Related papers: Optimal Quantum Algorithm for Vector Interpolation
In some fields such as Mathematics Mechanization, automated reasoning and Trustworthy Computing etc., exact results are needed. Symbolic computations are used to obtain the exact results. Symbolic computations are of high complexity. In…
We develop and analyze a class of matrix-valued spherical-convolution kernels stemming from scaled zonal functions on $\mathbb{S}^2,$ the unit sphere embedded in $\mathbb{R}^3$. The construct of these kernels utilizes the Legendre…
Quadratically optimized polynomials are described which are useful in multi-bosonic algorithms for Monte Carlo simulations of quantum field theories with fermions. Algorithms for the computation of the coefficients and roots of these…
In the near-term, hybrid quantum-classical algorithms hold great potential for outperforming classical approaches. Understanding how these two computing paradigms work in tandem is critical for identifying areas where such hybrid algorithms…
Using the properties of quantum superposition, we propose a quantum classification algorithm to efficiently perform multi-class classification tasks, where the training data are loaded into parameterized operators which are applied to the…
Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…
It is well known that, using fast algorithms for polynomial multiplication and division, evaluation of a polynomial $F \in \mathbb{C}[x]$ of degree $n$ at $n$ complex-valued points can be done with $\tilde{O}(n)$ exact field operations in…
We give the first almost optimal polynomial-time proper learning algorithm of Boolean sparse multivariate polynomial under the uniform distribution. For $s$-sparse polynomial over $n$ variables and $\epsilon=1/s^\beta$, $\beta>1$, our…
We consider the problem of identity testing and recovering (that is, interpolating) of a "hidden" monic polynomials $f$, given an oracle access to $f(x)^e$ for $x\in\mathbb F_q$, where $\mathbb F_q$ is the finite field of $q$ elements and…
In this paper, we consider methods to compute the coefficients of interpolants relative to a basis of polynomials satisfying a three-term recurrence relation. Two new algorithms are presented: the first constructs the coefficients of the…
This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…
Achieving superpolynomial speedups for optimization has long been a central goal for quantum algorithms. Here we introduce Decoded Quantum Interferometry (DQI), a quantum algorithm that uses the quantum Fourier transform to reduce…
Ordered search is the task of finding an item in an ordered list using comparison queries. The best exact classical algorithm for this fundamental problem uses $\lceil \log_{2}{n}\rceil$ queries for a list of length $n$. Quantum computers…
For $m,n \in \mathbb{N}$, $m\geq 1$ and a given function $f : \mathbb{R}^m\longrightarrow \mathbb{R}$ the polynomial interpolation problem (PIP) is to determine a \emph{generic node set} $P \subseteq \mathbb{R}^m$ and the coefficients of…
To know which operators to apply and in which order, as well as attributing good values to their parameters is a challenge for users of computer vision. This paper proposes a solution to this problem as a multi-agent system modeled…
Quantization is a fundamental optimization for many machine-learning use cases, including compressing gradients, model weights and activations, and datasets. The most accurate form of quantization is \emph{adaptive}, where the error is…
Vector-quantized networks (VQNs) have exhibited remarkable performance across various tasks, yet they are prone to training instability, which complicates the training process due to the necessity for techniques such as subtle…
Quantum algorithm is an algorithm for solving mathematical problems using quantum systems encoded as information, which is found to outperform classical algorithms in some specific cases. The objective of this study is to develop a quantum…
This thesis focuses on the intersection of mathematical and computational optimization and quantum information. Main contributions are open-source software code: A hybrid approach mixing "traditional" nonconvex and convex methods can make…
The goal of multi-objective optimization is to understand optimal trade-offs between competing objective functions by finding the Pareto front, i.e., the set of all Pareto optimal solutions, where no objective can be improved without…