Test of System Stability on Quantum Computer

A stability test of control engineering systems, implementable on a quantum computer, is presented in this contribution for the first time. It works for a very general class of systems which are unstable if any root of the generalized characteristic equation is localized on the right half-plane of the complex Laplace $s$-domain. Because the right half-plane is unbounded, the bilinear transformation is employed to map it onto the unit disc on the complex plane. Then, quantum implementation of the global roots and poles finding algorithm based on phase analysis is executed on the unit disc. That is, the roots of the generalized characteristic equation for the considered system are detected with quantum Grover's algorithm allowing one to obtain a quadratic speedup of this operation in comparison to the code executed on a classical computer. Unlike other stability tests, our approach can work with novel processing architecture, which will probably dominate the future of computing technology. In order to demonstrate the algorithm, we evaluate the stability of a memristor-based chaotic circuit, which is a nonlinear fractional-order system in terms of control engineering, by emulating quantum computations on a classical computer.