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: | , , , , , |
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| Format: | Article |
| Language: | English |
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IEEE
2025-01-01
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| Series: | IEEE Transactions on Quantum Engineering |
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| Online Access: | https://ieeexplore.ieee.org/document/11006966/ |
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| _version_ | 1849689608527282176 |
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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 2–18 qubits and 1–5 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. |
| format | Article |
| id | doaj-art-5669e0833aeb47fcafde7acdc6e5a865 |
| institution | DOAJ |
| issn | 2689-1808 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IEEE |
| record_format | Article |
| 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–DL Financial Technology Company Ltd., Tokyo, JapanMizuho–DL Financial Technology Company Ltd., Tokyo, JapanQuantum Laboratory of Fujitsu Ltd., Kawasaki, JapanQuantum Laboratory of Fujitsu Ltd., Kawasaki, JapanMizuho–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 2–18 qubits and 1–5 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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