Liquid Nuclear Magnetic Resonance Implementation of Quantum Computation in Subspace

Based on the logical labelling method, we prepare an effective pure state in a subsystem of a three spin system via liquid nuclear magnetic resonance technique. Then with this subspace effective pure state we implement the Deutsch--Jozsa algorithm. The tomography for the subspace effective pure state and the corresponding spectrum of the output for the Deutsch--Jozsa algorithm agree with theoretical predictions, which shows that we have successfully implemented the Deutsch--Jozsa algorithm in a subsystem of a nuclear spin system and demonstrated a subspace quantum computation.