A direct approach to fault-tolerance in measurement-based quantum computation via teleportation

Abstract

We discuss a simple variant of the one-way quantum computing model [R. Raussendorf and H.-J. Briegel, PRL 86, 5188, 2001], called the Pauli measurement model, where measurements are restricted to be along the eigenbases of the Pauli X and Y operators, while auxiliary qubits can be prepared both in the $\ket{+_{π\over 4}}:={1/\sqrt{2}}(\ket{0}+e^{i{π\over 4}}\ket{1})$ state, and the usual $\ket{+}:={1/ \sqrt{2}}(\ket{0}+\ket{1})$ state. We prove the universality of this quantum computation model, and establish a standardization procedure which permits all entanglement and state preparation to be performed at the beginning of computation. This leads us to develop a direct approach to fault-tolerance by simple transformations of the entanglement graph and preparation operations, while error correction is performed naturally via syndrome-extracting teleportations.

(v1) 5 pages, 2 figures (v2) Changed style file, 10 pages, 2 figures. New title. Added references to work by Fujii and Yamamoto (quant-ph/0611160), as well as prior work by R. Raussendorf and collaborators on topological codes. Minor revisions throughout. Submitted version