Related papers: Quantum Multi-Level Estimation of Functionals of D…
Finite-sum optimization has wide applications in machine learning, covering important problems such as support vector machines, regression, etc. In this paper, we initiate the study of solving finite-sum optimization problems by quantum…
The quantum algorithms for Monte Carlo integration (QMCI), which are based on quantum amplitude estimation (QAE), speed up expected value calculation compared with classical counterparts, and have been widely investigated along with their…
The simulation of electronic properties is a pivotal issue in modern electronic structure theory, driving significant efforts over the past decades to develop protocols for computing energy derivatives. In this work, we address this problem…
Nonuniform subsampling methods are effective to reduce computational burden and maintain estimation efficiency for massive data. Existing methods mostly focus on subsampling with replacement due to its high computational efficiency. If the…
Distributed quantum computation is often proposed to increase the scalability of quantum hardware, as it reduces cooperative noise and requisite connectivity by sharing quantum information between distant quantum devices. However, such…
We present quantum algorithms for sampling from non-logconcave probability distributions in the form of $\pi(x) \propto \exp(-\beta f(x))$. Here, $f$ can be written as a finite sum $f(x):= \frac{1}{N}\sum_{k=1}^N f_k(x)$. Our approach is…
Partial differential equation is a powerful tool to characterize various physics systems. In practice, measurement errors are often present and probability models are employed to account for such uncertainties. In this paper, we present a…
Many quantum algorithms involve the evaluation of expectation values. Optimal strategies for estimating a single expectation value are known, requiring a number of state preparations that scales with the target error $\varepsilon$ as…
We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…
Quantum-phase-estimation algorithms are critical subroutines in many applications for quantum computers and in quantum-metrology protocols. These algorithms estimate the unknown strength of a unitary evolution. By using coherence or…
Considering the issue of estimating small probabilities p, ie. measuring a rare domain F = {x | g(x) > q} with respect to the distribution of a random vector X, Multilevel Splitting strategies (also called Subset Simulation) aim at writing…
In this paper, we apply quasi-Monte Carlo (QMC) methods with an initial preintegration step to estimate cumulative distribution functions and probability density functions in uncertainty quantification (UQ). The distribution and density…
We present a fast, differentially private algorithm for high-dimensional covariance-aware mean estimation with nearly optimal sample complexity. Only exponential-time estimators were previously known to achieve this guarantee. Given $n$…
The quantum Fisher information matrix (QFIM) is central to multiparameter quantum metrology, dictating the attainable sensitivity via the quantum Cram\'er-Rao bound. In this work, we investigate the ultimate precision limits for…
In this thesis, we present optimization tools for different problems in quantum information theory. First, we introduce an algorithm for quantum estate estimation. The algorithm consists of orthogonal projections on intersecting…
This work studies the estimation of many statistical quantiles under differential privacy. More precisely, given a distribution and access to i.i.d. samples from it, we study the estimation of the inverse of its cumulative distribution…
We present two analytical formulae for estimating the sensitivity -- namely, the gradient or Jacobian -- at given realizations of an arbitrary-dimensional random vector with respect to its distributional parameters. The first formula…
We address the interaction-time optimization for frequency estimation in a two-level system. The goal is to estimate with maximum precision a stochastic perturbation. Our approach is valid for any figure of merit used to define optimality,…
In this work we consider practical implementations of Kitaev's algorithm for quantum phase estimation. We analyze the use of phase shifts that simplify the estimation of successive bits in the estimation of unknown phase $\varphi$. By using…
Estimating quantum entropies and divergences is an important problem in quantum physics, information theory, and machine learning. Quantum neural estimators (QNEs), which utilize a hybrid classical-quantum architecture, have recently…