  Recently it has been shown that time-optimal quantum computation is attained
by using the Cartan decomposition of a unitary matrix. We extend this approach
by noting that the unitary group is compact. This allows us to reduce the
execution time of a quantum algorithm $U_{\rm alg}$ further by adding an extra
gate $W$ to it. This gate $W$ sends $U_{\rm alg}$ to another algorithm $WU_{\rm
alg}$ which is executable in a shorter time than $U_{\rm alg}$. We call this
technique warp-drive. Here we show both theoretically and experimentally that
the execution time of Grover's algorithm is reduced in two-qubit NMR quantum
computer. Warp-drive is potentially a powerful tool in accelerating algorithms
and reducing the errors in any realization. of a quantum computer
