Towards Robust Quantum Computation

TL;DR

This paper explores methods to make quantum computation more practical by developing new error correction codes, fault-tolerant gates, and experimental techniques, including an NMR quantum error correction study.

Contribution

It introduces novel quantum error correction codes, fault-tolerant gate constructions, and experimental procedures to reduce resource requirements for robust quantum computing.

Findings

High rate quantum codes for amplitude damping

Relaxed criteria for quantum error correction

Experimental validation of quantum error correction in NMR

Abstract

Quantum computation is a subject of much theoretical promise, but has not been realized in large scale, despite the discovery of fault-tolerant procedures to overcome decoherence. Part of the reason is that the theoretically modest requirements still present daunting experimental challenges. The goal of this Dissertation is to reduce various resources required for robust quantum computation, focusing on quantum error correcting codes and solution NMR quantum computation. A variety of techniques have been developed, including high rate quantum codes for amplitude damping, relaxed criteria for quantum error correction, systematic construction of fault-tolerant gates, recipes for quantum process tomography, techniques in bulk thermal state computation, and efficient decoupling techniques to implement selective coupled logic gates. A detailed experimental study of a quantum error correcting code in NMR is also presented. The Dissertation clarifies and extends results previously reported in quant-ph/9610043, quant-ph/9704002, quant-ph/9811068, quant-ph/9904100, quant-ph/9906112, quant-ph/0002039. Additionally, a procedure for quantum process tomography using maximally entangled states, and a review on NMR quantum computation are included.