Related papers: Revisiting Quantum Algorithms for Linear Regressio…
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
The computation of \(\operatorname{tr}(AB)\) is essential in quantum science and artificial intelligence, yet classical methods for \( d \)-dimensional matrices \( A \) and \( B \) require \( O(d^2) \) complexity, which becomes infeasible…
Solving linear systems of equations is an important problem in science and engineering. Many quantum algorithms, such as the Harrow-Hassidim-Lloyd (HHL) algorithm (for quantum-gate computers) and the box algorithm (for quantum-annealing…
This paper considers the projection-free sparse convex optimization problem for the vector domain and the matrix domain, which covers a large number of important applications in machine learning and data science. For the vector domain…
In this work we study quantum algorithms for Hopcroft's problem which is a fundamental problem in computational geometry. Given $n$ points and $n$ lines in the plane, the task is to determine whether there is a point-line incidence. The…
As quantum hardware rapidly advances toward the early fault-tolerant era, a key challenge is to develop quantum algorithms that are not only theoretically sound but also hardware-friendly on near-term devices. In this work, we propose a…
Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…
Motivated by the quantum speedup for dynamic programming on the Boolean hypercube by Ambainis et al. (2019), we investigate which graphs admit a similar quantum advantage. In this paper, we examine a generalization of the Boolean hypercube…
We study a new linear up to quadratic time algorithm for linear regression in the absence of strong assumptions on the underlying distributions of samples, and in the presence of outliers. The goal is to design a procedure which comes with…
We study the estimation of repeatedly nested expectations (RNEs) with a constant horizon (number of nestings) using quantum computing. We propose a quantum algorithm that achieves $\varepsilon$-error with cost $\tilde O(\varepsilon^{-1})$,…
Change-point problems have appeared in a great many applications for example cancer genetics, econometrics and climate change. Modern multiscale type segmentation methods are considered to be a statistically efficient approach for multiple…
In this paper, we present efficient quantum algorithms that are exponentially faster than classical algorithms for solving the quantum optimal control problem. This problem involves finding the control variable that maximizes a physical…
We develop several efficient algorithms for the classical \emph{Matrix Scaling} problem, which is used in many diverse areas, from preconditioning linear systems to approximation of the permanent. On an input $n\times n$ matrix $A$, this…
The widespread use of quantile regression methods depends crucially on the existence of fast algorithms. Despite numerous algorithmic improvements, the computation time is still non-negligible because researchers often estimate many…
We provide faster algorithms for approximately solving $\ell_{\infty}$ regression, a fundamental problem prevalent in both combinatorial and continuous optimization. In particular, we provide accelerated coordinate descent methods capable…
Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning techniques to impressive results in regression, classification, data-generation and reinforcement learning tasks.…
Classical optimization algorithms in machine learning often take a long time to compute when applied to a multi-dimensional problem and require a huge amount of CPU and GPU resource. Quantum parallelism has a potential to speed up machine…
Following the breakthrough work of Tardos in the bit-complexity model, Vavasis and Ye gave the first exact algorithm for linear programming in the real model of computation with running time depending only on the constraint matrix. For…
We explain the mechanism of the quantum speed-up - quantum algorithms requiring fewer computation steps than their classical equivalent - for a family of algorithms. Bob chooses a function and gives to Alice the black box that computes it.…
The $k$-means algorithm (Lloyd's algorithm) is a widely used method for clustering unlabeled data. A key bottleneck of the $k$-means algorithm is that each iteration requires time linear in the number of data points, which can be expensive…