具有无界量子记忆优势的单次在线序列分类
Single-shot online sequence classification with unbounded quantum memory advantage
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中文总结 AI 辅助
本文针对在线多分类序列分类问题，证明精确经典智能体需无界记忆，而量子智能体仅需有界记忆即可解决所有任务，且量子方案是记忆最小化的，确立了二者的无界记忆成本分离
中文摘要 AI 辅助
智能体监控复杂环境，在每个时间步接收一个观测结果，最终需对所得序列进行标注。该序列是否表明存在异常，以及异常类型是什么？它是否预示着市场不稳定，不稳定程度如何？这就是在线多分类序列分类的场景：输入是顺序到达的，无法一次性获取完整的历史信息，智能体必须保留与最终决策相关的所有过往信息。随着环境变得愈发复杂，追踪这些信息所需的记忆会迅速增长，且无界。在此，我们引入这类多分类序列分类博弈的家族，并证明任何精确经典智能体都需要无界增长的记忆，而精确量子智能体则可以用有界记忆解决该家族中的所有任务。这种分离是严格的：在合适的输入分布下，任何使用少于所需记忆的经典智能体，其表现会任意接近随机猜测。此外，我们的量子构造被证明是记忆最小化的，这使我们能够推导出执行此类任务所需的精确经典和量子记忆复杂度。通过这项工作，我们确立了在线多分类序列分类中经典与量子记忆成本之间的无界分离。
英文摘要
An agent monitors a complex environment, receiving one observation at each time step and eventually deciding how to label the resulting sequence. Does the sequence indicate an anomaly, and if so, of what type? Does it signal market instability, and to what degree? This is the setting of online multi-class classification: the input arrives sequentially, the full history is never available at once, and the agent must retain any past information relevant to the eventual decision. As the environment becomes more complex, the memory needed to track this information can grow rapidly without bound. Here, we introduce families of such multi-class classification games and show that any exact classical agent requires memory that grows without bound, whereas exact quantum agents can solve all tasks in the family with bounded memory. This separation is sharp: any classical agent using less than the required memory, under suitable input distributions, performs arbitrarily close to random guessing. Moreover, our quantum constructions are provably memory minimal, allowing us to derive the exact classical and quantum memory complexities to perform such tasks. In doing so, we establish an unbounded separation between classical and quantum memory cost for online multi-class classification.
