Solving the many-particle Schrodinger equation to compute eigenpairs of a Hamiltonian operator is an important application in computational science. For example, it arises in the simulation of the electronic structure of molecules and materials, as well as in mathematical optimization problems.
In this talk, the role of digital quantum computers in the determination of approximate ground and excited Hamiltonian eigenstates is examined [1,2]. The particular way in which quantum computing extends classical computing means that one cannot expect arbitrary simulations to be sped up by a quantum computer, and that areas where quantum advantage may be achieved have to be carefully identified.
The structure and salient features of an important class of quantum algorithms for Hamiltonian diagonalization [3,4] are explored, highlighting methodological strengths and weaknesses, discussing aspects of implementations on actual quantum computing devices, and presenting opportunities for synergistic use and integration of independent techniques.
References:
[1] A. Yu. Kitaev et al, “Classical and Quantum Computation”, AMS (2002)
[2] B. Bauer et al, Chem. Rev. 120, 12685-12717 (2020)
[3] M. Motta et al, Nat. Phys. 16, 205-210 (2020)
[4] R. M. Parrish and P. L. McMahon, arXiv:1909.08925 (2019)