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 Tₜ specified by a generator L. This algorithm requires only single-qubit and controlled-not gates and approximates the channel Tₜ=etL up to the chosen accuracy ε, with a slightly superlinear cost O((∥L∥_(1→1)t)1+1/2k/ε1/2k) 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.