Enhanced Stability in Quantum Carleman Linearization through Pivot Switching
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Quantum Carleman linearization is a prominent technique for solving nonlinear equations on quantum computers. Despite its popularity, it often requires restrictive assumptions regarding the equation's coefficients to ensure convergence and stability, even when the underlying system is stable. In this work, we propose a novel technique to improve the convergence and stability of the quantum Carleman linearization algorithm. This method relies on a quantum realization of classical pivot switching. We theoretically demonstrate the advantages of this technique in stabilizing the algorithm in general stable systems. Furthermore, we provide concrete numerical examples to validate our theory and illustrate its implications for practical applications.
