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Preparing a Fast Pauli Decomposition for Variational Quantum Solving Linear Equations.
- Source :
-
Annalen der Physik . Nov2023, Vol. 535 Issue 11, p1-8. 8p. - Publication Year :
- 2023
-
Abstract
- Solving linear equations is a basic and significant mathematical task, and it can be executed by variational quantum algorithm (VQA) with quantum advantages by leveraging near‐term quantum device and classical optimizer. In the above algorithm, the coefficient matrix should be decomposed first but slowly with the traditional method, for realizing an effective quantum circuit. In this paper, a general framework for preparing a fast Pauli decomposition for solving arbitrary linear equations using VQA is proposed. This method has a simpler form and reduces the complexity of matrix decomposition compared with the traditional one. Moreover, the concrete tables of two and three qubits cases are given for looking up quickly and the instances of Toeplitz matrix, Yule–Walker, and arbitrary equations are demonstrated. Finally, numerical simulations are given to verify this method. This work provides a more convenient and faster preparatory phase for solving linear equations using VQA. [ABSTRACT FROM AUTHOR]
- Subjects :
- *TOEPLITZ matrices
*MATRIX decomposition
*QUBITS
*QUANTUM computing
Subjects
Details
- Language :
- English
- ISSN :
- 00033804
- Volume :
- 535
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- Annalen der Physik
- Publication Type :
- Academic Journal
- Accession number :
- 173553445
- Full Text :
- https://doi.org/10.1002/andp.202300212