Measurement-induced quantum phases realized in a trapped-ion quantum computer

Many-body open quantum systems balance internal dynamics against decoherence and measurements induced by interactions with an environment^1,2. Quantum circuits composed of random unitary gates with interspersed projective measurements represent a minimal model to study the balance between unitary dynamics and measurement processes^3–5. As the measurement rate is varied, a purification phase transition is predicted to emerge at a critical point akin to a fault-tolerant threshold⁶. Here we explore this purification transition with random quantum circuits implemented on a trapped-ion quantum computer. We probe the pure phase, where the system is rapidly projected to a pure 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 that keeps the memory of initial conditions for long times^6,7. We find experimental evidence of the two phases and show numerically that, with modest system scaling, critical properties of the transition emerge.