Related papers: Efficient Quantum Algorithms related to Autocorrel…
Quantum simulation is a prominent application of quantum computers. While there is extensive previous work on simulating finite-dimensional systems, less is known about quantum algorithms for real-space dynamics. We conduct a systematic…
We study the possibility of using multilevel algorithms for the computation of correlation functions of gradient flow observables. For each point in the correlation function an approximate flow is defined which depends only on links in a…
We analyze how the choice of the sampling weight affects the efficiency of the Monte Carlo evaluation of classical time autocorrelation functions. Assuming uncorrelated sampling or sampling with constant correlation length, we propose a…
We consider autocorrelation functions for supersymmetric quantum mechanical systems (consisting of a fermion and a boson) confined in trigonometric P\"oschl-Teller partner potentials. We study the limit of rescaled autocorrelation functions…
We present a computational method to automatically design the n-qubit realisations of quantum algorithms. Our approach leverages a domain-specific language (DSL) that enables the construction of quantum circuits via modular building blocks,…
We propose a new autocorrelation measure for functional time series that we term spherical autocorrelation. It is based on measuring the average angle between lagged pairs of series after having been projected onto the unit sphere. This new…
The measurement of correlations between different degrees of freedom is an important, but in general extremely difficult task in many applications of quantum mechanics. Here, we report an all-optical experimental detection and…
Analyzing large sparse electrical networks is a fundamental task in physics, electrical engineering and computer science. We propose two classes of quantum algorithms for this task. The first class is based on solving linear systems, and…
A diffusion probabilistic model (DPM) is a generative model renowned for its ability to produce high-quality outputs in tasks such as image and audio generation. However, training DPMs on large, high-dimensional datasets such as…
A quantum algorithm is exact if, on any input data, it outputs the correct answer with certainty (probability 1). A key question is: how big is the advantage of exact quantum algorithms over their classical counterparts: deterministic…
In this paper, we introduce an algorithm for performing spectral clustering efficiently. Spectral clustering is a powerful clustering algorithm that suffers from high computational complexity, due to eigen decomposition. In this work, we…
We investigate the problem of recovering coefficients in scalar nonlinear ordinary differential equations that can be exactly linearized. This contribution builds upon prior work by Lyakhov, Gerdt, and Michels, which focused on obtaining a…
Quantum entanglement is known as a unique quantum feature that cannot be obtained by classical physics. Over the last several decades, however, such an understanding on quantum entanglement might have confined us in a limited world of weird…
Stochastic spectral methods have achieved great success in the uncertainty quantification of many engineering problems, including electronic and photonic integrated circuits influenced by fabrication process variations. Existing techniques…
We present a novel approach to quantum algorithms, by taking advantage of modular values, i.e., complex and unbounded quantities resulting from specific post-selected measurement scenarios. Our focus is on the problem of ascertaining…
Feedback-based quantum algorithms (FQAs) operate by iteratively growing a quantum circuit to optimize a given task. At each step, feedback from qubit measurements is used to inform the next quantum circuit update. In practice, the sampling…
We achieve essentially the largest possible separation between quantum and classical query complexities. We do so using a property-testing problem called Forrelation, where one needs to decide whether one Boolean function is highly…
The problem "Given a Boolean function $f$ of $n$ variables by its truth table vector. Find (if exists) a vector $\alpha \in \{0,1\}^n$ of maximal (or minimal) weight, such that $f(\alpha)= 1$." is considered here. It is closely related to…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…
Probably the simplest and most frequently used way to illustrate the power of quantum computing is to solve the so-called {\it Deutsch's problem}. Consider a Boolean function $f: \{0,1\} \to \{0,1\}$ and suppose that we have a (classical)…