Probing the classical complexity of quantum dynamics experiments

2026-09-25

AI Summary

This study addresses the limitation of existing complexity metrics in accurately predicting the classical simulation hardness of quantum experiments. To this end, it proposes a novel metric termed "reactivity," which transcends conventional notions of entanglement and magic to enable, for the first time, complexity quantification of entire experiments rather than individual states. Furthermore, by introducing a local information tracking algorithm, the authors design a practically implementable measurement protocol for Pauli path spectra. The results demonstrate that quantum experiments exhibiting low reactivity are amenable to efficient classical simulation, learning, and time-evolution propagation. Ultimately, this work provides a rigorous theoretical foundation for identifying quantum systems that exhibit genuine resistance to classical simulation.

Abstract

A confluence of recent works has shown that many quantum circuits and dynamics are efficiently simulable by classical algorithms that track local information, even when conventional complexity measures such as the entanglement and magic are high. Here, we introduce a novel measure of complexity, the reactivity, to capture this new method of classical attack. Unlike conventional complexity measures, the reactivity does not capture a property of a quantum state or operator in isolation, but rather a quantum experiment as a whole. We provide numerical and rigorous evidence that quantum experiments with low reactivity are simple by a host of measures: they are efficient to classically simulate, learn, and fast-forward. This motivates the search for quantum experiments with high reactivity, which may evade these simplistic features. To this end, we introduce easily implementable experimental protocols---dubbed Pauli path spectroscopy---that allow one to efficiently measure the reactivity of any quantum experiment of interest. Our protocols are applicable even when the experiment itself is beyond the reach of classical simulation.

Problem

• quantum complexity
• classical simulation
• reactivity
• quantum dynamics
• Pauli path spectroscopy

Innovation

• reactivity
• classical simulation
• quantum complexity
• Pauli path spectroscopy
• quantum dynamics