Observation of a dynamical purification phase transition in a trapped-ion quantum computer
When measurements are interspersed in random quantum circuits, the long-time entanglement of the system exhibits a phase transition with the varying density of measurements. With high measurement rates, a "pure'' phase emerges where the measurements rapidly project the system into a deterministic state, conditioned on the measurement outcomes. However, in the "mixed'' phase, the dynamics successfully encode quantum information from the initial state into a quantum error correcting code-space. This "purification phase transition" is reminiscent of a fault-tolerant threshold. Here, we use a single reference qubit entangled with the larger system to efficiently study these quantum phases. We probe the purification dynamics by sampling hundreds of instances of random circuits using a quantum computer with 13 trapped 171Yb+ ions as the qubits. On the accessible circuit depths and system sizes, we find conclusive evidence of the two phases and show numerically that, with modest increases in circuit depth and system size, critical properties of the purification transition clearly emerge.
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