Level Reduction and the Quantum Threshold Theorem

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.