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 $|{+}_{\frac{\pi }{4}}⟩:=1/\sqrt{2}(|0⟩+e^{i\frac{\pi }{4}}|1⟩)$ state, and the usual $|+⟩:=1/\sqrt{2}(|0⟩+|1⟩)$ 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

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• Fault-Tolerant Measurement-Based Quantum Computing with Continuous-Variable Cluster States
• Experimental demonstration of graph-state quantum secret sharing
• Experimental demonstration of a graph state quantum error-correction code
• Quantum metrology beyond the classical limit under the effect of dephasing
• Topological One-Way Quantum Computation on Verified Logical Cluster States
• Cluster-based architecture for fault-tolerant quantum computation
• Computation with Coherent States via Teleportations to and from a Quantum Bus
• Error-correcting one-way quantum computation with global entangling gates
• Edge local complementation for logical cluster states