  We investigate the sign problem in 0+1 dimensional QCD at finite chemical
potential by using the path optimization method. The SU(3) link variable is
complexified to the SL(3,$\mathbb{C}$) link variable, and the integral path is
represented by a feedforward neural network. The integral path is then
optimized to weaken the sign problem. The average phase factor is enhanced to
be greater than 0.99 on the optimized path. Results with and without
diagonalized gauge fixing are compared and proven to be consistent. This is the
first step of applying the path optimization method to gauge theories.
