Constructive interference at the edge of quantum ergodic dynamics

TL;DR

This paper demonstrates that second-order out-of-time-order correlators (OTOC$^{(2)}$) in a 103-qubit quantum processor reveal persistent sensitivity to dynamics due to constructive interference, highlighting potential for quantum advantage in complex system characterization.

Contribution

It introduces a novel interference mechanism in OTOC$^{(2)}$ that sustains sensitivity at long times and shows how this leads to classical intractability, advancing understanding of quantum ergodic dynamics.

Findings

OTOC$^{(2)}$ remains sensitive at long times with time reversal protocols.

Constructive interference between Pauli strings dominates OTOC$^{(2)}$.

Large-scale OTOC$^{(2)}$ measurements surpass classical simulation capabilities.

Abstract

Quantum observables in the form of few-point correlators are the key to characterizing the dynamics of quantum many-body systems. In dynamics with fast entanglement generation, quantum observables generally become insensitive to the details of the underlying dynamics at long times due to the effects of scrambling. In experimental systems, repeated time-reversal protocols have been successfully implemented to restore sensitivities of quantum observables. Using a 103-qubit superconducting quantum processor, we characterize ergodic dynamics using the second-order out-of-time-order correlators, OTOC$^{(2)}$. In contrast to dynamics without time reversal, OTOC$^{(2)}$ are observed to remain sensitive to the underlying dynamics at long time scales. Furthermore, by inserting Pauli operators during quantum evolution and randomizing the phases of Pauli strings in the Heisenberg picture, we observe substantial changes in OTOC$^{(2)}$ values. This indicates that OTOC$^{(2)}$ is dominated by constructive interference between Pauli strings that form large loops in configuration space. The observed interference mechanism endows OTOC$^{(2)}$ with a high degree of classical simulation complexity, which culminates in a set of large-scale OTOC$^{(2)}$ measurements exceeding the simulation capacity of known classical algorithms. Further supported by an example of Hamiltonian learning through OTOC$^{(2)}$, our results indicate a viable path to practical quantum advantage.