Related papers: Quantum estimation bound of Gaussian matrix perman…
In this paper, we study the problem of quantitative group testing (QGT) and analyze the performance of three models: the noiseless model, the additive Gaussian noise model, and the noisy Z-channel model. For each model, we analyze two…
Gaussian quadrature rules are a classical tool for the numerical approximation of integrals with smooth integrands and positive weight functions. We derive and expicitly list asymptotic expressions for the points and weights of Gaussian…
Gaussian quantum channels are relevant operations in continuous variable systems. In general, given an arbitrary state, the action on it is well-known provided that the quantum channels are completely characterized. In this work, we…
To estimate a sparse linear model from data with Gaussian noise, consilience from lasso and compressed sensing literatures is that thresholding estimators like lasso and the Dantzig selector have the ability in some situations to identify…
We study a classical model for the accumulation of errors in multi-qubit quantum computations. By modeling the error process in a quantum computation using two coupled Markov chains, we are able to capture a weak form of time-dependency…
Gaussian Boson Sampling (GBS), which can be realized with a photonic quantum computing model, perform some special kind of sampling tasks. In [4], we introduced algorithms that use GBS samples to approximate Gaussian expectation problems.…
Practical Bayes filters often assume the state distribution of each time step to be Gaussian for computational tractability, resulting in the so-called Gaussian filters. When facing nonlinear systems, Gaussian filters such as extended…
The use of Gaussian processes (GPs) is supported by efficient sampling algorithms, a rich methodological literature, and strong theoretical grounding. However, due to their prohibitive computation and storage demands, the use of exact GPs…
In 1-bit compressive sensing, each measurement is quantized to a single bit, namely the sign of a linear function of an unknown vector, and the goal is to accurately recover the vector. While it is most popular to assume a standard Gaussian…
Quantum measurements and the associated state changes are properly described in the language of instruments. We investigate the properties of a time continuous family of instruments associated with the recently introduced family of general…
We address the issue of knots selection for Gaussian predictive process methodology. Predictive process approximation provides an effective solution to the cubic order computational complexity of Gaussian process models. This approximation…
We address the problem of estimating the mass of a quantum particle in a gravitational field and seek the ultimate bounds to precision of quantum-limited detection schemes. In particular, we study the effect of the field on the achievable…
Maximum entropy inference and learning of graphical models are pivotal tasks in learning theory and optimization. This work extends algorithms for these problems, including generalized iterative scaling (GIS) and gradient descent (GD), to…
Generalized matrix approximation plays a fundamental role in many machine learning problems, such as CUR decomposition, kernel approximation, and matrix low rank approximation. Especially with today's applications involved in larger and…
A quantum stochastic model for an open dynamical system (quantum receiver) and output multi-channel of observation with an additive nonvacuum quantum noise is given. A quantum stochastic Master equation for the corresponding instrument is…
Experimentally realizable quantum computers are rapidly approaching the threshold of quantum supremacy. Quantum Hamiltonian simulation promises to be one of the first practical applications for which such a device could demonstrate an…
Quantum generative modeling has emerged as a promising application of quantum computers, aiming to model complex probability distributions beyond the reach of classical methods. In practice, however, training such models often requires…
Quantum algorithms for estimating the eigenvalues of matrices, including the phase estimation algorithm, serve as core subroutines in a wide range of quantum algorithms, including those in quantum chemistry and quantum machine learning. The…
Finding a good approximation of the top eigenvector of a given $d\times d$ matrix $A$ is a basic and important computational problem, with many applications. We give two different quantum algorithms that, given query access to the entries…
A desirable property of an autocovariance estimator is to be robust to the presence of additive outliers. It is well-known that the sample autocovariance, being based on moments, does not have this property. Hence, the use of an…