Gradient-based QHD, a quantum Hamiltonian descent variant that inserts the gradient into the kinetic term, is claimed to converge at O(t^-2) in theory and to outperform QHD and classical methods in 2D tests.
Time-dependent hamiltonian simulation of highly oscillatory dynamics and superconvergence for schr \"o dinger equation
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Quantum Optimization via Gradient-Based Hamiltonian Descent
Gradient-based QHD, a quantum Hamiltonian descent variant that inserts the gradient into the kinetic term, is claimed to converge at O(t^-2) in theory and to outperform QHD and classical methods in 2D tests.