Analysis of Parameterized Quantum Circuits: On the Connection Between Expressibility and Types of Quantum Gates

Expressibility is a crucial factor of a parameterized quantum circuit (PQC). In the context of variational-quantum-algorithm-based quantum machine learning (QML), a QML model composed of a highly expressible PQC and a sufficient number of qubits is theoretically capable of approximating any arbitrar...

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Main Authors: Yu Liu, Kazuya Kaneko, Kentaro Baba, Jumpei Koyama, Koichi Kimura, Naoyuki Takeda
Format: Article
Language:English
Published: IEEE 2025-01-01
Series:IEEE Transactions on Quantum Engineering
Subjects:
Online Access:https://ieeexplore.ieee.org/document/11006966/
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author Yu Liu
Kazuya Kaneko
Kentaro Baba
Jumpei Koyama
Koichi Kimura
Naoyuki Takeda
author_facet Yu Liu
Kazuya Kaneko
Kentaro Baba
Jumpei Koyama
Koichi Kimura
Naoyuki Takeda
author_sort Yu Liu
collection DOAJ
description Expressibility is a crucial factor of a parameterized quantum circuit (PQC). In the context of variational-quantum-algorithm-based quantum machine learning (QML), a QML model composed of a highly expressible PQC and a sufficient number of qubits is theoretically capable of approximating any arbitrary continuous function. While much research has explored the relationship between expressibility and learning performance, as well as the number of layers in PQCs, the connection between expressibility and PQC structure has received comparatively less attention. In this article, we analyze the connection between expressibility and the types of quantum gates within PQCs using a gradient boosting tree model and Shapley additive explanations values. Our analysis is performed on 1615 instances of PQC derived from 19 PQC topologies, each with 2&#x2013;18 qubits and 1&#x2013;5 layers. The findings of our analysis provide guidance for designing highly expressible PQCs, suggesting the integration of more X-rotation or Y-rotation gates while maintaining a careful balance with the number of <sc>cnot</sc> gates . Furthermore, our evaluation offers an additional evidence of expressibility saturation, as observed by previous studies.
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publishDate 2025-01-01
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series IEEE Transactions on Quantum Engineering
spelling doaj-art-5669e0833aeb47fcafde7acdc6e5a8652025-08-20T03:21:34ZengIEEEIEEE Transactions on Quantum Engineering2689-18082025-01-01611210.1109/TQE.2025.357148411006966Analysis of Parameterized Quantum Circuits: On the Connection Between Expressibility and Types of Quantum GatesYu Liu0https://orcid.org/0009-0009-8874-228XKazuya Kaneko1https://orcid.org/0000-0002-2017-5890Kentaro Baba2https://orcid.org/0000-0001-6879-6146Jumpei Koyama3https://orcid.org/0009-0006-9208-824XKoichi Kimura4Naoyuki Takeda5Quantum Laboratory of Fujitsu Ltd., Kawasaki, JapanMizuho&#x2013;DL Financial Technology Company Ltd., Tokyo, JapanMizuho&#x2013;DL Financial Technology Company Ltd., Tokyo, JapanQuantum Laboratory of Fujitsu Ltd., Kawasaki, JapanQuantum Laboratory of Fujitsu Ltd., Kawasaki, JapanMizuho&#x2013;DL Financial Technology Company Ltd., Tokyo, JapanExpressibility is a crucial factor of a parameterized quantum circuit (PQC). In the context of variational-quantum-algorithm-based quantum machine learning (QML), a QML model composed of a highly expressible PQC and a sufficient number of qubits is theoretically capable of approximating any arbitrary continuous function. While much research has explored the relationship between expressibility and learning performance, as well as the number of layers in PQCs, the connection between expressibility and PQC structure has received comparatively less attention. In this article, we analyze the connection between expressibility and the types of quantum gates within PQCs using a gradient boosting tree model and Shapley additive explanations values. Our analysis is performed on 1615 instances of PQC derived from 19 PQC topologies, each with 2&#x2013;18 qubits and 1&#x2013;5 layers. The findings of our analysis provide guidance for designing highly expressible PQCs, suggesting the integration of more X-rotation or Y-rotation gates while maintaining a careful balance with the number of <sc>cnot</sc> gates . Furthermore, our evaluation offers an additional evidence of expressibility saturation, as observed by previous studies.https://ieeexplore.ieee.org/document/11006966/Expressibilitynoisy intermediate-scale quantum (NISQ)parameterized quantum circuit (PQC)quantum machine learning (QML)variational quantum algorithms (VQAs)
spellingShingle Yu Liu
Kazuya Kaneko
Kentaro Baba
Jumpei Koyama
Koichi Kimura
Naoyuki Takeda
Analysis of Parameterized Quantum Circuits: On the Connection Between Expressibility and Types of Quantum Gates
IEEE Transactions on Quantum Engineering
Expressibility
noisy intermediate-scale quantum (NISQ)
parameterized quantum circuit (PQC)
quantum machine learning (QML)
variational quantum algorithms (VQAs)
title Analysis of Parameterized Quantum Circuits: On the Connection Between Expressibility and Types of Quantum Gates
title_full Analysis of Parameterized Quantum Circuits: On the Connection Between Expressibility and Types of Quantum Gates
title_fullStr Analysis of Parameterized Quantum Circuits: On the Connection Between Expressibility and Types of Quantum Gates
title_full_unstemmed Analysis of Parameterized Quantum Circuits: On the Connection Between Expressibility and Types of Quantum Gates
title_short Analysis of Parameterized Quantum Circuits: On the Connection Between Expressibility and Types of Quantum Gates
title_sort analysis of parameterized quantum circuits on the connection between expressibility and types of quantum gates
topic Expressibility
noisy intermediate-scale quantum (NISQ)
parameterized quantum circuit (PQC)
quantum machine learning (QML)
variational quantum algorithms (VQAs)
url https://ieeexplore.ieee.org/document/11006966/
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