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 postselection. Recently, an alternative protocol to detect entanglement phase transitions using linear cross entropy was proposed, attempting to eliminate both bottlenecks. Here, we report demonstrations 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 postselection is required. We demonstrate data collapses onto scaling functions with critical exponents in semiquantitative agreement with theory. Our demonstration of the cross entropy benchmark (XEB) protocol paves the way for studies of measurement-induced entanglement phase transitions and associated critical phenomena on larger near-term quantum systems.