Introduction to Quantum Error Correction
  In this introduction we motivate and explain the ``decoding'' and ``subsystems'' view of quantum error correction. We explain how quantum noise in QIP can be described and classified, and summarize the requirements that need to be satisfied for fault tolerance. Considering the capabilities of currently available quantum technology, the requirements appear daunting. But the idea of ``subsystems'' shows that these requirements can be met in many different, and often unexpected ways. 
E. Knill, R. Laflamme, A. Ashikhmin, H. Barnum, L. Viola, W.H. Zurek