  The quantum threshold theorem shows that a noisy quantum computer can
accurately and efficiently simulate any ideal quantum computation provided that
noise is weakly correlated and its strength is below a critical value known as
the quantum accuracy threshold. This thesis provides a simpler and more
transparent non-inductive proof of this theorem based on the concept of level
reduction. This concept is also used in proving the quantum threshold theorem
for coherent and leakage noise and for quantum computation by measurements. In
addition, the proof provides a methodology which allows us to establish
improved rigorous lower bounds on the value of the quantum accuracy threshold.
