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Methods to control errors will be essential for quantum informationprocessing. It is widely believed that fault-tolerant quantum error correctionis the leading contender to achieve this goal. Although the theory offault-tolerant quantum error correction is very well understood, experimentalimplementation has been lagging. We study the feasibility of implementingrepeated rounds of quantum error correction with refreshed ancillas in solidstate nuclear magnetic resonance (NMR). In particular we study the procedureproposed for extracting entropy that consists of two stages; an errorcorrecting code optimized to function at finite temperature, and animplementation of heat-bath algorithmic cooling to refresh the ancilla qubits.Two algorithms are presented which implement this method, one for performingtests on 4 qubits, the other for practical implementation on 6 qubits. Theeffects of imperfect implementation are examined in both the error correctionand refreshing stages.

Study of Multiple Rounds of Error Correction in Solid State NMR QIP