Phase transition of computational power in the resource states for one-way quantum computation

Details Phase transition of computational power in the resource states for one-way quantum computation Phase transition of computational power in the resource states for one-way quantum computation

2007-09-11

arxiv.org/abs/0709.1729v3

New J. Phys. 10, 023010 (2008)

Physics

Quantum Physics

12 pages, 10 figures, and a Michelangelo quote. published version: some improvements in presentation following referee comment

Scientific paper

10.1088/1367-2630/10/2/023010

We study how heralded qubit losses during the preparation of a two-dimensional cluster state, a universal resource state for one-way quantum computation, affect its computational power. Above the percolation threshold we present a polynomial-time algorithm that concentrates a universal cluster state, using resources that scale optimally in the size of the original lattice. On the other hand, below the percolation threshold, we show that single qubit measurements on the faulty lattice can be efficiently simulated classically. We observe a phase transition at the threshold when the amount of entanglement in the faulty lattice directly relevant to the computational power changes exponentially.

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