Quantum Random Forest for the Regression Problem

Kamil Khadiev; Liliya Safina

quant-phMar 24, 2026

Quantum Random Forest for the Regression Problem

Authors: Kamil Khadiev, Liliya Safina

Organizations: Institute of Computational Mathematics and IT, Kazan Federal University, Kazan, Russia · Zavoisky Physical-Technical Institute, FRC Kazan Scientific Center of RAS, Kazan, Russia

Abstract

The Random Forest model is one of the popular models of Machine learning. We present a quantum algorithm for testing (forecasting) process of the Random Forest machine learning model for the Regression problem. The presented algorithm is more efficient (in terms of query complexity or running time) than the classical counterpart.

Quantum Machine Learning

Quantum machine learning uses quantum circuits and quantum data to build learning algorithms and study their computational and statistical limits.

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A Quantum-Inspired Dequantization Method for Diagonally Weighted Matrix Functions: Application to Learning with Optimized Random Features

Natsuto Isogai, Mio Murao, Hayata Yamasaki

Department of Physics, Graduate School of Science, The University of Tokyo, Tokyo, Japan · Department of Computer Science, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, Japan

Quantum-Inspired ML Random Feature Methods

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Quantum-inspired classical algorithms have dequantized several quantum machine learning routines by replacing quantum linear-algebra subroutines with classical counterparts. However, the sampler based on quantum singular value transformation (QSVT) for learning with optimized random features is not covered by existing dequantization frameworks, because the matrix to be inverted is not itself available through sampling access. In this work, we develop a classical algorithm to address this type of quantum-advantage candidate. Our method samples heavy indices, reduces the transformation to a small principal block, and outputs a sparse classical representation with operator-norm guarantees. Applying this method dequantizes the sampler for optimized random features, giving a classical sampler with prescribed accuracy and polynomially related runtime. These results show that the factorization underlying a quantum block encoding can itself provide sufficient classical structure even when sampling-and-query access to the composite matrix is unavailable.

Abstract

Quantum Machine Learning

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