Scaling and renormalization in fault-tolerant quantum computers

Abstract

This work is concerned with phrasing the concepts of fault-tolerant quantum computation within the framework of disordered systems, Bernoulli site percolation in particular. We show how the so-called "threshold theorems" on the possibility of fault-tolerant quantum computation with constant error rate can be cast as a renormalization (coarse-graining) of the site percolation process describing the occurrence of errors during computation. We also use percolation techniques to derive a trade-off between the complexity overhead of the fault-tolerant circuit and the threshold error rate.

4 pages, 2 eps figures; revtex4; based on talk given at the Simons Conference on Quantum and Reversible Computation, Stony Brook NY, May 28-31; minor typographical changes