Fault-tolerant quantum computation with cluster states

The one-way quantum computing model introduced by Raussendorf and Briegel [Phys. Rev. Lett. 86, 5188 (2001)] shows that it is possible to quantum compute using only a fixed entangled resource known as a cluster state, and adaptive single-qubit measurements. This model is the basis for several practical proposals for quantum computation, including a promising proposal for optical quantum computation based on cluster states [M. A. Nielsen, Phys. Rev. Lett. (to be published), quant-ph/0402005]. A significant open question is whether such proposals are scalable in the presence of physically realistic noise. In this paper we prove two threshold theorems which show that scalable fault-tolerant quantum computation may be achieved in implementations based on cluster states, provided the noise in the implementations is below some constant threshold value. Our first threshold theorem applies to a class of implementations in which entangling gates are applied deterministically, but with a small amount of noise. We expect this threshold to be applicable in a wide variety of physical systems. Our second threshold theorem is specifically adapted to proposals such as the optical cluster-state proposal, in which nondeterministic entangling gates are used. A critical technical component of our proofs is two powerful theorems which relate the properties of noisy unitary operations restricted to act on a subspace of state space to extensions of those operations acting on the entire state space. We expect these theorems to have a variety of applications in other areas of quantum-information science.

Traditional architecture in the Pacific

Architecture of the Pacific covers a region of more than third of the earth’s surface. The sparse Pacific population spreads over some 30 000 islands, which graduate in size from small atolls to the largest island, Australia, a continent. Pacific architecture can be studied as four cultural units: Micronesia, Polynesia, Melanesia, and Australasia (Australia and New Zealand). While many of the islands of Micronesia lie above the Equator, the remaining Pacific islands are in the southern hemisphere. With the exception of Australia, most of the islands have a warm and humid tropical climate with high rainfalls and lush vegetation. Some islands lie in the cyclonic and earthquake belts. Two distinct racial groups settled the region. The indigenous people, the Micronesians, Melanesians, Polynesians, Australian Aborigines and New Zealand Maoris, migrated from Asia thousands of years ago. The second group, the recent immigrants, were Europeans, who occupied the region during the last two centuries, and pockets of Asians brought in by colonial administrations as labourers during the early twentieth century.