相关论文: An iterative approach for amplitude amplification …
Here we discuss a regularized version of the factorization method for positive operators acting on a Hilbert Space. The factorization method is a qualitative reconstruction method that has been used to solve many inverse shape problems. In…
We propose novel coherent-state phase concentration by probabilistic measurement-induced ampli- fication. The amplification scheme uses novel architecture, thermal noise addition (instead of single photon addition) followed by feasible…
The method of sub-iteration, which was previously applied to the higher-order coupled cluster amplitude equations, is extended to the case of the coupled cluster $\Lambda$ equations. The sub-iteration procedure for the $\Lambda$ equations…
In this article we will apply the first- and second-order supersymmetric quantum mechanics to obtain new exactly-solvable real potentials departing from the inverted oscillator potential. This system has some special properties; in…
Inertia amplification is a mechanism coupling degrees of freedom within a vibrating structure. Its goal is to achieve an apparent high dynamic mass and, accordingly, a low resonance frequency. Such structures have been described for use in…
A general formalism for joint weak measurements of a pair of complementary observables is given. The standard process of optical three-wave mixing in a nonlinear crystal (such as in parametric down-conversion) is suitable for such tasks. To…
Non-stationary signals are ubiquitous in real life. Many techniques have been proposed in the last decades which allow decomposing multi-component signals into simple oscillatory mono-components, like the groundbreaking Empirical Mode…
We provide a robust and general algorithm for computing distribution functions associated to induced orthogonal polynomial measures. We leverage several tools for orthogonal polynomials to provide a spectrally-accurate method for a broad…
We study the iterative algorithm proposed by S. Armstrong, A. Hannukainen, T. Kuusi, J.-C. Mourrat to solve elliptic equations in divergence form with stochastic stationary coefficients. Such equations display rapidly oscillating…
A deterministic algorithm for factoring $n$ using $n^{1/3+o(1)}$ bit operations is presented. The algorithm tests the divisibility of $n$ by all the integers in a short interval at once, rather than integer by integer as in trial division.…
Linear mechanical oscillators have been applied to measure very small forces, mostly with the help of noise suppression. In contrast, adding noise to non-linear oscillators can improve the measurement conditions. Here, this effect of…
We present three methods for calculating the Feynman propagator for the non-relativistic harmonic oscillator. The first method was employed by Schwinger a half a century ago, but has rarely been used in non-relativistic problems since. Also…
Iterative filtering methods were introduced around 2010 to improve definitions and measurements of structural features in signal processing. Like many applied techniques, they present considerable challenges for mathematicians to theorize…
We consider the acoustic source imaging problems using multiple frequency data. Using the data of one observation direction/point, we prove that some information (size and location) of the source support can be recovered. A non-iterative…
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…
A modular method was suggested before to recover a band limited signal from the sample and hold and linearly interpolated (or, in general, an nth-order-hold) version of the regular samples. In this paper a novel approach for compensating…
Amplification underlies the operation of many biological and engineering systems. Simple electrical, optical, and mechanical amplifiers are reciprocal: the backward coupling of the output to the input equals the forward coupling of the…
High-gain optical parametric amplification is an important nonlinear process used both as a source of coherent infrared light and as a source of nonclassical light. In this work, we experimentally demonstrate an approach to optical…
We show that $n$-bit integers can be factorized by independently running a quantum circuit with $\tilde{O}(n^{3/2})$ gates for $\sqrt{n}+4$ times, and then using polynomial-time classical post-processing. The correctness of the algorithm…
We prove that the generic quantum speedups for brute-force search and counting only hold when the process we apply them to can be efficiently inverted. The algorithms speeding up these problems, amplitude amplification and amplitude…