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A universal variational quantum eigensolver for non-Hermitian systems.

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This study introduces a Variational Quantum Universal Eigensolver (VQUE) for non-Hermitian matrices, crucial for power systems. VQUE is the first universal quantum algorithm for this problem, validated on real quantum hardware.

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Area of Science:

  • Quantum computing
  • Linear algebra
  • Power systems analysis

Background:

  • Quantum algorithms primarily target Hermitian matrices.
  • Eigenanalysis of non-Hermitian matrices is challenging for current quantum methods due to non-unitary eigenvectors.
  • Applications in modern power systems require efficient non-Hermitian matrix eigenanalysis.

Purpose of the Study:

  • To develop a practical quantum algorithm for the eigenanalysis of non-Hermitian matrices.
  • To enable the application of quantum computation to problems in fields like power systems.
  • To create a universal eigensolver deployable on noisy intermediate-scale quantum (NISQ) computers.

Main Methods:

  • Introduced the Variational Quantum Universal Eigensolver (VQUE), a universal variational quantum algorithm.
  • Utilized Schur's triangularization theory to transform the non-Hermitian eigenvalue problem into a search for unitary matrices.
  • Developed a Quantum Process Snapshot technique to maintain quantum advantage and efficiently test for triangularity.

Main Results:

  • VQUE is the first universal variational quantum algorithm for non-Hermitian matrix eigenvalues.
  • The algorithm was successfully deployed and validated on a real noisy quantum computer, demonstrating feasibility.
  • Parametric studies confirmed VQUE's scalability, generality, and performance in realistic scenarios.

Conclusions:

  • VQUE offers a viable quantum approach for the eigenanalysis of non-Hermitian matrices.
  • The algorithm bridges the gap between quantum methods and practical applications involving non-Hermitian matrices.
  • Successful hardware implementation paves the way for quantum advantage in complex system analysis.