论文标题
用单位甲骨口进行量子计算的拓扑障碍
Topological obstructions to quantum computation with unitary oracles
论文作者
论文摘要
带有单一甲骨沟的算法可以嵌套,这使其非常通用。一个示例是用于量子加速的许多候选算法中使用的相位估计算法。寻找新的量子算法的搜索受益于理解其局限性:量子电路中的某些任务是不可能的,尽管它们的经典版本很容易,例如克隆。具有单一Oracle $ u $的示例是IF子句,即实现控制的$ U $的任务(在$ u $上达到阶段)。在经典计算中,条件语句简单且必不可少。在量子电路中,从一个查询到$ u $不可能显示IF子句。从多项式的查询中可以看出吗?在这里,我们将算法与单一的甲骨文统一,并开发出一种拓扑方法来证明其局限性:即使承认近似,分组后和放松因果关系,也没有量子电路来实现fastum电路。我们还显示了过程断层扫描,甲骨文中和的局限性,以及$ \ sqrt [\ dim u} $,$ u^t $和$ u^\ u^\ dagger $算法。我们的结果增强了线性光学的优势,对放松因果关系的实验挑战,并通过许多结果测量来激励新算法。
Algorithms with unitary oracles can be nested, which makes them extremely versatile. An example is the phase estimation algorithm used in many candidate algorithms for quantum speed-up. The search for new quantum algorithms benefits from understanding their limitations: Some tasks are impossible in quantum circuits, although their classical versions are easy, for example, cloning. An example with a unitary oracle $U$ is the if clause, the task to implement controlled $U$ (up to the phase on $U$). In classical computation the conditional statement is easy and essential. In quantum circuits the if clause was shown impossible from one query to $U$. Is it possible from polynomially many queries? Here we unify algorithms with a unitary oracle and develop a topological method to prove their limitations: No number of queries to $U$ and $U^\dagger$ lets quantum circuits implement the if clause, even if admitting approximations, postselection and relaxed causality. We also show limitations of process tomography, oracle neutralization, and $\sqrt[\dim U]{U}$, $U^T$, and $U^\dagger$ algorithms. Our results strengthen an advantage of linear optics, challenge the experiments on relaxed causality, and motivate new algorithms with many-outcome measurements.