  While quantum computing provides an exponential advantage in solving linear
differential equations, there are relatively few quantum algorithms for solving
nonlinear differential equations. In our work, based on the homotopy
perturbation method, we propose a quantum algorithm for solving $n$-dimensional
nonlinear dissipative ordinary differential equations (ODEs). Our algorithm
first converts the original nonlinear ODEs into the other nonlinear ODEs which
can be embedded into finite-dimensional linear ODEs. Then we solve the embedded
linear ODEs with quantum linear ODEs algorithm and obtain a state
$\epsilon$-close to the normalized exact solution of the original nonlinear
ODEs with success probability $\Omega(1)$. The complexity of our algorithm is
$O(g\eta T{\rm poly}(\log(nT/\epsilon)))$, where $\eta$, $g$ measure the decay
of the solution. Our algorithm provides exponential improvement over the best
classical algorithms or previous quantum algorithms in $n$ or $\epsilon$.
