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.
Hirsh Kamakari Jiace Sun Yaodong Li Jonathan J. Thio Tanvi P. Gujarati Matthew P. A. Fisher Mario Motta Austin J. Minnich