Quantum Chaos: Two Papers
Two new papers in Phys Rev E address quantum (computing) chaos for very different purposes. I haven't yet had time to digest them thoroughly, but thought others might be interested.
The first one (PRE 74, 035203) analyzes Shor's algorithm and is heavy on the math and jargon, but if I understand it right, implies that the states necessary for Shor demonstrate chaos, i.e. are sensitive to small perturbations. This would, I think, be bad news for Shor. They simplify the algorithm to the point that they treat the modular exponentiation as a single step, and the QFT as a single step, which of course is not very representative of the way the algorithm will really be run (I believe), but that doesn't mean that their analysis is necessarily off base. I've discussed this issue of real-world perturbations and Shor's alogithm with a number of people in the last couple of years, and I'm not completely satisfied with the answer yet. Probably I'm just being dense, or my intuition is off somewhere, but in my opinion, there is still work to do here, and this paper comes at the problem from a different angle.
The second paper (PRE 74, 026208) analyzes the all-silicon NMR quantum computer being developed by the Yamamoto group at Stanford and the Itoh group at Keio (see PRL 89, 017901 and a whole string of papers both earlier and later). The paper appears to be good news, saying that the strong magnetic fields help suppress chaos. (Disclaimer: I work with the Keio and Stanford people.)