Related papers: A perturbative analysis for noisy spectral estimat…
An estimation method is presented for polynomial phase signals, i.e., those adopting the form of a complex exponential whose phase is polynomial in its indices. Transcending the scope of existing techniques, the proposed estimator can…
The study of information scrambling has profoundly deepened our understanding of many-body quantum systems. Much recent research has been devote to understanding the interplay between scrambling and decoherence in open systems. Continuing…
MUltiple SIgnal Classification (MUSIC) and Estimation of signal parameters via rotational via rotational invariance (ESPRIT) has been widely used in super resolution direction of arrival estimation (DoA) in both Uniform Linear Arrays (ULA)…
A key conjecture about the evolution of complex quantum systems towards an ergodic steady state, known as scrambling, is that this process acquires universal features when it is most efficient. We develop a single-parameter scaling theory…
In model-free deep reinforcement learning (RL) algorithms, using noisy value estimates to supervise policy evaluation and optimization is detrimental to the sample efficiency. As this noise is heteroscedastic, its effects can be mitigated…
Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of large models in statistics and machine learning, can be…
Phase estimation in quantum interferometry is a major scenario where the quantum advantage is significantly revealed. Recently, the optimal finite-dimensional probe states (OFPSs) for phase estimation in two-mode quantum interferometry have…
The problem of imaging point objects can be formulated as estimation of an unknown atomic measure from its $M+1$ consecutive noisy Fourier coefficients. The standard resolution of this inverse problem is $1/M$ and super-resolution refers to…
This paper deals with the problem of parameter estimation based on certain eigenspaces of the empirical covariance matrix of an observed multidimensional time series, in the case where the time series dimension and the observation window…
Quantum phase estimation is a central primitive in quantum algorithms and sensing, where performance is governed by the sensitivity of measurement signals to the target parameter. While existing methods have developed increasingly…
In this brief paper, we go through the theoretical steps of the spectral clustering on quantum computers by employing the phase estimation and the amplitude amplification algorithms. We discuss circuit designs for each step and show how to…
Adaptive random search approaches have been shown to be effective for global optimization problems, where under certain conditions, the expected performance time increases only linearly with dimension. However, previous analyses assume that…
This note considers the problem of approximating the locations of dominant spikes for a probability measure from noisy spectrum measurements under the condition of residue signal, significant noise level, and no minimum spectrum separation.…
This paper establishes a nearly optimal algorithm for estimating the frequencies and amplitudes of a mixture of sinusoids from noisy equispaced samples. We derive our algorithm by viewing line spectral estimation as a sparse recovery…
We present a quantum algorithm for estimating the matrix determinant based on quantum spectral sampling. The algorithm estimates the logarithm of the determinant of an $n \times n$ positive sparse matrix to an accuracy $\epsilon$ in time…
Line spectral estimation theory aims to estimate the off-the-grid spectral components of a time signal with optimal precision. Recent results have shown that it is possible to recover signals having sparse line spectra from few temporal…
Pitch estimation is to estimate the fundamental frequency and the midi number and plays a critical role in music signal analysis and vocal signal processing. In this work, we proposed a new architecture based on a learning-based enhancement…
This paper addresses the estimation of uncertain distributed diffusion coefficients in elliptic systems based on noisy measurements of the model output. We formulate the parameter identification problem as an infinite dimensional…
We consider a perturbed integrable system with one frequency, and the approximate dynamics for the actions given by averaging over the angle. The classical theory grants that, for a perturbation of order epsilon, the error of this…
Efficiently characterizing large quantum states and processes is a central yet notoriously challenging task in quantum information science, as conventional tomography methods typically require resources that grow exponentially with system…