  Quantum simulation on emerging quantum hardware is a topic of intense
interest. While many studies focus on computing ground state properties or
simulating unitary dynamics of closed systems, open quantum systems are an
interesting target of study owing to their ubiquity and rich physical behavior.
However, their non-unitary dynamics are also not natural to simulate on
near-term quantum hardware. Here, we report algorithms for the digital quantum
simulation of the dynamics of open quantum systems governed by a Lindblad
equation using an adaptation of the quantum imaginary time evolution (QITE)
algorithm. We demonstrate the algorithms on IBM Quantum's hardware with
simulations of the spontaneous emission of a two level system and the
dissipative transverse field Ising model. Our work shows that the dynamics of
open quantum systems can be efficiently simulated on near-term quantum
hardware.
