This paper presents our theoretical and nuclear magnetic resonance(NMR) experimental work on several QIPs including quantum super dense coding (QSDC), quantum algorithms, quantum error correction, and decoherence-free subspace. The main contents are, 1) Using NMR technique, we realize two kinds of QSDC. The experimental results show that QSDC only needs to transfer (N-1) qubits during transmitting N bits classical information; 2) On NMR quantum computers, we realize three kinds of quantum algorithms that including four-qubit summing algorithm, four-qubit Deutsch-like algorithm and seven-qubit Deutsch-Jozsa algorithm. 3) We present a quantum error correction scheme based on quantum cloning. This scheme shows the relationship between quantum cloning and quantum error correction. 4) To avoid decoherence in quantum algorithms, we construct a decoherence-free subspace (DFS) by using multiple quantum coherences. The validity of this DFS is also experimentally verified on our NMR quantum computers. The DFS makes the three unaddressed protons in a CH3 group distinguished in two-dimensional (2D) NMR. It can protect against more error operators. This idea may provide new insights into extending the number of qubits in the sense that it effectively utilizes the magnetically equivalent nuclei.