Elliott Thomas J, Yang Chengran, Binder Felix C, Garner Andrew J P, Thompson Jayne, Gu Mile
Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom.
Complexity Institute, Nanyang Technological University, Singapore 637335, Singapore.
Phys Rev Lett. 2020 Dec 31;125(26):260501. doi: 10.1103/PhysRevLett.125.260501.
Effective and efficient forecasting relies on identification of the relevant information contained in past observations-the predictive features-and isolating it from the rest. When the future of a process bears a strong dependence on its behavior far into the past, there are many such features to store, necessitating complex models with extensive memories. Here, we highlight a family of stochastic processes whose minimal classical models must devote unboundedly many bits to tracking the past. For this family, we identify quantum models of equal accuracy that can store all relevant information within a single two-dimensional quantum system (qubit). This represents the ultimate limit of quantum compression and highlights an immense practical advantage of quantum technologies for the forecasting and simulation of complex systems.
有效且高效的预测依赖于识别过去观测数据中包含的相关信息——预测特征——并将其与其他信息隔离开来。当一个过程的未来强烈依赖于其遥远过去的行为时，就需要存储许多这样的特征，这就需要具有广泛记忆的复杂模型。在这里，我们重点介绍一类随机过程，其最小经典模型必须投入无限多的比特来跟踪过去。对于这类过程，我们识别出了具有相同精度的量子模型，这些模型可以将所有相关信息存储在单个二维量子系统（量子比特）中。这代表了量子压缩的最终极限，并凸显了量子技术在复杂系统预测和模拟方面的巨大实际优势。
