Simulation of single-qubit open quantum systems

A quantum algorithm is presented for the simulation of arbitrary Markovian dynamics of a qubit, described by a semigroup of single-qubit quantum channels {T-t} specified by a generator L. This algorithm requires only single-qubit and controlled-NOT gates and approximates the channel T-t = e(tL) up to the chosen accuracy epsilon, with a slightly superlinear cost O((parallel to L parallel to((1 -> 1))t)(1+1/2k)/epsilon(1/2k)) for any integer k. Inspired by developments in Hamiltonian simulation, a decomposition and recombination technique is utilized which allows for the exploitation of recently developed methods for the approximation of arbitrary single-qubit channels. In particular, as a result of these methods the algorithm requires only a single ancilla qubit, the minimal possible dilation for a nonunitary single-qubit quantum channel.