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Although the laws of classical physics are deterministic, thermodynamics gives rise to an arrow of time through irreversible processes. In quantum mechanics the unitary nature of the time evolution makes it intrinsically reversible, however the question of how to revert an unknown time evolution nevertheless remains. Remarkably, there have been several recent demonstrations of protocols for reverting unknown unitaries in scenarios where even the interactions with the target system are unknown. The practical use of these universal rewinding protocols is limited by their probabilistic nature, raising the fundamental question of whether time-reversal could be performed deterministically. Here we show that quantum physics indeed allows for deterministic universal time-reversal by exploiting the non-commuting nature of quantum operators, and demonstrate a recursive protocol for two-level quantum systems with an arbitrarily high probability of success. Using a photonic platform we demonstrate our protocol, reverting the discrete time evolution of a polarization state with an average state fidelity of over 95%. Our protocol, requiring no knowledge of the quantum process to be rewound, is optimal in its running time, and brings quantum rewinding into a regime of practical relevance.