State preparation and evolution in quantum computing: A perspective from Hamiltonian moments
Abstract
Abstract Quantum algorithms on noisy intermediate‐scale quantum (NISQ) devices are expected to soon simulate quantum systems that are classically intractable. However, the non‐negligible gate error present on NISQ devices impedes the implementation of many purely quantum algorithms, necessitating the use of hybrid quantum‐classical algorithms. One such hybrid quantum‐classical algorithm, is based upon quantum computed Hamiltonian moments , with respect to quantum state . In this tutorial review, we will give a brief review of these quantum algorithms with focuses on the typical ways of computing Hamiltonian moments using quantum hardware and improving the accuracy of the estimated state energies based on the quantum computed moments. We also present a computation of the Hamiltonian moments of a four‐site Heisenberg model and compute the energy and magnetization of the model utilizing the imaginary time evolution on current IBM‐Q hardware. Finally, we discuss some possible developments and applications of Hamiltonian moment methods.
- Authors:
-
[2];
[3]
- Pritzker Molecular Engineering, University of Chicago Chicago Illinois USA
- Department of Physics and Astronomy University of Tennessee Knoxville Tennessee USA
- Physical Sciences and Computational Division Pacific Northwest National Laboratory Richland Washington USA
- Publication Date:
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1833097
- Resource Type:
- Publisher's Accepted Manuscript
- Journal Name:
- International Journal of Quantum Chemistry
- Additional Journal Information:
- Journal Name: International Journal of Quantum Chemistry Journal Volume: 122 Journal Issue: 5; Journal ID: ISSN 0020-7608
- Publisher:
- Wiley Blackwell (John Wiley & Sons)
- Country of Publication:
- United States
- Language:
- English
Citation Formats
Aulicino, Joseph C., Keen, Trevor, and Peng, Bo. State preparation and evolution in quantum computing: A perspective from Hamiltonian moments. United States: N. p., 2021.
Web. doi:10.1002/qua.26853.
Aulicino, Joseph C., Keen, Trevor, & Peng, Bo. State preparation and evolution in quantum computing: A perspective from Hamiltonian moments. United States. https://doi.org/10.1002/qua.26853
Aulicino, Joseph C., Keen, Trevor, and Peng, Bo. Tue .
"State preparation and evolution in quantum computing: A perspective from Hamiltonian moments". United States. https://doi.org/10.1002/qua.26853.
@article{osti_1833097,
title = {State preparation and evolution in quantum computing: A perspective from Hamiltonian moments},
author = {Aulicino, Joseph C. and Keen, Trevor and Peng, Bo},
abstractNote = {Abstract Quantum algorithms on noisy intermediate‐scale quantum (NISQ) devices are expected to soon simulate quantum systems that are classically intractable. However, the non‐negligible gate error present on NISQ devices impedes the implementation of many purely quantum algorithms, necessitating the use of hybrid quantum‐classical algorithms. One such hybrid quantum‐classical algorithm, is based upon quantum computed Hamiltonian moments , with respect to quantum state . In this tutorial review, we will give a brief review of these quantum algorithms with focuses on the typical ways of computing Hamiltonian moments using quantum hardware and improving the accuracy of the estimated state energies based on the quantum computed moments. We also present a computation of the Hamiltonian moments of a four‐site Heisenberg model and compute the energy and magnetization of the model utilizing the imaginary time evolution on current IBM‐Q hardware. Finally, we discuss some possible developments and applications of Hamiltonian moment methods.},
doi = {10.1002/qua.26853},
journal = {International Journal of Quantum Chemistry},
number = 5,
volume = 122,
place = {United States},
year = {Tue Nov 30 00:00:00 EST 2021},
month = {Tue Nov 30 00:00:00 EST 2021}
}
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