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

The non-negligible gate error present on NISQ devices impedes the implementation of conventional quantum algorithms. Practical strategies usually exploit hybrid quantum-classical algorithms to demonstrate potentially useful applications of quantum computing in the NISQ era. Recent efforts highlight the development of quantum algorithms based upon quantum computed Hamiltonian moments with respect to a given trial quantum state. In this talk, we will briefly introduce 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. We will present an example 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 on the real IBM-Q NISQ hardware. We will further discuss some practical issues associated with these algorithms, and conclude this talk by discussing some possible developments and applications in this direction in the near future.