State preparation and evolution in quantum computing: a perspective from Hamiltonian moments

Aulicino, Joseph C.; Keen, Trevor; Peng, Bo

doi:10.1002/qua.26853

Title: State preparation and evolution in quantum computing: a perspective from Hamiltonian moments

Journal Article · 05 March 2022 · International Journal of Quantum Chemistry

DOI:https://doi.org/10.1002/qua.26853· OSTI ID:1888003

Aulicino, Joseph C. ^[1]; Keen, Trevor ^[2];

^[1]

BATTELLE (PACIFIC NW LAB)
University of Tennessee

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.

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Research Organization:: Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Sponsoring Organization:: USDOE

DOE Contract Number:: AC05-76RL01830

OSTI ID:: 1888003

Report Number(s):: PNNL-SA-166879

Journal Information:: International Journal of Quantum Chemistry, Vol. 122, Issue 5

Country of Publication:: United States

Language:: English

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