Walker, E.; Gupta, S.; Prabhu, A.; Simha Velpur, S.C.; Rongali, M.S. Teaching Quantum Algorithms Using the Harmonic Oscillator Example. Preprints2023, 2023101030. https://doi.org/10.20944/preprints202310.1030.v1
APA Style
Walker, E., Gupta, S., Prabhu, A., Simha Velpur, S.C., & Rongali, M.S. (2023). Teaching Quantum Algorithms Using the Harmonic Oscillator Example. Preprints. https://doi.org/10.20944/preprints202310.1030.v1
Chicago/Turabian Style
Walker, E., Sri Charan Simha Velpur and Mary Sharmila Rongali. 2023 "Teaching Quantum Algorithms Using the Harmonic Oscillator Example" Preprints. https://doi.org/10.20944/preprints202310.1030.v1
Abstract
This Article demonstrates how an eigendecomposition problem is inputted into a quantum circuit, how gates are applied in the quantum circuit, and how the output measurements are the correct eigenvalues. This process is known as quantum phase estimation (QPE). A quantum harmonic oscillator example, a foundational quantum physical chemistry problem, is demonstrated within the context of QPE. A particle in a box example, another quantum physical chemistry problem, may be solved by QPE with a caveat. These examples are of the limiting cases of diagonal matrices. Future advances in taking matrix inverses for solving linear sets of equations or finding ground state energies in the Schrödinger equation will use the principles implemented in this Article.
Chemistry and Materials Science, Theoretical Chemistry
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
