  Cooling the qubit into a pure initial state is crucial for realizing
fault-tolerant quantum information processing. Here we envisage a star-topology
arrangement of reset and computation qubits for this purpose. The reset qubits
cool or purify the computation qubit by transferring its entropy to a heat-bath
with the help of a heat-bath algorithmic cooling procedure. By combining
standard NMR methods with powerful quantum control techniques, we cool central
qubits of two large star topology systems, with 13 and 37 spins respectively.
We obtain polarization enhancements by a factor of over 24, and an associated
reduction in the spin temperature from 298 K down to 12 K. Exploiting the
enhanced polarization of computation qubit, we prepare combination-coherences
of orders up to 15. By benchmarking the decay of these coherences we
investigate the underlying noise process. Further, we also cool a pair of
computation qubits and subsequently prepare them in an effective pure-state.
