Percolation in quantum computation and

Konrad Kieling, Jens Eisert

This article is a draft of a book chapter of the book entitled "Quantum Percolation and Breakdown", to appear 2008.

Liang Cao, M. Jeng, Jennifer M. Schwarz

Antonio Acín, J. I. Cirac, Maciej Lewenstein

Terry Rudolph

I review recent results, including robust methods for ballistic linear optical quantum computing, and phases of matter defined by their quantum computational universality, which make use of percolation theory – a fascinating phenomenon of classical statistical mechanics.

K. C. Chang

Sam Morley-Short, Sara Bartolucci, Mercedes Gimeno-Segovia +3 more

Most leading proposals for linear-optical quantum computing (LOQC) use cluster states, which act as a universal resource for measurement-based (one-way) quantum computation. In ballistic approaches to LOQC, cluster states are generated passively from small entangled resource states using so-called fusion operations. Results from percolation theory have previously been used to argue that universal cluster states can be generated in the ballistic approach using schemes which exceed the critical threshold for percolation, but these results consider cluster states with unbounded size. Here we consider how successful percolation can be maintained using a physical architecture with fixed physical depth, assuming that the cluster state is continuously generated and measured, and therefore that only a finite portion of it is visible at any one point in time. We show that universal LOQC can be implemented using a constant-size device with modest physical depth, and that percolation can be exploited using simple pathfinding strategies without the need for high-complexity algorithms.