Experimental demonstration of scalable cross-entropy benchmarking to detect measurement-induced phase transitions on a superconducting quantum processor

Quantum systems subject to random unitary evolution and measurements at random points in spacetime exhibit entanglement phase transitions which depend on the frequency of these measurements. Past work has experimentally observed entanglement phase transitions on near-term quantum computers, but the characterization approach using entanglement entropy is not scalable due to exponential overhead of quantum state tomography and post selection. Recently, an alternative protocol to detect entanglement phase transitions using linear cross-entropy was proposed which eliminates both bottlenecks. Here, we report the demonstration of this protocol in systems with one-dimensional and all-to-all connectivities on IBM's quantum hardware on up to 22 qubits, a regime which is presently inaccessible if post-selection is required. We demonstrate a collapse of the data into a scale-invariant form with critical exponents agreeing with theory within uncertainty. Our demonstration paves the way for studies of measurement-induced entanglement phase transitions and associated critical phenomena on larger near-term quantum systems.