A simplified version of the quantum OTOC$^{(2)}$ problem

TL;DR

The paper proposes a simplified, theory-friendly version of the Google Quantum AI OTOC^(2) problem to study verifiable quantum advantage in function-like tasks. It defines the problem via random quantum circuits on a 2D qubit grid, constructs the correlation operator C=U^†BU M, and targets the observable ⟨0^n|C^4|0^n⟩ with additive error ε, outlining quantum vs. classical hardness expectations. The note emphasizes an average-case hardness scenario, discusses scalability to larger n and higher moments, and contrasts the simplified model with the actual experiment where hardware-specific choices and different observables are involved. The work aims to spur theoretical investigations into verifiable, observable-based quantum advantages for quantum simulation and challenges classical algorithms under plausible growth conditions.}

Abstract

This note presents a simplified version of the OTOC$^{(2)}$ problem that was recently experimentally implemented by Google Quantum AI and collaborators. We present a formulation of the problem for growing input size and hope this spurs further theoretical work on the problem.