Using Graph States for Quantum Computation and Communication

Author: Goyal, Kovid

Year: 2009

Degree: Dissertation (Ph.D.)

Advisor: Preskill, John P.

Committee Members: Preskill, John P.; Kitaev, Alexei; Wise, Mark B.; Yeh, Nai-Chang

Option: Physics

DOI: 10.7907/WR8C-1H18

Abstract

In this work, we describe a method to achieve fault tolerant measurement based quantum computation in two and three dimensions. The proposed scheme has an threshold of 7.8*10^-3 and poly-logarithmic overhead scaling. The overhead scaling below the threshold is also studied. The scheme uses a combination of topological error correction and magic state distillation to construct a universal quantum computer on a qubit lattice. The chapters on measurement based quantum computation are written in review form with extensive discussion and illustrative examples.

In addition, we describe and analyze a family of entanglement purification protocols that provide a flexible trade-off between overhead, threshold and output quality. The protocols are studied analytically, with closed form expressions for their threshold.

Files