Abstract Pricing of financial derivatives, in particular early exercisable options such as Bermudan options, is an important but heavy numerical task institutions, and its speed-up will provide a large business impact. Recently, applications quantum computing to problems have been started be investigated. In this paper, we first propose algorithm for option pricing. This method performs the app...

Abstrac t The paper presents simple single-step algorithms for fast measurement and estimation of the amplitude ratio of the sinusoidal signals with the same frequency from two channels. The idea of the systematic error reduction with the weighted amplitude DFT coefficients around the component peaks is used in the comparative measurement procedure. Paper analyses and compares the systematic bi...

Amplitude estimation (AE) is a fundamental quantum algorithmic primitive that enables computers to achieve quadratic speedups for large class of statistical problems, including Monte Carlo methods. Recent works have succeeded in somewhat reducing the necessary resources AE by trading off some speedup lower depth circuits, but high quality qubits are still needed demonstrating such algorithms. H...

This paper examines the problem of complex amplitude estimation of a multichannel signal in the presence of colored noise with unknown spatial and temporal correlation. A number of amplitude estimators are developed, including the optimum maximum likelihood (ML) estimator, which involves nonlinear optimization, and several suboptimal but computationally more efficient estimators based on least-...

In this paper we present a robust noise estimation for speech enhancement algorithms. The robust noise estimation based on a modified minima controlled recursive averaging noise estimator was applied to different speech estimators. The investigated speech estimators were spectral substraction (SS), log spectral amplitude speech estimator (LSA) and optimally modified log spectral amplitude estim...

While often overlooked, one of the prerequisites for high-speed amplitude modulation atomic force microscopy is a high-bandwidth amplitude estimation technique. Conventional techniques, such as RMS to DC conversion and the lock-in amplifier, have proven useful, but offer limited measurement bandwidth and are not suitable for high-speed imaging. Several groups have developed techniques, but many...

The goal of this paper is finding an asymptotic equation which determines the amplitude range of asymptotically optimal scalar quantizers for Laplacian input signals with an unrestricted amplitude range. It is very important to show how the amplitude range depends on the number of quantization levels. The approximation method for determining the amplitude range is suggested. This method can be ...

Using higher-order derivative with respect to the parameter, we will give lower bounds for variance of unbiased estimators in quantum estimation problems. This is a quantum version of the Bhattacharyya inequality in the classical statistical estimation. Because of non-commutativity of operator multiplication, we obtain three different types of lower bounds; Type S, Type R and Type L. If the par...