  Designing quantum algorithms for simulating quantum systems has seen enormous
progress, yet few studies have been done to develop quantum algorithms for open
quantum dynamics despite its importance in modeling the system-environment
interaction found in most realistic physical models. In this work we propose
and demonstrate a general quantum algorithm to evolve open quantum dynamics on
quantum computing devices. The Kraus operators governing the time evolution can
be converted into unitary matrices with minimal dilation guaranteed by the
Sz.-Nagy theorem. This allows the evolution of the initial state through
unitary quantum gates, while using significantly less resource than required by
the conventional Stinespring dilation. We demonstrate the algorithm on an
amplitude damping channel using the IBM Qiskit quantum simulator and the IBM Q
5 Tenerife quantum device. The proposed algorithm does not require particular
models of dynamics or decomposition of the quantum channel, and thus can be
easily generalized to other open quantum dynamical models.
