776,675 research outputs found
Simulated Quantum Computation of Global Minima
Finding the optimal solution to a complex optimization problem is of great
importance in practically all fields of science, technology, technical design
and econometrics. We demonstrate that a modified Grover's quantum algorithm can
be applied to real problems of finding a global minimum using modest numbers of
quantum bits. Calculations of the global minimum of simple test functions and
Lennard-Jones clusters have been carried out on a quantum computer simulator
using a modified Grover's algorithm. The number of function evaluations
reduced from O(N) in classical simulation to in quantum
simulation. We also show how the Grover's quantum algorithm can be combined
with the classical Pivot method for global optimization to treat larger
systems.Comment: 6 figures. Molecular Physics, in pres
Global detailed geoid computation and model analysis
Comparisons and analyses were carried out through the use of detailed gravimetric geoids which we have computed by combining models with a set of 26,000 1 deg x 1 deg mean free air gravity anomalies. The accuracy of the detailed gravimetric geoid computed using the most recent Goddard earth model (GEM-6) in conjunction with the set of 1 deg x 1 deg mean free air gravity anomalies is assessed at + or - 2 meters on the continents of North America, Europe, and Australia, 2 to 5 meters in the Northeast Pacific and North Atlantic areas, and 5 to 10 meters in other areas where surface gravity data are sparse. The R.M.S. differences between this detailed geoid and the detailed geoids computed using the other satellite gravity fields in conjuction with same set of surface data range from 3 to 7 meters
Quantum computation in optical lattices via global laser addressing
A scheme for globally addressing a quantum computer is presented along with
its realisation in an optical lattice setup of one, two or three dimensions.
The required resources are mainly those necessary for performing quantum
simulations of spin systems with optical lattices, circumventing the necessity
for single qubit addressing. We present the control procedures, in terms of
laser manipulations, required to realise universal quantum computation. Error
avoidance with the help of the quantum Zeno effect is presented and a scheme
for globally addressed error correction is given. The latter does not require
measurements during the computation, facilitating its experimental
implementation. As an illustrative example, the pulse sequence for the
factorisation of the number fifteen is given.Comment: 11 pages, 10 figures, REVTEX. Initialisation and measurement
procedures are adde
Decoherence in adiabatic quantum computation
We have studied the decoherence properties of adiabatic quantum computation
(AQC) in the presence of in general non-Markovian, e.g., low-frequency, noise.
The developed description of the incoherent Landau-Zener transitions shows that
the global AQC maintains its properties even for decoherence larger than the
minimum gap at the anticrossing of the two lowest energy levels. The more
efficient local AQC, however, does not improve scaling of the computation time
with the number of qubits as in the decoherence-free case. The scaling
improvement requires phase coherence throughout the computation, limiting the
computation time and the problem size n.Comment: 4 pages, 2 figures, published versio
Complexity Analysis and Efficient Measurement Selection Primitives for High-Rate Graph SLAM
Sparsity has been widely recognized as crucial for efficient optimization in
graph-based SLAM. Because the sparsity and structure of the SLAM graph reflect
the set of incorporated measurements, many methods for sparsification have been
proposed in hopes of reducing computation. These methods often focus narrowly
on reducing edge count without regard for structure at a global level. Such
structurally-naive techniques can fail to produce significant computational
savings, even after aggressive pruning. In contrast, simple heuristics such as
measurement decimation and keyframing are known empirically to produce
significant computation reductions. To demonstrate why, we propose a
quantitative metric called elimination complexity (EC) that bridges the
existing analytic gap between graph structure and computation. EC quantifies
the complexity of the primary computational bottleneck: the factorization step
of a Gauss-Newton iteration. Using this metric, we show rigorously that
decimation and keyframing impose favorable global structures and therefore
achieve computation reductions on the order of and , respectively,
where is the pruning rate. We additionally present numerical results
showing EC provides a good approximation of computation in both batch and
incremental (iSAM2) optimization and demonstrate that pruning methods promoting
globally-efficient structure outperform those that do not.Comment: Pre-print accepted to ICRA 201
A Simple Cellular Automation that Solves the Density and Ordering Problems
Cellular automata (CA) are discrete, dynamical systems that perform computations
in a distributed fashion on a spatially extended grid. The dynamical behavior
of a CA may give rise to emergent computation, referring to the appearance of
global information processing capabilities that are not explicitly represented in the
system's elementary components nor in their local interconnections.1 As such, CAs
o?er an austere yet versatile model for studying natural phenomena, as well as a
powerful paradigm for attaining ?ne-grained, massively parallel computation.
An example of such emergent computation is to use a CA to determine the
global density of bits in an initial state con?guration. This problem, known as
density classi?cation, has been studied quite intensively over the past few years. In
this short communication we describe two previous versions of the problem along with their CA solutions, and then go on to show that there exists yet a third version
| which admits a simple solution
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