Quantum algorithms on the noisy intermediate-scale quantum (NISQ) devices are expected to simulate quan- tum systems that are classically intractable to demonstrate quantum advantages. However, the non-negligible gate error on the NISQ devices impedes the conventional quantum algorithms to be implemented. Practical strategies usually exploit hybrid quantum-classical quantum algorithms to demonstrate potentially useful ap- plications of quantum computing in the NISQ era. Among the numerous hybrid quantum-classical algorithms, recent efforts highlight the development of quantum algorithms based upon quantum computed Hamiltonian moments, ?f|Hˆn|f? (n = 1, 2, · · · ), with respect to quantum state |f?. In this tutorial, 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. Furthermore, we will present a tutorial to show how we can measure and compute the Hamiltonian moments of a four-site Heisenberg model, and compute the energy and magnetization of the model utilizing the imaginary time evolution in the real IBM-Q NISQ hardware environment. Along this line, we will further discuss some practical issues associated with these algorithms. We will conclude this tutorial review by overviewing some possible developments and applications in this direction in the near future.
Aulicino, Joseph C., et al. "State preparation and evolution in quantum computing: a perspective from Hamiltonian moments." International Journal of Quantum Chemistry, vol. 122, no. 5, Mar. 2022. https://doi.org/10.1002/qua.26853
Aulicino, Joseph C., Keen, Trevor, & Peng, Bo (2022). State preparation and evolution in quantum computing: a perspective from Hamiltonian moments. International Journal of Quantum Chemistry, 122(5). https://doi.org/10.1002/qua.26853
Aulicino, Joseph C., Keen, Trevor, and Peng, Bo, "State preparation and evolution in quantum computing: a perspective from Hamiltonian moments," International Journal of Quantum Chemistry 122, no. 5 (2022), https://doi.org/10.1002/qua.26853
@article{osti_1888003,
author = {Aulicino, Joseph C. and Keen, Trevor and Peng, Bo},
title = {State preparation and evolution in quantum computing: a perspective from Hamiltonian moments},
annote = {Quantum algorithms on the noisy intermediate-scale quantum (NISQ) devices are expected to simulate quan- tum systems that are classically intractable to demonstrate quantum advantages. However, the non-negligible gate error on the NISQ devices impedes the conventional quantum algorithms to be implemented. Practical strategies usually exploit hybrid quantum-classical quantum algorithms to demonstrate potentially useful ap- plications of quantum computing in the NISQ era. Among the numerous hybrid quantum-classical algorithms, recent efforts highlight the development of quantum algorithms based upon quantum computed Hamiltonian moments, ?f|Hˆn|f? (n = 1, 2, · · · ), with respect to quantum state |f?. In this tutorial, 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. Furthermore, we will present a tutorial to show how we can measure and compute the Hamiltonian moments of a four-site Heisenberg model, and compute the energy and magnetization of the model utilizing the imaginary time evolution in the real IBM-Q NISQ hardware environment. Along this line, we will further discuss some practical issues associated with these algorithms. We will conclude this tutorial review by overviewing some possible developments and applications in this direction in the near future.},
doi = {10.1002/qua.26853},
url = {https://www.osti.gov/biblio/1888003},
journal = {International Journal of Quantum Chemistry},
number = {5},
volume = {122},
place = {United States},
year = {2022},
month = {03}}
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 226, Issue 636-646https://doi.org/10.1098/rsta.1927.0008
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 276, Issue 1365, p. 238-257https://doi.org/10.1098/rspa.1963.0204