We study the robustness of quantum computers under the influence of errors
modelled by strictly contractive channels. A channel T is defined to be
strictly contractive if, for any pair of density operators ρ,σ in its
domain, ∥Tρ−Tσ∥1≤k∥ρ−σ∥1 for some 0≤k<1 (here ∥⋅∥1 denotes the trace norm). In other words, strictly
contractive channels render the states of the computer less distinguishable in
the sense of quantum detection theory. Starting from the premise that all
experimental procedures can be carried out with finite precision, we argue that
there exists a physically meaningful connection between strictly contractive
channels and errors in physically realizable quantum computers. We show that,
in the absence of error correction, sensitivity of quantum memories and
computers to strictly contractive errors grows exponentially with storage time
and computation time respectively, and depends only on the constant k and the
measurement precision. We prove that strict contractivity rules out the
possibility of perfect error correction, and give an argument that approximate
error correction, which covers previous work on fault-tolerant quantum
computation as a special case, is possible.Comment: 14 pages; revtex, amsfonts, amssymb; made some changes (recommended
by Phys. Rev. A), updated the reference