Many-body open quantum systems balance internal dynamics against decoherence from interactions with an environment. Here, we explore this balance via random quantum circuits implemented on a trapped ion quantum computer, where the system evolution is represented by unitary gates with interspersed projective measurements. As the measurement rate is varied, a purification phase transition is predicted to emerge at a critical point akin to a fault-tolerent threshold. We probe the "pure" phase, where the system is rapidly projected to a deterministic state conditioned on the measurement outcomes, and the "mixed" or "coding" phase, where the initial state becomes partially encoded into a quantum error correcting codespace. We find convincing evidence of the two phases and show numerically that, with modest system scaling, critical properties of the transition clearly emerge.

1 aNoel, Crystal1 aNiroula, Pradeep1 aZhu, Daiwei1 aRisinger, Andrew1 aEgan, Laird1 aBiswas, Debopriyo1 aCetina, Marko1 aGorshkov, Alexey, V.1 aGullans, Michael1 aHuse, David, A.1 aMonroe, Christopher uhttps://arxiv.org/abs/2106.05881