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Abstract Many quantum algorithms are developed to evaluate eigenvalues for Hermitian matrices. However, few practical approach exists for the eigenanalysis of non-Hermintian ones, such as arising from modern power systems. The main difficulty lies in the fact that, as the eigenvector matrix of a general matrix can be non-unitary, solving a general eigenvalue problem is inherently incompatible with existing unitary-gate-based quantum methods. To fill this gap, this paper introduces a Variational Quantum Universal Eigensolver (VQUE), which is deployable on noisy intermediate scale quantum computers. Our new contributions include: (1) The first universal variational quantum algorithm capable of evaluating the eigenvalues of non-Hermitian matrices—Inspired by Schur’s triangularization theory, VQUE unitarizes the eigenvalue problem to a procedure of searching unitary transformation matrices via quantum devices; (2) A Quantum Process Snapshot technique is devised to make VQUE maintain the potential quantum advantage inherited from the original variational quantum eigensolver—With additional$$O(log_{2}{N})$$ $O\left(lo{g}_{2}N\right)$ quantum gates, this method efficiently identifies whether a unitary operator is triangular with respect to a given basis; (3) Successful deployment and validation of VQUE on a real noisy quantum computer, which demonstrates the algorithm’s feasibility. We also undertake a comprehensive parametric study to validate VQUE’s scalability, generality, and performance in realistic applications. 

This paper presents Barrier-based Simplex (Bb-Simplex), a new, provably correct design for runtime assurance of continuous dynamic systems. Bb-Simplex is centered around the Simplex control architecture, which consists of a high-performance advanced controller that is not guaranteed to maintain safety of the plant, a verified-safe baseline controller, and a decision module that switches control of the plant between the two controllers to ensure safety without sacrificing performance. In Bb-Simplex, Barrier certificates are used to prove that the baseline controller ensures safety. Furthermore, Bb-Simplex features a new automated method for deriving, from the barrier certificate, the conditions for switching between the controllers. Our method is based on the Taylor expansion of the barrier certificate and yields computationally inexpensive switching conditions. We also propose extensions to Bb-Simplex to enable its use in hybrid systems, which have multiple modes each with its own dynamics, and to support its use when only approximate dynamics (not exact dynamics) are available, for both continuous and hybrid dynamic systems. We consider significant applications of Bb-Simplex to microgrids featuring advanced controllers in the form of neural networks trained using reinforcement learning. These microgrids are modeled in RTDS, an industry-standard high-fidelity, real-time power systems simulator. Our results demonstrate that Bb-Simplex can automatically derive switching conditions for complex continuous and hybrid dynamic systems, the switching conditions are not overly conservative, and Bb-Simplex ensures safety even in the presence of adversarial attacks on the neural controller when only approximate dynamics (with an error bound) are available. Our experiments to evaluate conservativeness of the switching conditions show that switches from an unsafe advanced controller to a baseline controller occur on average only a few control periods before a safety violation would have occurred.