  Classical-quantum hybrid algorithms have recently garnered significant
attention, which are characterized by combining quantum and classical computing
protocols to obtain readout from quantum circuits of interest. Recent progress
due to Lubasch et al in a 2019 paper provides readout for solutions to the
Schrodinger and Inviscid Burgers equations, by making use of a new variational
quantum algorithm (VQA) which determines the ground state of a cost function
expressed with a superposition of expectation values and variational
parameters. In the following, we analyze additional computational prospects in
which the VQA can reliably produce solutions to other PDEs that are comparable
to solutions that have been previously realized classically, which are
characterized with noiseless quantum simulations. To determine the range of
nonlinearities that the algorithm can process for other IVPs, we study several
PDEs, first beginning with the Navier-Stokes equations and progressing to other
equations underlying physical phenomena ranging from electromagnetism,
gravitation, and wave propagation, from simulations of the Einstein,
Boussniesq-type, Lin-Tsien, Camassa-Holm, Drinfeld-Sokolov-Wilson (DSW), and
Hunter-Saxton equations. To formulate optimization routines that the VQA
undergoes for numerical approximations of solutions that are obtained as
readout from quantum circuits, cost functions corresponding to each PDE are
provided in the supplementary section after which simulations results from
hundreds of ZGR-QFT ansatzae are generated.
