Parallel quantum computing in a single ensemble quantum computer

We propose a parallel quantum computing mode for ensemble quantum computer. In this mode, some qubits are in pure states while other qubits are in mixed states. It enables a single ensemble quantum computer to perform ``single-instruction-multidata'' type of parallel computation. Parallel quantum computing can provide additional speedup in Grover's algorithm and Shor's algorithm. In addition, it also makes a fuller use of qubit resources in an ensemble quantum computer. As a result, some qubits discarded in the preparation of an effective pure state in the Schulman-Varizani and the Cleve-DiVincenzo algorithms can be reutilized.