Optimal feedback control for the rapid preparation of a single qubit

We consider the use of feedback control during a measurement to increase the rate at which a single qubit is purified, and more generally the rate at which near-pure states may be prepared. We derive the optimal bang-bang algorithm for rapid state preparation from an initially completely mixed state when the measurement basis is unrestricted, and evaluate its performance numerically. We also consider briefly the case in which the measurement basis is fixed with respect to the state to be prepared, and describe the qualitative structure of the optimal bang-bang algorithm.Comment: 8 pages, revtex4-1, 3 pdf figures. v2: corrects an error in Eqs (12) and (13

A wave-function Monte Carlo method for simulating conditional master equations

Wave-function Monte Carlo methods are an important tool for simulating quantum systems, but the standard method cannot be used to simulate decoherence in continuously measured systems. Here we present a new Monte Carlo method for such systems. This was used to perform the simulations of a continuously measured nano-resonator in [Phys. Rev. Lett. 102, 057208 (2009)].Comment: 4 pages, revtex 4, 1 eps figure. v2: correction to Eqs (3),(9), and (11); v3 added further informatio