  We show experimental results demonstrating multiple rounds of heat-bath
algorithmic cooling in a 3 qubit solid-state nuclear magnetic resonance quantum
information processor. By dynamically pumping entropy out of the system of
interest and into the heat-bath, we are able show purification of a single
qubit to a polarization 1.69 times that of the heat-bath and thus go beyond the
Shannon bound for closed system cooling. The cooling algorithm implemented
requires both high fidelity coherent control and a deliberate controlled
interaction with the environment. We discuss the improvements in control that
allowed this demonstration. This experimental work shows that given this level
of quantum control in systems with sufficiently large polarizations, nearly
pure qubits should be achievable.
