Related papers: Rational approximations and quantum algorithms wit…
This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundamental difficulty of simple bilevel problems, that the…
This paper describes a class of probabilistic approximation algorithms based on bucket elimination which offer adjustable levels of accuracy and efficiency. We analyze the approximation for several tasks: finding the most probable…
Finding a high (or low) energy state of a given quantum Hamiltonian is a potential area to gain a provable and practical quantum advantage. A line of recent studies focuses on Quantum Max Cut, where one is asked to find a high energy state…
$Q$-learning with function approximation is one of the most popular methods in reinforcement learning. Though the idea of using function approximation was proposed at least 60 years ago, even in the simplest setup, i.e, approximating…
We study the optimization of any quantum process by minimizing the "randomness" in the measurement result at the output of that quantum process. We conceptualize and propose a measure of such randomness and inquire whether an optimization…
We study the computational power of polynomial threshold functions, that is, threshold functions of real polynomials over the boolean cube. We provide two new results bounding the computational power of this model. Our first result shows…
We establish essentially optimal bounds on the complexity of initial-value problems in the randomized and quantum settings. For this purpose we define a sequence of new algorithms whose error/cost properties improve from step to step. These…
$k$-Clustering in $\mathbb{R}^d$ (e.g., $k$-median and $k$-means) is a fundamental machine learning problem. While near-linear time approximation algorithms were known in the classical setting for a dataset with cardinality $n$, it remains…
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…
This article investigates the probabilistic relationship between quantum classification of Boolean functions and their Hamming distance. By integrating concepts from quantum computing, information theory, and combinatorics, we explore how…
We define and study the complexity of robust polynomials for Boolean functions and the related fault-tolerant quantum decision trees, where input bits are perturbed by noise. We compare several different possible definitions. Our main…
In a recent preprint by Deutsch et al. [1995] the authors suggest the possibility of polynomial approximability of arbitrary unitary operations on $n$ qubits by 2-qubit unitary operations. We address that comment by proving strong lower…
We study the arbitrary cost case of the unweighted Stochastic Score Classification (SSClass) problem. We show two constant approximation algorithms and both algorithms are 6-approximation non-adaptive algorithms with respect to the optimal…
We present a simple randomized algorithm that approximates the number of satisfying assignments of Boolean formulas in conjunctive normal form. To the best of our knowledge this is the first algorithm which approximates #k-SAT for any k >=…
Quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given in a black box, but the aim is to compute function value for arbitrary input using as few queries as possible. In this paper we…
Loading classical data into quantum computers represents an essential stage in many relevant quantum algorithms, especially in the field of quantum machine learning. Therefore, the inefficiency of this loading process means a major…
The quantum approximate optimization algorithm (QAOA) is one of the most prominent proposed applications for near-term quantum computing. Here we study the ability of QAOA to solve hard constraint satisfaction problems, as opposed to…
The traditional view in numerical conformal mapping is that once the boundary correspondence function has been found, the map and its inverse can be evaluated by contour integrals. We propose that it is much simpler, and 10-1000 times…
The Pandora's Box problem and its extensions capture optimization problems with stochastic input where the algorithm can obtain instantiations of input random variables at some cost. To our knowledge, all previous work on this class of…
We propose a novel sparse preference learning/ranking algorithm. Our algorithm approximates the true utility function by a weighted sum of basis functions using the squared loss on pairs of data points, and is a generalization of the kernel…