Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Optimizing Multidimensional Pooling for Variational Quantum Algorithms

Mingyoung Jeng
,
Alvir Nobel
ORCID logo ,
Vinayak Jha
,
David Levy
ORCID logo ,
Dylan Kneidel
,
Manu Chaudhary
,
Ishraq Islam
,
Evan Baumgartner
,
Eade L Vanderhoof
,
Audrey Facer
,
Manish Singh
,
Abina Arshad
,
Esam El-Araby
* ORCID logo
Version 1 : Received: 4 January 2024 / Approved: 4 January 2024 / Online: 5 January 2024 (10:58:20 CET)

A peer-reviewed article of this Preprint also exists.

Jeng, M.; Nobel, A.; Jha, V.; Levy, D.; Kneidel, D.; Chaudhary, M.; Islam, I.; Baumgartner, E.; Vanderhoof, E.; Facer, A.; Singh, M.; Arshad, A.; El-Araby, E. Optimizing Multidimensional Pooling for Variational Quantum Algorithms. Algorithms 2024, 17, 82. Jeng, M.; Nobel, A.; Jha, V.; Levy, D.; Kneidel, D.; Chaudhary, M.; Islam, I.; Baumgartner, E.; Vanderhoof, E.; Facer, A.; Singh, M.; Arshad, A.; El-Araby, E. Optimizing Multidimensional Pooling for Variational Quantum Algorithms. Algorithms 2024, 17, 82.

Abstract

Convolutional neural networks (CNNs) have proven to be a very efficient class of machine learning (ML) architectures for handling multidimensional data by maintaining data locality, especially in the field of computer vision. Data pooling, a major component of CNNs, plays a crucial role for extracting important features of the input data and downsampling its dimensionality. Multidimensional pooling, however, is not efficiently implemented in existing ML algorithms. In particular, quantum machine learning (QML) algorithms have a tendency to ignore data locality for higher dimensions by representing/flattening multidimensional data as simple one-dimensional data. In this work, we propose using the quantum Haar transform (QHT) and quantum partial measurement for performing generalized pooling operations on multidimensional data. We present the corresponding decoherence-optimized quantum circuits for the proposed techniques along with their theoretical circuit depth analysis. Our experimental work was conducted using multidimensional data, ranging from 1-D audio data, to 2-D image data, to 3-D hyperspectral data, to demonstrate the scalability of the proposed methods. In our experiments, we utilized both noisy and noise-free quantum simulations on a state-of-the-art quantum simulator from IBM Quantum. We also show the efficiency of our proposed techniques for multidimensional data by reporting the fidelity of results.

Keywords

quantum computing; convolutional neural networks; quantum machine learning; pooling layers

Subject

Computer Science and Mathematics, Artificial Intelligence and Machine Learning

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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