Out-of-Time-Order Correlation function measures transport properties of dynamical systems. They are ubiquitously used to measure quantum mechanical quantities, such as scrambling times, criticality in phase transitions, and detect onset of thermalisation. We characterise the computational complexity of estimating OTOCs over all eigenstates and show it is Complete for the One Clean Qubit model (DQC1). We then generalise our setup to establish DQC1-Completeness of N-time Correlation functions over all eigenstates. Building on previous results, the DQC1-Completeness of OTOCs and N-time Correlation functions then allows us to highlight a dichotomy between query complexity and circuit complexity of estimating correlation functions.

翻译：时序失序关联函数用于度量动力学系统的输运性质。这类函数被广泛应用于测量量子力学量，如量子混沌时间、相变临界性以及热化起始的检测。我们刻画了在所有本征态上估计时序失序关联函数的计算复杂性，并证明其对于单清洁量子比特模型具有完全性。随后我们将研究框架推广至N点关联函数，建立了在所有本征态上估计N点关联函数的DQC1完全性。基于已有研究成果，时序失序关联函数与N点关联函数的DQC1完全性使我们能够揭示估计关联函数时查询复杂度与电路复杂度之间的二分性。