Title: Accelerating Regression Tasks with Quantum Algorithms
Primary area: optimization
Keywords: Quantum Algorithms, Regression

Abstract: Regression is a cornerstone of statistics and machine learning, with
  applications spanning science, engineering, and economics.
  While quantum algorithms for regression have attracted considerable attention,
  most existing work has focused on linear regression, leaving many more complex
  yet practically important variants unexplored.
  In this work, we present a unified quantum framework for accelerating a broad
  class of regression tasks---including linear and multiple regression, Lasso,
  Ridge, Huber, $\ell_p$-, and $\delta_p$-type regressions---achieving up to a
  quadratic improvement in the number of samples $m$ over the best classical
  algorithms.
  This speedup is achieved by extending the recent classical breakthrough of
 Jambulapati et al. (STOC'24) using several quantum techniques, including
  quantum leverage score approximation (Apers &Gribling, 2024) and the
  preparation of many copies of a quantum state (Hamoudi, 2022).
  For problems of dimension $n$, sparsity $r < n$, and error parameter
  $\epsilon$, our algorithm solves the problem in
  $\widetilde{O}(r\sqrt{mn}/\epsilon + \mathrm{poly}(n,1/\epsilon))$
  quantum time, demonstrating both the applicability and the efficiency of
  quantum computing in accelerating regression tasks.

TL;DR: We develop a unified quantum framework that accelerates a broad range of regression tasks (linear, Lasso, Ridge, Huber, $\ell_p$, etc.), achieving quadratic runtime improvements in data size.