Massively parallel hybrid quantum-classical machine learning for kernelized time-series classification - arXiv:2305.05881

Aug 4, 2026

Upload by Logic

Supervised time-series classification is widely used across finance, astronomy, biosensors, and other domains. This work develops hybrid quantum-classical machine learning that infers pairwise temporal relationships via a time-series Hamiltonian kernel (TSHK). The TSHK is built from sums of quantum-state inner products generated with a parameterized time evolution operator and then optimally weighted using multiple-kernel-learning ideas. Treating kernel weighting as differentiable convex optimization yields an end-to-end learnable QCC-net whose TSHK generalizes for kernelized methods like SVM, implemented in parallel on quantum hardware.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages23

Reading Time58 min

AccessFree to download

Introduction

Time-series classification and kernelized methods

Time-series Hamiltonian kernel (TSHK) and QCC-net

Efficient NISQ implementation and parallel deployment

Massively parallel hybrid quantum-classical machine learning for kernelized time-series classi􀀌cation arXiv :2305 .05881v1 [ quant-ph] 10 May 2023 Jack S. Baker 1 , Gilchan Park2 , Kwangmin Yu2 ,􀀃 Ara Ghukasyan 1 , Oktay Goktas 1 , and Santosh Kumar Radha 1y 1 Agnostiq Inc. , 325 Front St W, Toronto, ON M5V 2Y1 and 2 Computational Science Initiative, Brookhaven National Laboratory, Upton, New York 11973, USA (Dated: May 11, 2023) Supervised time-series classi􀀌cation garners widespread interest because of its applicability throughout a broad application domain including 􀀌nance, astronomy, biosensors, and many others. In this work, we tackle this problem with hybrid quantum-classical machine learning, deducing pairwise temporal relationships between time-series instances using a time-series Hamiltonian kernel (TSHK) . A TSHK is constructed with a sum of inner products generated by quantum states evolved using a parameterized time evolution operator. This sum is then optimally weighted using techniques derived from multiple kernel learning. Because we treat the kernel weighting step as adi􀀋erentiable convex optimization problem, our method can be regarded as an end-to-end learnable hybrid quantum-classical-convex neural network, or QCC-net, whose output is a data set-generalized kernel function suitable for use in any kernelized machine learning technique such as the support vector machine (SVM) . Using our TSHK as input to a SVM, we classify univariate and multivariate time-series using quantum circuit simulators and demonstrate the e􀀎cient parallel deployment of the algorithm to 127-qubit superconducting quantum processors using quantum multi-programming. I. INTRODUCTION Processes and systems which produce observable characteristics evolving with time are present in topics as disparate as 􀀌nance, sensor technologies, medicine, astronomy and many others. As a result, new techniques for time-series analysis have become among the most sought after in machine learning where we seek to learn temporal trends and correlations from time-series data to perform classi􀀌cation [1], anomaly detection [2, 3], regression [4], forecasting [5, 6] and to generate synthetic time-series instances [7] . Focusing on classi􀀌cation, classical machine learning has provided a zoo of algorithms where the present state-of-the-artis centered around deep learning. Popular approaches include recurrent neural networks like long-short-termmemory [8] (and its variations [9, 10]), gated recurrent units and, more recently, transformer networks [11{13] . While popular for static data (i.e. data without time dependence), kernelized methods like the wellknown support vector machine (SVM) [14] see limited use in time-series analysis. Although time-series kernel methods have been proposed [15{18], none are tailored to encode temporal trends by way of an explicit and learnable time-dependent inner product space. In this work, we show that time evolution as generated by a parameterized Hamiltonian operator within quantum mechanics is a natural approach for achieving such an objective. Indeed, by combining inner products evolved to di􀀋erent points of time, we achieve a quantum kernel function adapted for time-series data which we call the Time-Series Hamiltonian Kernel (TSHK) . 􀀃 [kyu@bnl.gov](kyu@bnl.gov)[ ](kyu@bnl.gov)[y](y research@agnostiq.ai)[ research@agnostiq.ai](y research@agnostiq.ai) The construction of the TSHK is tied to a 􀀌eld known as Multiple Kernel Learning (MKL) . In MKL, multiple kernel functions are combined using various tactics [19, 20] to give rise to a combined kernel that is by some measure superior. The TSHK is a combined kernel built using a weighted linear combination of quantum kernel functions each de􀀌ned at di􀀋erent instances of time t. These weights are chosen to maximize the separation between labeled data classes as was proposed in the well-known EasyMKL [20] algorithm. Furthermore, as was originally suggested in [2

FAQs

What is the main goal of the proposed method for time-series classification?

It targets supervised time-series classification by learning temporal relationships using a hybrid quantum-classical approach based on a time-series Hamiltonian kernel (TSHK).

How is the TSHK constructed in the method?

The TSHK is formed by summing inner products from quantum states evolved under a parameterized time evolution operator, then optimally weighting those kernel components using techniques from multiple kernel learning.

What allows the approach to be efficiently run on NISQ quantum processors?

The method uses shallow variational circuits for time evolution (leveraging an eigendecomposition-based strategy) and parallelizes the kernel-matrix computations, enabling deployment on multi-programmed superconducting processors.

Aug 4, 2026

Upload by Logic