Related papers: Quantum estimation bound of Gaussian matrix perman…
Known quantum error correction schemes are typically able to take advantage of only a limited class of classical error-correcting codes. Entanglement-assisted quantum error correction is a partial solution which made it possible to exploit…
The goal of this paper is to show that a single robust estimator of the mean of a multivariate Gaussian distribution can enjoy five desirable properties. First, it is computationally tractable in the sense that it can be computed in a time…
Quantum metrology holds the promise of an early practical application of quantum technologies, in which measurements of physical quantities can be made with much greater precision than what is achievable with classical technologies. In this…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
Identifying the boundary beyond which quantum machines provide a computational advantage over their classical counterparts is a crucial step in charting their usefulness. Gaussian Boson Sampling (GBS), in which photons are measured from a…
The Expectation-Maximization (EM) algorithm is a fundamental tool in unsupervised machine learning. It is often used as an efficient way to solve Maximum Likelihood (ML) estimation problems, especially for models with latent variables. It…
The computational cost for inference and prediction of statistical models based on Gaussian processes with Mat\'ern covariance functions scales cubicly with the number of observations, limiting their applicability to large data sets. The…
Amplitude estimation algorithms are based on Grover's algorithm: alternating reflections about the input state and the desired outcome. But what if we are given the ability to perform arbitrary rotations, instead of just reflections? In…
Since its introduction Boson Sampling has been the subject of intense study in the world of quantum computing. The task is to sample independently from the set of all $n \times n$ submatrices built from possibly repeated rows of a larger $m…
Quantum error correction is essential for robust quantum information processing with noisy devices. As bosonic quantum systems play a crucial role in quantum sensing, communication, and computation, it is important to design error…
We study the algorithmic problem of robust mean estimation of an identity covariance Gaussian in the presence of mean-shift contamination. In this contamination model, we are given a set of points in $\mathbb{R}^d$ generated i.i.d. via the…
Generalized master equations (GMEs) -- time-local but generally neither trace-preserving nor Hermiticity-preserving -- are convenient tools to compute properties of the environment of an open or continuously monitored quantum system. A…
Quantum error mitigation has been proposed as a means to combat unwanted and unavoidable errors in near-term quantum computing without the heavy resource overheads required by fault tolerant schemes. Recently, error mitigation has been…
1. A standard Gaussian random matrix has full rank with probability 1 and is well-conditioned with a probability quite close to 1 and converging to 1 fast as the matrix deviates from square shape and becomes more rectangular. 2. If we…
We study some extensions of Grover's quantum searching algorithm. First, we generalize the Grover iteration in the light of a concept called amplitude amplification. Then, we show that the quadratic speedup obtained by the quantum searching…
The estimation of the density matrix of a $k$-level quantum system is studied when the parametrization is given by the real and imaginary part of the entries and they are estimated by independent measurements. It is established that the…
Consider a statistical model with an epistemic restriction such that, unlike in classical mechanics, the allowed distribution of positions is fundamentally restricted by the form of an underlying momentum field. Assume an agent (observer)…
We consider a general model of unitary parameter estimation in presence of Markovian noise, where the parameter to be estimated is associated with the Hamiltonian part of the dynamics. In absence of noise, unitary parameter can be estimated…
In this work, we consider the deterministic optimization using random projections as a statistical estimation problem, where the squared distance between the predictions from the estimator and the true solution is the error metric. In…
An important step in building a quantum computer is calibrating experimentally implemented quantum gates to produce operations that are close to ideal unitaries. The calibration step involves estimating the systematic errors in gates and…