  The eligibility of various advanced quantum algorithms will be questioned if
they can not guarantee privacy. To fill this knowledge gap, here we devise an
efficient quantum differentially private (QDP) Lasso estimator to solve sparse
regression tasks. Concretely, given $N$ $d$-dimensional data points with $N\ll
d$, we first prove that the optimal classical and quantum non-private Lasso
requires $\Omega(N+d)$ and $\Omega(\sqrt{N}+\sqrt{d})$ runtime, respectively.
We next prove that the runtime cost of QDP Lasso is \textit{dimension
independent}, i.e., $O(N^{5/2})$, which implies that the QDP Lasso can be
faster than both the optimal classical and quantum non-private Lasso. Last, we
exhibit that the QDP Lasso attains a near-optimal utility bound
$\tilde{O}(N^{-2/3})$ with privacy guarantees and discuss the chance to realize
it on near-term quantum chips with advantages.
