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Simultaneous estimation of multiple eigenvalues with short-depth quantum circuit on early fault-tolerant quantum computers
We introduce a multi-modal, multi-level quantum complex exponential least squares (MM-
QCELS) method to simultaneously estimate multiple eigenvalues of a quantum Hamiltonian …
QCELS) method to simultaneously estimate multiple eigenvalues of a quantum Hamiltonian …
Super-resolution techniques for biomedical applications and challenges
Super-resolution (SR) techniques have revolutionized the field of biomedical applications by
detailing the structures at resolutions beyond the limits of imaging or measuring tools. These …
detailing the structures at resolutions beyond the limits of imaging or measuring tools. These …
End-to-end nanophotonic inverse design for imaging and polarimetry
By codesigning a metaoptical front end in conjunction with an image-processing back end,
we demonstrate noise sensitivity and compactness substantially superior to either an optics …
we demonstrate noise sensitivity and compactness substantially superior to either an optics …
Tensor decompositions meet control theory: learning general mixtures of linear dynamical systems
Abstract Recently Chen and Poor initiated the study of learning mixtures of linear dynamical
systems. While linear dynamical systems already have wide-ranging applications in …
systems. While linear dynamical systems already have wide-ranging applications in …
Generalized leverage score sampling for neural networks
Leverage score sampling is a powerful technique that originates from theoretical computer
science, which can be used to speed up a large number of fundamental questions, eg linear …
science, which can be used to speed up a large number of fundamental questions, eg linear …
The ESPRIT algorithm under high noise: Optimal error scaling and noisy super-resolution
Subspace-based signal processing techniques, such as the Estimation of Signal Parameters
via Rotational Invariant Techniques (ESPRIT) algorithm, are popular methods for spectral …
via Rotational Invariant Techniques (ESPRIT) algorithm, are popular methods for spectral …
A mathematical theory of computational resolution limit in multi-dimensional spaces
Resolving a linear combination of point sources from their Fourier data in a bounded domain
is a fundamental problem in imaging and signal processing. With incomplete Fourier data …
is a fundamental problem in imaging and signal processing. With incomplete Fourier data …
A fourier approach to mixture learning
We revisit the problem of learning mixtures of spherical Gaussians. Given samples from a
mixture $\frac {1}{k}\sum_ {j= 1}^{k}\mathcal {N}(\mu_j, I_d) $, the goal is to estimate the …
mixture $\frac {1}{k}\sum_ {j= 1}^{k}\mathcal {N}(\mu_j, I_d) $, the goal is to estimate the …
Information-theoretic perspective on performance assessment and fundamental limit of quantum imaging
Performance assessment of an imaging system is important for the optimization design with
various technologies. The information-theoretic viewpoint based on communication theory …
various technologies. The information-theoretic viewpoint based on communication theory …
Super-resolution of positive near-colliding point sources
In this paper, we analyze the capacity of super-resolution (SR) of one-dimensional positive
sources. In particular, we consider a similar setting as in Batenkov et al.(2020, Inf. Inference …
sources. In particular, we consider a similar setting as in Batenkov et al.(2020, Inf. Inference …