Simulation of single-qubit open quantum systems
Ryan Sweke, Ilya Sinayskiy, Francesco Petruccione · Physical Review A · 2014
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 $\mathcal{L}$. This algorithm requires only single-qubit and controlled-not gates and approximates the channel ${T}_{t}={e}^{t\mathcal{L}}$ up to the chosen accuracy $\ensuremath{\epsilon}$, with a slightly superlinear cost ${O((\ensuremath{\parallel}\mathcal{L}\ensuremath{\parallel}}_{(1\ensuremath{\rightarrow}1)}t{)}^{1+1/2k}/{\ensuremath{\epsilon}}^{1/2k})$ 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.