Quantum phase estimation for a class of generalized eigenvalue problems

• URL: http://arxiv.org/abs/2002.08497v3
• Date: Wed, 26 Aug 2020 19:27:40 GMT
• Title: Quantum phase estimation for a class of generalized eigenvalue problems
• Authors: Jeffrey B. Parker and Ilon Joseph
• Abstract summary: Quantum phase estimation provides a path to quantum computation of solutions to Hermitian eigenvalue problems. A restricted class of generalized eigenvalue problems could be solved as efficiently as standard eigenvalue problems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $Av = \lambda B v$, 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.

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