  Parameterized quantum circuits are a promising technology for achieving a
quantum advantage. An important application is the variational simulation of
time evolution of quantum systems. To make the most of quantum hardware,
variational algorithms need to be as hardware-efficient as possible. Here we
present alternatives to the time-dependent variational principle that are
hardware-efficient and do not require matrix inversion. In relation to
imaginary time evolution, our approach significantly reduces the hardware
requirements. With regards to real time evolution, where high precision can be
important, we present algorithms of systematically increasing accuracy and
hardware requirements. We numerically analyze the performance of our algorithms
using quantum Hamiltonians with local interactions.
