This paper considers the problem of estimating probability density functions on the rotation group SO(3). Two distinct approaches are proposed, one based on characteristic functions and the other on wavelets using the heat kernel. Expressions are derived for their Mean Integrated Squared Errors. The performance of the estimators is studied numerically and compared with the performance of an exi...

In this paper a novel method based on evolutionary algorithms is presented to estimate the harmonic components. In general, the optimization of the harmonic estimation process is a multi-component problem, in which evaluation of the phase and harmonic frequency is the nonlinear part of the problem and is solved based on the mathematical and evolutionary methods; while estimation of amplitude of...

Amplitude estimation algorithms are based on Grover's algorithm: alternating reflections about the input state and desired outcome. But what if we given ability to perform arbitrary rotations, instead of just reflections? In this situation, find that quantum signal processing lets us estimate amplitude in a more flexible way. We leverage technique give improved simplified for many tasks: non-de...

Consider a Boolean function χ : X → {0, 1} that partitions set X between its good and bad elements, where x is good if χ(x) = 1 and bad otherwise. Consider also a quantum algorithm A such that A|0〉 = ∑ x∈X αx|x〉 is a quantum superposition of the elements of X, and let a denote the probability that a good element is produced if A|0〉 is measured. If we repeat the process of running A, measuring t...

We provide a new method for estimating spectral gaps in low-dimensional systems. Unlike traditional phase estimation, our approach does not require ancillary qubits nor does it require well characterised gates. Instead, it only requires the ability to perform approximate Haar–random unitary operations, applying the unitary whose eigenspectrum is sought out and performing measurements in the com...

This paper considers the problem of amplitude estimation of sinusoidal signals from observations corrupted by colored noise. A relatively large number of amplitude estimators, which encompass least lquares (LS) and weighted least squares (WLS) methods, are described. Additionally, filterbank approaches, which are widely used for spectral analysis, are extended to amplitude estimation. More exac...

Quantum Amplitude Estimation (QAE) can achieve a quadratic speed-up for applications classically solved by Monte Carlo simulation. A key requirement to realize this advantage is efficient state preparation. If preparation too expensive, it diminish the quantum advantage. Preparing arbitrary states has exponential complexity with respect number of qubits, thus, not applicable. Currently known te...