Related papers: More-efficient Quantum Multivariate Mean Value Est…
Quantum-enhanced (i.e., higher performance by quantum effects than any classical methods) mean value estimation of observables is a fundamental task in various quantum technologies; in particular, it is an essential subroutine in quantum…
In this paper, we will use a quantum operator which performs the inversion about the mean operation only on a subspace of the system ({\it Partial Diffusion Operator}) to propose a quantum search algorithm runs in $O(\sqrt N/M})$ for…
In this article we consider an experimental study showing the influence of emotion regulation strategies on human memory performance: part of such experimental results are difficult to explain within a classic cognitive allocation model. We…
Grover's algorithm is a quantum query algorithm solving the unstructured search problem of size $N$ using $O(\sqrt{N})$ queries. It provides a significant speed-up over any classical algorithm \cite{Gro96}. The running time of the…
The Quantum Alternating Operator Ansatz (QAOA) represents a branch of quantum algorithms for solving combinatorial optimization problems. A specific variant, the Grover-Mixer Quantum Alternating Operator Ansatz (GM-QAOA), ensures uniform…
Quantum algorithms use the principles of quantum mechanics, as for example quantum superposition, in order to solve particular problems outperforming standard computation. They are developed for cryptography, searching, optimisation,…
In this paper, we will define a quantum operator that performs the inversion about the mean only on a subspace of the system (Partial Diffusion Operator). This operator is used in a quantum search algorithm that runs in O(sqrt{N/M}) for…
We consider a generic framework of optimization algorithms based on gradient descent. We develop a quantum algorithm that computes the gradient of a multi-variate real-valued function $f:\mathbb{R}^d\rightarrow \mathbb{R}$ by evaluating it…
Let Boolean function $f:\{0,1\}^n\longrightarrow \{0,1\}$ where $|\{x\in\{0,1\}^n| f(x)=1\}|=a\geq 1$. To search for an $x\in\{0,1\}^n$ with $f(x)=1$, by Grover's algorithm we can get the objective with query times $\lfloor…
The Goldreich-Levin algorithm was originally proposed for a cryptographic purpose and then applied to learning. The algorithm is to find some larger Walsh coefficients of an $n$ variable Boolean function. Roughly speaking, it takes a…
Evaluating the expectation of a quantum circuit is a classically difficult problem known as the quantum mean value problem (QMV). It is used to optimize the quantum approximate optimization algorithm and other variational quantum…
We describe an algorithm for using a quantum computer to calculate mean values of observables and the partition function of a quantum system. Our algorithm includes two sub-algorithms. The first sub-algorithm is for calculating, with…
The logarithm-determinant is an widely-present operation in many areas of physics and computer science. Derivatives of the logarithm-determinant compute physically relevant quantities in statistical physics models, quantum field theories,…
Grover's algorithm provides a quadratic speedup over classical algorithms to search for marked elements in an unstructured database. The original algorithm is probabilistic, returning a marked element with bounded error. There are several…
We propose an improved estimator for the multi-task averaging problem, whose goal is the joint estimation of the means of multiple distributions using separate, independent data sets. The naive approach is to take the empirical mean of each…
This paper presents an enhancement to Grover's search algorithm for instances where the number of items (or the size of the search problem) $N$ is not a power of 2. By employing an efficient algorithm for the preparation of uniform quantum…
We introduce and study Multi-Quantile estimators for the parameters $( \xi, \sigma, \mu)$ of Generalized Extreme Value (GEV) distributions to provide a robust approach to extreme value modeling. Unlike classical estimators, such as the…
We consider the problem of distributed mean estimation (DME), in which $n$ machines are each given a local $d$-dimensional vector $x_v \in \mathbb{R}^d$, and must cooperate to estimate the mean of their inputs $\mu = \frac 1n\sum_{v = 1}^n…
We construct an algorithm, running in time $\tilde{\mathcal O}(N d + uK d)$, which is robust to outliers and heavy-tailed data and which achieves the subgaussian rate from [Lugosi, Mendelson] \begin{equation}\label{eq:intro_subgaus_rate}…
Multivariate Gaussian is often used as a first approximation to the distribution of high-dimensional data. Determining the parameters of this distribution under various constraints is a widely studied problem in statistics, and is often…