Inductive Supervised Quantum Learning
Inductive Supervised Quantum Learning
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DOI：
10.1103/physrevlett.118.190503
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发表时间：
2017-05-12
影响因子：
8.6
通讯作者：
Wittek, Peter
中科院分区：
文献类型：
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作者：
Monras, Alex;Sentis, Gael;Wittek, Peter
在监督学习中，归纳学习算法从观察到的训练实例中提取一般规则，然后将规则应用于测试实例。我们表明，这种分裂的培训和应用程序自然产生，在经典的设置，从一个简单的独立性要求与物理解释是nonsignaling。因此，归纳学习的两个看似不同的定义恰好重合。这是从经典信息在量子设置中被分解的性质得出的。我们证明了一个量子德Finetti定理的量子信道，这表明，在量子的情况下，等价持有的渐近设置，也就是说，大量的测试实例。这揭示了经典学习协议与量子协议之间的自然类比，证明了类似的处理方法，并允许我们询问计算学习理论中的标准元素，例如结构风险最小化和样本复杂性。
In supervised learning, an inductive learning algorithm extracts general rules from observed training instances, then the rules are applied to test instances. We show that this splitting of training and application arises naturally, in the classical setting, from a simple independence requirement with a physical interpretation of being nonsignaling. Thus, two seemingly different definitions of inductive learning happen to coincide. This follows from the properties of classical information that break down in the quantum setup. We prove a quantum de Finetti theorem for quantum channels, which shows that in the quantum case, the equivalence holds in the asymptotic setting, that is, for large numbers of test instances. This reveals a natural analogy between classical learning protocols and their quantum counterparts, justifying a similar treatment, and allowing us to inquire about standard elements in computational learning theory, such as structural risk minimization and sample complexity.