Optimal Parallel Quantum Query Algorithms
Optimal Parallel Quantum Query Algorithms
复制标题
最优并行量子查询算法
作者：
S. Jeffery;F. Magniez;R. D. Wolf
我们研究了在每个时间段中并行的量子查询的复杂性显示许多问题的紧密界限，特别是$$ theta（（n/p）^{2/3}）$$θ（（（n/p）2/3）p-paralallel查询元素独特性和$$ theta （（n/p）^{k/（k+1）}）$$θ（（n/p）k/（k+1））$$ k $$ k-sum。平行的量子步行算法，我们的下限是基于对敌方下限方法的相对较小的修饰，并在学习图上的最新结果。 - 平行查询复杂性在多个方面都相关与F的块灵敏度相比，当P很小时，总功能F。
We study the complexity of quantum query algorithms that make p queries in parallel in each timestep. This model is in part motivated by the fact that decoherence times of qubits are typically small, so it makes sense to parallelize quantum algorithms as much as possible. We show tight bounds for a number of problems, specifically $$Theta ((n/p)^{2/3})$$Θ((n/p)2/3)p-parallel queries for element distinctness and $$Theta ((n/p)^{k/(k+1)})$$Θ((n/p)k/(k+1)) for $$k$$k-sum. Our upper bounds are obtained by parallelized quantum walk algorithms, and our lower bounds are based on a relatively small modification of the adversary lower bound method, combined with recent results of Belovs et al. on learning graphs. We also prove some general bounds, in particular that quantum and classical p-parallel query complexity are polynomially related for all total functions f when p is small compared to f’s block sensitivity.