量子DNF可学习性再探
Quantum DNF Learnability Revisited
摘要：
提出了一种基于均匀分布的DNF公式的量子PAC学习算法，其查询复杂度为$\tilde{O}(s^{3}/ε+ s^{2}/ε^{2})$，其中$s$为DNF公式的长度，$ε$为PAC的误差精度.如果$s$和$1/ε$是可比的，这给出了对先前已知的经典查询复杂度$\tilde{O}(ns^{2}/ε^{2})$的适度改进。我们还显示了查询复杂性的任何量子PAC算法学习DNF的大小$s$与$n$输入下的均匀分布的$Ω(s\log n/n)$的下界。
英文摘要：
We describe a quantum PAC learning algorithm for DNF formulae under the uniform distribution with a query complexity of $\tilde{O}(s^{3}/ε+ s^{2}/ε^{2})$, where $s$ is the size of DNF formula and $ε$ is the PAC error accuracy. If $s$ and $1/ε$ are comparable, this gives a modest improvement over a previously known classical query complexity of $\tilde{O}(ns^{2}/ε^{2})$. We also show a lower bound of $Ω(s\log n/n)$ on the query complexity of any quantum PAC algorithm for learning a DNF of size $s$ with $n$ inputs under the uniform distribution.
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