Quantum phase estimation for a class of generalized eigenvalue problems

Abstract

Quantum phase estimation provides a path to quantum computation of solutions to Hermitian eigenvalue problems $Hv=\lambda v$, such as those occurring in quantum chemistry. It is natural to ask whether the same technique can be applied to generalized eigenvalue problems $Av=\lambda Bv$, which arise in many areas of science and engineering. We answer this question affirmatively. A restricted class of generalized eigenvalue problems could be solved as efficiently as standard eigenvalue problems. A paradigmatic example is provided by Sturm--Liouville problems. Another example comes from linear ideal magnetohydrodynamics, where phase estimation could be used to determine the stability of magnetically confined plasmas in fusion reactors.

5 pages

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• On applications of quantum computing to plasma simulations
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• Quantum Computing for Fusion Energy Science Applications
• Quantum algorithms for the generalized eigenvalue problem
• Variational quantum algorithm for generalized eigenvalue problems and its application to the finite element method
• Detection of energy levels of a spin system on a quantum computer by probe spin evolution
• Quantum phase estimation using squeezed quasi-Bell states
• A Cutting-plane Method for Semidefinite Programming with Potential Applications on Noisy Quantum Devices
• Energy levels estimation on a quantum computer by evolution of a physical quantity
• Quantum computation of nonlinear maps
• Molecular resonance identification in complex absorbing potentials via integrated quantum computing and high-throughput computing