32,925 research outputs found
Effects of Noisy Oracle on Search Algorithm Complexity
Grover's algorithm provides a quadratic speed-up over classical algorithms
for unstructured database or library searches. This paper examines the
robustness of Grover's search algorithm to a random phase error in the oracle
and analyzes the complexity of the search process as a function of the scaling
of the oracle error with database or library size. Both the discrete- and
continuous-time implementations of the search algorithm are investigated. It is
shown that unless the oracle phase error scales as O(N^(-1/4)), neither the
discrete- nor the continuous-time implementation of Grover's algorithm is
scalably robust to this error in the absence of error correction.Comment: 16 pages, 4 figures, submitted to Phys. Rev.
Gravitational waves from Sco X-1: A comparison of search methods and prospects for detection with advanced detectors
The low-mass X-ray binary Scorpius X-1 (Sco X-1) is potentially the most
luminous source of continuous gravitational-wave radiation for interferometers
such as LIGO and Virgo. For low-mass X-ray binaries this radiation would be
sustained by active accretion of matter from its binary companion. With the
Advanced Detector Era fast approaching, work is underway to develop an array of
robust tools for maximizing the science and detection potential of Sco X-1. We
describe the plans and progress of a project designed to compare the numerous
independent search algorithms currently available. We employ a mock-data
challenge in which the search pipelines are tested for their relative
proficiencies in parameter estimation, computational efficiency, robust- ness,
and most importantly, search sensitivity. The mock-data challenge data contains
an ensemble of 50 Scorpius X-1 (Sco X-1) type signals, simulated within a
frequency band of 50-1500 Hz. Simulated detector noise was generated assuming
the expected best strain sensitivity of Advanced LIGO and Advanced VIRGO ( Hz). A distribution of signal amplitudes was then
chosen so as to allow a useful comparison of search methodologies. A factor of
2 in strain separates the quietest detected signal, at
strain, from the torque-balance limit at a spin frequency of 300 Hz, although
this limit could range from (25 Hz) to (750 Hz) depending on the unknown frequency of Sco X-1. With future
improvements to the search algorithms and using advanced detector data, our
expectations for probing below the theoretical torque-balance strain limit are
optimistic.Comment: 33 pages, 11 figure
A methodology for airplane parameter estimation and confidence interval determination in nonlinear estimation problems
An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. With the fitted surface, sensitivity information can be updated at each iteration with less computational effort than that required by either a finite-difference method or integration of the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, and thus provides flexibility to use model equations in any convenient format. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. The degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels and to predict the degree of agreement between CR bounds and search estimates
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