  We have performed density-matrix renormalization group studies of a square
lattice $t$-$J$ model with small hole doping, $\delta\ll 1$, on long 4 and 6
leg cylinders. We include frustration in the form of a second-neighbor exchange
coupling, $J_2 = J_1/2$, such that the undoped ($\delta=0$) "parent" state is a
quantum spin liquid. In contrast to the relatively short range superconducting
(SC) correlations that have been observed in recent studies of the 6-leg
cylinder in the absence of frustration, we find power law SC correlations with
a Luttinger exponent, $K_{sc} \approx 1$, consistent with a strongly diverging
SC susceptibility, $\chi \sim T^{-(2-K_{sc})}$ as the temperature $T\to 0$. The
spin-spin correlations - as in the undoped state - fall exponentially
suggesting that the SC "pairing" correlations evolve smoothly from the
insulating parent state.
