Postselection-free experimental observation of the measurement-induced phase transition in circuits with universal gates

Monitored many-body quantum systems can exhibit a measurement-induced phase transition (MIPT) between entangling and disentangling dynamical phases. Proposed approaches to study the MIPT experimentally typically rely on a classical decoding process, but the complexity of this decoding generally grows exponentially with the system size unless the dynamics is restricted to a fine-tuned set of unitary operators. In this work we overcome this difficulty in the context of tree-shaped quantum circuits. We construct a hybrid circuit with Haar-random unitary operators, and we show that the MIPT can be detected without postselection using a simple decoding process whose complexity grows linearly with the number of qubits. The tree structure also enables a complete theoretical description of the MIPT and all its critical properties. We experimentally realize the MIPT on a trapped-ion quantum computer and show that the results are precisely described by theory without the need for error mitigation. To overcome the exponential complexity of measurement induced phase transition (MIPT), the authors propose a protocol which can detect MIPT easily on a tree-like quantum circuit. They experimentally realize the MIPT on a trapped-ion quantum computer and show that the results are precisely described by theory without the need for error mitigation.