arXiv subjects

Alexandr Sergeevich

Publications and source records attributed to Alexandr Sergeevich.

4 recordsLinked to original sources

arXiv2012

Optimizing qubit Hamiltonian parameter estimation algorithms using PSO

We develop qubit Hamiltonian single parameter estimation techniques using a Bayesian approach. The algorithms considered are restricted to projective measurements in a fixed basis, and are derived under the assumption that the qubit measurement is much slower than the characteristic qubit evolution. We optimize a non-adaptive algorithm using particle swarm optimization (PSO) and compare with a previously-developed locally-optimal scheme.

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arXiv2011

Characterization of a qubit Hamiltonian using adaptive measurements in a fixed basis

We investigate schemes for Hamiltonian parameter estimation of a two-level system using repeated measurements in a fixed basis. The simplest (Fourier based) schemes yield an estimate with a mean square error (MSE) that decreases at best as a power law ~N^{-2} in the number of measurements N. By contrast, we present numerical simulations indicating that an adaptive Bayesian algorithm, where the time between measurements can be adjusted based on prior measurement results, yields a MSE which appears to scale close to \exp(-0.3 N). That is, measurements in a single fixed basis are sufficient to achieve exponential scaling in N.

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arXiv2010

Scaling Separability Criterion: Application To Gaussian States

We introduce examples of three- and four-mode entangled Gaussian mixed states that are not detected by the scaling and Peres-Horodecki separability criteria. The presented modification of the scaling criterion resolves this problem. Also it is shown that the new criterion reproduces the main features of the scaling pictures for different cases of entangled states, while the previous versions lead to completely different outcomes. This property of the presented scheme is evidence of its higher generality.

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arXiv2009

Frank-Condon principle and adjustment of optical waveguides with nonhomogeneous refractive indices

The adjustment of two different selfocs is considered using both exact formulas for the mode-connection coefficients expressed in terms of Hermite polynomials of several variables and a qualitative approach based on the Frank-Condon principle. Several examples of the refractive-index dependence are studied and illustrative plots for these examples are presented. The connection with the tomographic approach to quantum states of a two-dimensional oscillator and the Frank-Condon factors is established.

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