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In light of recent exciting progress in building up quantum computingfacilities based on both optical and cold-atom techniques, the algorithms forquantum simulations of particle-physics systems are in rapid progress. In thispaper, we propose an efficient algorithm for simulating the non-unitary timeevolution of neutral-kaon oscillations $K^0 \leftrightarrow \overline{K}^0$,with or without CP conservation, on the quantum computers provided by the IBMcompany. The essential strategy is to realize the time-evolution operator withbasic quantum gates and an extra qubit corresponding to some externalenvironment. The final results are well consistent with theoreticalexpectations, and the algorithm can also be applied to open systems beyondelementary particles.

Quantum Simulations of the Non-Unitary Time Evolution and Applications to Neutral-Kaon Oscillations