  In light of recent exciting progress in building up quantum computing
facilities based on both optical and cold-atom techniques, the algorithms for
quantum simulations of particle-physics systems are in rapid progress. In this
paper, we propose an efficient algorithm for simulating the non-unitary time
evolution of neutral-kaon oscillations $K^0 \leftrightarrow \overline{K}^0$,
with or without CP conservation, on the quantum computers provided by the IBM
company. The essential strategy is to realize the time-evolution operator with
basic quantum gates and an extra qubit corresponding to some external
environment. The final results are well consistent with theoretical
expectations, and the algorithm can also be applied to open systems beyond
elementary particles.
