We report the first experimental demonstration of quantum synchronization. This is achieved by performing a digital simulation of a single spin-$1$ limit-cycle oscillator on the quantum computers of the IBM Q System. Applying an external signal to the oscillator, we verify typical features of quantum synchronization and demonstrate an interference-based quantum synchronization blockade. Our results show that state-of-the-art noisy intermediate-scale quantum computers are powerful enough to implement realistic dissipative quantum systems. Finally, we discuss limitations of current quantum hardware and define requirements necessary to investigate more complex problems.
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