Exploring the Hamiltonian inversion landscape

Ashley Donovan, Herschel Rabitz

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

The identification of quantum system Hamiltonians through the use of experimental data remains an important research goal. Seeking a Hamiltonian that is consistent with experimental measurements constitutes an excursion over a Hamiltonian inversion landscape, which is the quality of reproducing the data as a function of the Hamiltonian parameters. Recent theoretical work showed that with sufficient experimental data there should be local convexity about the true Hamiltonian on the landscape. The present paper builds on this result and performs simulations to test whether such convexity is observed. A gradient-based Hamiltonian search algorithm is incorporated into an inversion routine as a means to explore the local inversion landscape. The simulations consider idealized noise-free as well as noise-ridden experimental data. The results suggest that a sizable convex domain exists about the true Hamiltonian, even with a modest amount of experimental data and in the presence of a reasonable level of noise. This journal is

Original languageEnglish (US)
Pages (from-to)15615-15622
Number of pages8
JournalPhysical Chemistry Chemical Physics
Volume16
Issue number29
DOIs
StatePublished - Aug 7 2014

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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