Related papers: Following Forrelation -- Quantum Algorithms in Exp…
In this work, we unify several quantum algorithmic frameworks for boolean functions that are based on the quantum adversary bound. First, we show that the $st$-connectivity framework subsumes the (adaptive/extended) learning graph…
We address the challenge of estimation in the context of constant linear effect models with dense functional responses. In this framework, the conditional expectation of the response curve is represented by a linear combination of…
In this paper we introduce the study of quantum boolean functions, which are unitary operators f whose square is the identity: f^2 = I. We describe several generalisations of well-known results in the theory of boolean functions, including…
By selecting different filter functions, spectral algorithms can generate various regularization methods to solve statistical inverse problems within the learning-from-samples framework. This paper combines distributed spectral algorithms…
Numerical calculus algorithms which estimate derivatives and integrals from data series acquired either via measurements or by sampling functions are essential in scientific computing. To date, a few quantum algorithms have been developed…
Recently the general form of a translation-covariant quantum Boltzmann equation has been derived which describes the dynamics of a tracer particle in a quantum gas. We develop a stochastic wave function algorithm that enables full…
In this paper, we study the query complexity of Boolean functions in the presence of uncertainty, motivated by parallel computation with an unlimited number of processors where inputs are allowed to be unknown. We allow each query to…
A fuzzy Boolean function is a map $f:\cube^n\to [0,1]$, where $n\in\mathbb N$. We introduce and compare three ways of saying that such a function has bounded complexity. The first is a sampling property: the value $f(x)$ can be recovered,…
We study nondeterministic quantum algorithms for Boolean functions f. Such algorithms have positive acceptance probability on input x iff f(x)=1. In the setting of query complexity, we show that the nondeterministic quantum complexity of a…
The current paper improves the number of queries of the previous quantum multi-collision finding algorithms presented by Hosoyamada et al. at Asiacrypt 2017. Let an $l$-collision be a tuple of $l$ distinct inputs that result in the same…
We examine the "Guessing Secrets" problem arising in internet routing, in which the goal is to discover two or more objects from a known finite set. We propose a quantum algorithm using O(1) calls to an O(logN) oracle. This improves upon…
Correlation clustering is a widely studied framework for clustering based on pairwise similarity and dissimilarity scores, but its best approximation algorithms rely on impractical linear programming relaxations. We present faster…
Spectral clustering is a powerful unsupervised machine learning algorithm for clustering data with non convex or nested structures. With roots in graph theory, it uses the spectral properties of the Laplacian matrix to project the data in a…
We investigate the entanglement features of the quantum states employed in quantum algorithms. In particular, we analyse the multipartite entanglement properties in the Deutsch-Jozsa, Grover and Simon algorithms. Our results show that for…
The Deutsch-Jozsa algorithm is experimentally demonstrated for three-qubit functions using pure coherent superpositions of Li$_{2}$ rovibrational eigenstates. The function's character, either constant or balanced, is evaluated by first…
A new approach to the correlation functions is presented for the XXZ model in the anti-ferroelectric regime. The method is based on the recent realization of the quantum affine symmetry using vertex operators. With the aid of a boson…
We describe the first experimental realization of the Deutsch-Jozsa quantum algorithm to evaluate the properties of a 2-bit boolean function in the framework of one-way quantum computation. For this purpose a novel two-photon six-qubit…
Two contrasting algorithmic paradigms for constraint satisfaction problems are successive local explorations of neighboring configurations versus producing new configurations using global information about the problem (e.g. approximating…
We study general correlation functions of various quantum field theories in the holographic setup. Following the holographic proposal, we investigate correlation functions via a geodesic length connecting boundary operators. We show that…
This work studies the quantum query complexity of Boolean functions in a scenario where it is only required that the query algorithm succeeds with a probability strictly greater than 1/2. We show that, just as in the communication…