  We propose a novel method to sequentially optimize arbitrary single-qubit
gates in parameterized quantum circuits for simulating real and imaginary time
evolution. The method utilizes full degrees of freedom of single-qubit gates
and therefore can potentially obtain better performance. Specifically, it
simultaneously optimizes both the axis and the angle of a single-qubit gate,
while the known methods either optimize the angle with the axis fixed, or vice
versa. It generalizes the known methods and utilizes sinusoidal cost functions
parameterized by the axis and angle of rotation. Furthermore, we demonstrate
how it can be extended to optimize a set of parameterized two-qubit gates with
excitation-conservation constraints, which includes the Hop and the
Reconfigurable Beam Splitter gates. We perform numerical experiments showing
the power of the proposed method to find ground states of typical Hamiltonians
with quantum imaginary time evolution using parameterized quantum circuits. In
addition, we show the method can be applied to real time evolution and discuss
the tradeoff between its simulation accuracy and hardware efficiency.
