Related papers: Quantum Multi-Level Estimation of Functionals of D…
We present an algorithmic approach to estimate the value distributions of random variables of probabilistic loops whose statistical moments are (partially) known. Based on these moments, we apply two statistical methods, Maximum Entropy and…
Modern statistical estimation is often performed in a distributed setting where each sample belongs to a single user who shares their data with a central server. Users are typically concerned with preserving the privacy of their samples,…
We present a quantum algorithm for estimating the matrix determinant based on quantum spectral sampling. The algorithm estimates the logarithm of the determinant of an $n \times n$ positive sparse matrix to an accuracy $\epsilon$ in time…
Quantum phase estimation is one of the critical building blocks of quantum computing. For early fault-tolerant quantum devices, it is desirable for a quantum phase estimation algorithm to (1) use a minimal number of ancilla qubits, (2)…
We study the accuracy and precision for estimating the fraction of observed levels $\varphi$ in quantum chaotic spectra through long-range correlations. We focus on the main statistics where theoretical formulas for the fraction of missing…
Partial differential equation (PDE) models with multiple temporal/spatial scales are prevalent in several disciplines such as physics, engineering, and many others. These models are of great practical importance but notoriously difficult to…
We describe a quantum algorithm based on an interior point method for solving a linear program with $n$ inequality constraints on $d$ variables. The algorithm explicitly returns a feasible solution that is $\varepsilon$-close to optimal,…
Real-world time series data often exhibits substantial missing values, posing challenges for advanced analysis. A common approach to addressing this issue is imputation, where the primary challenge lies in determining the appropriate values…
Multilevel Splitting methods, also called Sequential Monte-Carlo or \emph{Subset Simulation}, are widely used methods for estimating extreme probabilities of the form $P[S(\mathbf{U}) > q]$ where $S$ is a deterministic real-valued function…
We propose an efficient block-encoding technique for the implementation of the Linear Combination of Hamiltonian Simulations (LCHS) for simulating dissipative initial-value problems. This algorithm approximates a target nonunitary operator…
Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for…
We propose communication-efficient distributed estimation and inference methods for the transelliptical graphical model, a semiparametric extension of the elliptical distribution in the high dimensional regime. In detail, the proposed…
This paper presents a quantum algorithm for efficiently computing partial sums and specific weighted partial sums of quantum state amplitudes. Computation of partial sums has important applications, including numerical integration,…
We propose a Jacobi-style distributed algorithm to solve convex, quadratically constrained quadratic programs (QCQPs), which arise from a broad range of applications. While small to medium-sized convex QCQPs can be solved efficiently by…
The limited number of qubits per chip remains a critical bottleneck in quantum computing, motivating the use of distributed architectures that interconnect multiple quantum processing units (QPUs). However, executing quantum algorithms…
This paper introduces a numerical framework for establishing lower bounds on the conditional von-Neumann entropy in device-independent quantum cryptography and randomness extraction scenarios. Leveraging a hierarchy of semidefinite programs…
We introduce a distributed resource allocation framework for the Quantum Internet that relies on feedback-based, fully decentralized coordination to serve multiple co-existing applications. We develop quantum network control algorithms…
We present quantum algorithms to efficiently perform discriminant analysis for dimensionality reduction and classification over an exponentially large input data set. Compared with the best-known classical algorithms, the quantum algorithms…
We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an…
The expectation-maximization (EM) algorithm is a powerful computational technique for finding the maximum likelihood estimates for parametric models when the data are not fully observed. The EM is best suited for situations where the…