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Variational Quantum Algorithm for Solving Second-Order Linear Differential Equations Cover

Variational Quantum Algorithm for Solving Second-Order Linear Differential Equations

Open Access
|Jul 2025

Figures & Tables

Figure 1.

Quantum circuit diagram for generating |ϕ, ψ⟩.
Quantum circuit diagram for generating |ϕ, ψ⟩.

Figure 2.

Quantum circuit diagram for UGHZ
Quantum circuit diagram for UGHZ

Figure 3.

Quantum circuit diagram for UGHZ+
Quantum circuit diagram for UGHZ+

Figure 4.

Quantum circuit diagram for UGHZ–
Quantum circuit diagram for UGHZ–

Figure 5.

Quantum circuit diagram of VBC.
Quantum circuit diagram of VBC.

Figure 6.

Quantum circuit diagram of WBC.
Quantum circuit diagram of WBC.

Figure 7.

Quantum circuit diagram for the ansatz gate U(θ).
Quantum circuit diagram for the ansatz gate U(θ).

Figure 8.

Plot of the analytical solution of Eq. (24) for 5 qubits, and the solution obtained using the proposed method.
Plot of the analytical solution of Eq. (24) for 5 qubits, and the solution obtained using the proposed method.

Relative errors, ϵc and ϵ for n = 3, 4 and 5 qubit cases_

the number of qubitsthe relative error ϵcthe relative error ϵq
3 qubits7.8455 × 10−47.8478 × 10−4
4 qubits2.2014 × 10−42.2027 × 10−4
5 qubits5.8441 × 10−54.4997 × 10−4
DOI: https://doi.org/10.2478/qic-2025-0012 | Journal eISSN: 3106-0544 | Journal ISSN: 1533-7146
Language: English
Page range: 232 - 247
Submitted on: Feb 17, 2025
Accepted on: Apr 17, 2025
Published on: Jul 1, 2025
Published by: Cerebration Science Publishing Co., Limited
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
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© 2025 Ryo Sugaya, Tomohiro Sogabe, Tomoya Kemmochi, Shao-Liang Zhang, published by Cerebration Science Publishing Co., Limited
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.