Observation of constructive interference at the edge of quantum ergodicity

The dynamics of quantum many-body systems is characterized by quantum observables that are reconstructed from correlation functions at separate points in space and time^{1, 2–3}. In dynamics with fast entanglement generation, however, quantum observables generally become insensitive to the details of the underlying dynamics at long times due to the effects of scrambling. To circumvent this limitation and enable access to relevant dynamics in experimental systems, repeated time-reversal protocols have been successfully implemented⁴. Here we experimentally measure the second-order out-of-time-order correlators (OTOC⁽²⁾)^{5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17–18} on a superconducting quantum processor and find that they remain sensitive to the underlying dynamics at long timescales. Furthermore, OTOC⁽²⁾ manifests quantum correlations in a highly entangled quantum many-body system that are inaccessible without time-reversal techniques. This is demonstrated through an experimental protocol that randomizes the phases of Pauli strings in the Heisenberg picture by inserting Pauli operators during quantum evolution. The measured values of OTOC⁽²⁾ are substantially changed by the protocol, thereby revealing constructive interference between Pauli strings that form large loops in the configuration space. The observed interference mechanism also endows OTOC⁽²⁾ with high degrees of classical simulation complexity. These results, combined with the capability of OTOC⁽²⁾ in unravelling useful details of quantum dynamics, as shown through an example of Hamiltonian learning, indicate a viable path to practical quantum advantage.