量子模板匹配
Quantum Template Matching
摘要：
我们认为量子模拟的模式匹配问题，其中包括根据某些预定义的模式类分类一个给定的未知系统。我们解决量子模板匹配的问题，其中每个模式类${\cal C}_i$表示由一个已知的量子态$\hat g_i$称为模板状态，我们的任务是找到一个模板，最佳匹配一个给定的未知量子态$\hat f$。我们建立了一个精确的配方，这个问题的最佳策略相关联的量子贝叶斯推断问题。然后，我们研究了量子比特系统的量子模板匹配的各种例子，考虑允许有限数量的输入状态$\hat f$的副本的效果。我们比较了量子最佳匹配策略和半经典策略，并证明了在一般量子最佳策略中，纠缠辅助的性能增强。
英文摘要：
We consider the quantum analogue of the pattern matching problem, which consists of classifying a given unknown system according to certain predefined pattern classes. We address the problem of quantum template matching in which each pattern class ${\cal C}_i$ is represented by a known quantum state $\hat g_i$ called a template state, and our task is to find a template which optimally matches a given unknown quantum state $\hat f$. We set up a precise formulation of this problem in terms of the optimal strategy for an associated quantum Bayesian inference problem. We then investigate various examples of quantum template matching for qubit systems, considering the effect of allowing a finite number of copies of the input state $\hat f$. We compare quantum optimal matching strategies and semiclassical strategies and demonstrate an entanglement assisted enhancement of performance in the general quantum optimal strategy.
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