贝叶斯网络上的量子推理
Quantum Inference on Bayesian Networks
摘要：
在贝叶斯网络上执行精确推理是一个#P-hard问题。典型地，近似推理技术被用来替代地从给定证据变量的值$e$的查询变量的分布中采样。传统上，从$n$变量的贝叶斯网络中获得单个无偏样本，其中每个节点在时间$\mathcal{O}(nmP(e)^{-1})$上具有最多$m$父节点，关键取决于$P(e)$，即证据可能首先出现的概率。通过实现拒绝采样的量子版本，我们获得了平方根加速，每个样本需要$\mathcal{O}(n2^mP(e)^{-\frac12})$时间。我们利用贝叶斯网络的图形结构，有效地构建一个量子态，一个q样本，代表预期的经典分布，也有效地应用振幅放大，我们的加速源。因此，我们的加速是值得注意的，因为它是非相对化的-我们计算原始操作，不需要黑盒Oracle查询。
英文摘要：
Performing exact inference on Bayesian networks is known to be #P-hard. Typically approximate inference techniques are used instead to sample from the distribution on query variables given the values $e$ of evidence variables. Classically, a single unbiased sample is obtained from a Bayesian network on $n$ variables with at most $m$ parents per node in time $\mathcal{O}(nmP(e)^{-1})$, depending critically on $P(e)$, the probability the evidence might occur in the first place. By implementing a quantum version of rejection sampling, we obtain a square-root speedup, taking $\mathcal{O}(n2^mP(e)^{-\frac12})$ time per sample. We exploit the Bayesian network's graph structure to efficiently construct a quantum state, a q-sample, representing the intended classical distribution, and also to efficiently apply amplitude amplification, the source of our speedup. Thus, our speedup is notable as it is unrelativized -- we count primitive operations and require no blackbox oracle queries.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
