79 research outputs found
Open system quantum annealing in mean field models with exponential degeneracy
Real life quantum computers are inevitably affected by intrinsic noise
resulting in dissipative non-unitary dynamics realized by these devices. We
consider an open system quantum annealing algorithm optimized for a realistic
analog quantum device which takes advantage of noise-induced thermalization and
relies on incoherent quantum tunneling at finite temperature. We analyze the
performance of this algorithm considering a p-spin model which allows for a
mean field quasicalssical solution and at the same time demonstrates the 1st
order phase transition and exponential degeneracy of states. We demonstrate
that finite temperature effects introduced by the noise are particularly
important for the dynamics in presence of the exponential degeneracy of
metastable states. We determine the optimal regime of the open system quantum
annealing algorithm for this model and find that it can outperform simulated
annealing in a range of parameters.Comment: 11 pages, 5 figure
Inference of stochastic nonlinear oscillators with applications to physiological problems
A new method of inferencing of coupled stochastic nonlinear oscillators is
described. The technique does not require extensive global optimization,
provides optimal compensation for noise-induced errors and is robust in a broad
range of dynamical models. We illustrate the main ideas of the technique by
inferencing a model of five globally and locally coupled noisy oscillators.
Specific modifications of the technique for inferencing hidden degrees of
freedom of coupled nonlinear oscillators is discussed in the context of
physiological applications.Comment: 11 pages, 10 figures, 2 tables Fluctuations and Noise 2004, SPIE
Conference, 25-28 May 2004 Gran Hotel Costa Meloneras Maspalomas, Gran
Canaria, Spai
Scaling laws for precision in quantum interferometry and bifurcation landscape of optimal state
Phase precision in optimal 2-channel quantum interferometry is studied in the
limit of large photon number , for losses occurring in either one or
both channels. For losses in one channel an optimal state undergoes an
intriguing sequence of local bifurcations as the losses or the number of
photons increase. We further show that fixing the loss paramater determines a
scale for quantum metrology -- a crossover value of the photon number
beyond which the supra-classical precision is progressively lost. For large
losses the optimal state also has a different structure from those considered
previously.Comment: 4 pages, 3 figures, v3 is modified in response to referee comment
Dynamics of quantum adiabatic evolution algorithm for Number Partitioning
We have developed a general technique to study the dynamics of the quantum
adiabatic evolution algorithm applied to random combinatorial optimization
problems in the asymptotic limit of large problem size . We use as an
example the NP-complete Number Partitioning problem and map the algorithm
dynamics to that of an auxilary quantum spin glass system with the slowly
varying Hamiltonian. We use a Green function method to obtain the adiabatic
eigenstates and the minimum excitation gap, ,
corresponding to the exponential complexity of the algorithm for Number
Partitioning. The key element of the analysis is the conditional energy
distribution computed for the set of all spin configurations generated from a
given (ancestor) configuration by simulteneous fipping of a fixed number of
spins. For the problem in question this distribution is shown to depend on the
ancestor spin configuration only via a certain parameter related to the energy
of the configuration. As the result, the algorithm dynamics can be described in
terms of one-dimenssional quantum diffusion in the energy space. This effect
provides a general limitation on the power of a quantum adiabatic computation
in random optimization problems. Analytical results are in agreement with the
numerical simulation of the algorithm.Comment: 32 pages, 5 figures, 3 Appendices; List of additions compare to v.3:
(i) numerical solution of the stationary Schroedinger equation for the
adiabatic eigenstates and eigenvalues; (ii) connection between the scaling
law of the minimum gap with the problem size and the shape of the
coarse-grained distribution of the adiabatic eigenvalues at the
avoided-crossing poin
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