages, 3 figure
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