State preparation and evolution in quantum computing: a perspective from Hamiltonian moments
Abstract
Quantum algorithms on the noisy intermediatescale quantum (NISQ) devices are expected to simulate quantum systems that are classically intractable to demonstrate quantum advantages. However, the nonnegligible gate error on the NISQ devices impedes the conventional quantum algorithms to be implemented. Practical strategies usually exploit hybrid quantum classical algorithms to demonstrate potentially useful applications of quantum computing in the NISQ era. Among the numerous hybrid algorithms, recent efforts highlight the development of quantum algorithms based upon quantum computed Hamiltonian moments, $\langle \phi  \hat{\mathcal{H}}^n  \phi \rangle$ ($n=1,2,\cdots$), with respect to quantum state $\phi\rangle$. 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 foursite Heisenberg model, and compute the energy and magnetization of the model utilizing the imaginary time evolution in the real IBMQ 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.12790
 Bibcode:
 2021arXiv210912790A
 Keywords:

 Quantum Physics
 EPrint:
 Int J Quantum Chem. 2021