1,000 research outputs found
On Quantum Algorithms
Quantum computers use the quantum interference of different computational
paths to enhance correct outcomes and suppress erroneous outcomes of
computations. In effect, they follow the same logical paradigm as
(multi-particle) interferometers. We show how most known quantum algorithms,
including quantum algorithms for factorising and counting, may be cast in this
manner. Quantum searching is described as inducing a desired relative phase
between two eigenvectors to yield constructive interference on the sought
elements and destructive interference on the remaining terms.Comment: 15 pages, 8 figure
CHOOSING ALTERNATIVES TO CONTAMINATED GROUND WATER SUPPLIES: A SEQUENTIAL DECISION FRAMEWORK UNDER UNCERTAINTY
In increasing numbers, communities that rely on groundwater for drinking supplies have discovered contamination from agricultural pesticides and herbicides, road salt, underground fuel storage, and septic systems. A variety of short- and long-run remedies are available with highly uncertain outcomes. An appropriate technique for solving a benefit-cost problem of this type is a sequential decision framework using stochastic dynamic programming procedures for solution. The approach is illustrated here by means of an application to the problem of the recent contamination of the groundwater of Whately, Massachusetts by the agricultural fumigant EDB and the pesticide aldicarb.Environmental Economics and Policy,
Tsirelson's bound and supersymmetric entangled states
A superqubit, belonging to a -dimensional super-Hilbert space,
constitutes the minimal supersymmetric extension of the conventional qubit. In
order to see whether superqubits are more nonlocal than ordinary qubits, we
construct a class of two-superqubit entangled states as a nonlocal resource in
the CHSH game. Since super Hilbert space amplitudes are Grassmann numbers, the
result depends on how we extract real probabilities and we examine three
choices of map: (1) DeWitt (2) Trigonometric (3) Modified Rogers. In cases (1)
and (2) the winning probability reaches the Tsirelson bound
of standard quantum mechanics. Case (3)
crosses Tsirelson's bound with . Although all states used
in the game involve probabilities lying between 0 and 1, case (3) permits other
changes of basis inducing negative transition probabilities.Comment: Updated to match published version. Minor modifications. References
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Efficient discrete-time simulations of continuous-time quantum query algorithms
The continuous-time query model is a variant of the discrete query model in
which queries can be interleaved with known operations (called "driving
operations") continuously in time. Interesting algorithms have been discovered
in this model, such as an algorithm for evaluating nand trees more efficiently
than any classical algorithm. Subsequent work has shown that there also exists
an efficient algorithm for nand trees in the discrete query model; however,
there is no efficient conversion known for continuous-time query algorithms for
arbitrary problems.
We show that any quantum algorithm in the continuous-time query model whose
total query time is T can be simulated by a quantum algorithm in the discrete
query model that makes O[T log(T) / log(log(T))] queries. This is the first
upper bound that is independent of the driving operations (i.e., it holds even
if the norm of the driving Hamiltonian is very large). A corollary is that any
lower bound of T queries for a problem in the discrete-time query model
immediately carries over to a lower bound of \Omega[T log(log(T))/log (T)] in
the continuous-time query model.Comment: 12 pages, 6 fig
A Spitzer Spectrum of the Exoplanet HD 189733b
We report on the measurement of the 7.5-14.7 micron spectrum for the
transiting extrasolar giant planet HD 189733b using the Infrared Spectrograph
on the Spitzer Space Telescope. Though the observations comprise only 12 hours
of telescope time, the continuum is well measured and has a flux ranging from
0.6 mJy to 1.8 mJy over the wavelength range, or 0.49 +/- 0.02% of the flux of
the parent star. The variation in the measured fractional flux is very nearly
flat over the entire wavelength range and shows no indication of significant
absorption by water or methane, in contrast with the predictions of most
atmospheric models. Models with strong day/night differences appear to be
disfavored by the data, suggesting that heat redistribution to the night side
of the planet is highly efficient.Comment: 12 pages, 3 figures, accepted for publication in the Astrophysical
Journal Letter
Universal quantum computation by discontinuous quantum walk
Quantum walks are the quantum-mechanical analog of random walks, in which a
quantum `walker' evolves between initial and final states by traversing the
edges of a graph, either in discrete steps from node to node or via continuous
evolution under the Hamiltonian furnished by the adjacency matrix of the graph.
We present a hybrid scheme for universal quantum computation in which a quantum
walker takes discrete steps of continuous evolution. This `discontinuous'
quantum walk employs perfect quantum state transfer between two nodes of
specific subgraphs chosen to implement a universal gate set, thereby ensuring
unitary evolution without requiring the introduction of an ancillary coin
space. The run time is linear in the number of simulated qubits and gates. The
scheme allows multiple runs of the algorithm to be executed almost
simultaneously by starting walkers one timestep apart.Comment: 7 pages, revte
Quantum phase estimation algorithm in presence of static imperfections
We study numerically the effects of static imperfections and residual
couplings between qubits for the quantum phase estimation algorithm with two
qubits. We show that the success probability of the algorithm is affected
significantly more by static imperfections than by random noise errors in
quantum gates. An improvement of the algorithm accuracy can be reached by
application of the Pauli-random-error-correction method (PAREC).Comment: 5 pages, 5 figures. Research avilable at
http://www.quantware.ups-tlse.fr
Deutsch-Jozsa algorithm as a test of quantum computation
A redundancy in the existing Deutsch-Jozsa quantum algorithm is removed and a
refined algorithm, which reduces the size of the register and simplifies the
function evaluation, is proposed. The refined version allows a simpler analysis
of the use of entanglement between the qubits in the algorithm and provides
criteria for deciding when the Deutsch-Jozsa algorithm constitutes a meaningful
test of quantum computation.Comment: 10 pages, 2 figures, RevTex, Approved for publication in Phys Rev
Quantum information cannot be split into complementary parts
We prove a new impossibility for quantum information (the no-splitting
theorem): an unknown quantum bit (qubit) cannot be split into two complementary
qubits. This impossibility, together with the no-cloning theorem, demonstrates
that an unknown qubit state is a single entity, which cannot be cloned or
split. This sheds new light on quantum computation and quantum information.Comment: 9 pages, 1 figur
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