Related papers: Efficient recovery of variational quantum algorith…
In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…
The Quantum Approximate Optimization Algorithm (QAOA) adopts a hybrid quantum-classical approach to find approximate solutions to variational optimization problems. In fact, it relies on a classical subroutine to optimize the parameters of…
Motivated by the recent advancement of quantum processors, we investigate quantum approximate optimization algorithm (QAOA) to employ quasi-maximum-likelihood (ML) decoding of classical channel codes. QAOA is a hybrid quantum-classical…
The Quantum Approximate Optimization Algorithm (QAOA), which is a variational quantum algorithm, aims to give sub-optimal solutions of combinatorial optimization problems. It is widely believed that QAOA has the potential to demonstrate…
Due to excessive need for faster propagations of signals and necessity to reduce number of measurements and rapidly increase efficiency, new sensing theories have been proposed. Conventional sampling approaches that follow Shannon-Nyquist…
We study the computational cost of recovering a unit-norm sparse principal component $x \in \mathbb{R}^n$ planted in a random matrix, in either the Wigner or Wishart spiked model (observing either $W + \lambda xx^\top$ with $W$ drawn from…
Hybrid quantum-classical algorithms such as the quantum approximate optimization algorithm (QAOA) are considered one of the most promising approaches for leveraging near-term quantum computers for practical applications. Such algorithms are…
Structured variational quantum algorithms such as the Quantum Approximate Optimisation Algorithm (QAOA) have emerged as leading candidates for exploiting advantages of near-term quantum hardware. They interlace classical computation, in…
In this paper, we propose a general scale invariant approach for sparse signal recovery via the minimization of the $q$-ratio sparsity. When $1 < q \leq \infty$, both the theoretical analysis based on $q$-ratio constrained minimal singular…
Compressed sensing has a wide range of applications that include error correction, imaging, radar and many more. Given a sparse signal in a high dimensional space, one wishes to reconstruct that signal accurately and efficiently from a…
Sparse modeling is one of the efficient techniques for imaging that allows recovering lost information. In this paper, we present a novel iterative phase-retrieval algorithm using a sparse representation of the object amplitude and phase.…
Recovering complex-valued image recovery from noisy indirect data is important in applications such as ultrasound imaging and synthetic aperture radar. While there are many effective algorithms to recover point estimates of the magnitude,…
In many data acquisition systems it is common to observe signals whose amplitudes have been clipped. We present two new algorithms for recovering a clipped signal by leveraging the model assumption that the underlying signal is sparse in…
We investigate the reconstruction of multivariate functions from samples using sparse recovery techniques. For Square Root Lasso, Orthogonal Matching Pursuit, and Compressive Sampling Matching Pursuit, we demonstrate both theoretically and…
The Quantum Approximate Optimization Algorithm (QAOA) is a highly promising variational quantum algorithm that aims to solve combinatorial optimization problems that are classically intractable. This comprehensive review offers an overview…
Sparse recovery is widely applied in many fields, since many signals or vectors can be sparsely represented under some frames or dictionaries. Most of fast algorithms at present are based on solving $l^0$ or $l^1$ minimization problems and…
We analyze a practical algorithm for sparse PCA on incomplete and noisy data under a general non-random sampling scheme. The algorithm is based on a semidefinite relaxation of the $\ell_1$-regularized PCA problem. We provide theoretical…
We show the potential of greedy recovery strategies for the sparse approximation of multivariate functions from a small dataset of pointwise evaluations by considering an extension of the orthogonal matching pursuit to the setting of…
Spectrum sensing is an important process in cognitive radio. A number of sensing techniques that have been proposed suffer from high processing time, hardware cost and computational complexity. To address these problems, compressive sensing…
Variational Quantum optimization algorithms, such as the Variational Quantum Eigensolver (VQE) or the Quantum Approximate Optimization Algorithm (QAOA), are among the most studied quantum algorithms. In our work, we evaluate and improve an…