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Quantum algorithm for solving a quadratic nonlinear system of equations
- Source :
- Physical Review A. 106
- Publication Year :
- 2022
- Publisher :
- American Physical Society (APS), 2022.
-
Abstract
- Solving a quadratic nonlinear system of equations (QNSE) is a fundamental, but important, task in nonlinear science. We propose an efficient quantum algorithm for solving $n$-dimensional QNSE. Our algorithm embeds QNSE into a finite-dimensional system of linear equations using the homotopy perturbation method and a linearization technique; then we solve the linear equations with a quantum linear system solver and obtain a state which is $\epsilon$-close to the normalized exact solution of the QNSE with success probability $\Omega(1)$. The complexity of our algorithm is $O({\rm polylog}(n/\epsilon))$, which provides an exponential improvement over the optimal classical algorithm in dimension $n$, and the dependence on $\epsilon$ is almost optimal. Therefore, our algorithm exponentially accelerates the solution of QNSE and has wide applications in all kinds of nonlinear problems, contributing to the research progress of nonlinear science.<br />Comment: 12 pages
Details
- ISSN :
- 24699934 and 24699926
- Volume :
- 106
- Database :
- OpenAIRE
- Journal :
- Physical Review A
- Accession number :
- edsair.doi.dedup.....bf339e9adf13d74380e9a717d96bddfd