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This dissertation treats the topics of threshold calculation, ancillaconstruction, and non-standard error models. Chapter 2 introduces backgroundmaterial ranging from quantum mechanics to classical coding to thresholds forquantum computation. In Chapter 3 numerical and analytical means are used togenerate estimates of and bounds on the threshold given an error modeldescribed by a restricted stochastic Pauli channel. Chapter 4 develops asimple, flexible means of estimating the threshold and applies it to some casesof interest. Finally, a novel method of ancilla construction is proposed inChapter 5, and the difficulties associated with implementing it are discussed.

Error Channels and the Threshold for Fault-tolerant Quantum Computation