For some certain problems, quantum algorithms are theoretically able to solve them quickly than classical algorithms. But the role of entanglement in achieving the quantum computational speedup is not fully understood. By theoretical analysis and numerical calculation of four practical use cases, we investigate the entanglement features of the quantum states employed in quantum phase estimation algorithm and quantum counting algorithm. The results show that whether these two algorithms generate entanglement depend on whether the input quantum state of the second register is a superposition state of the eigenstates.

中文翻译：

---

相位估计算法和量子计数算法中的纠缠

对于某些特定问题，量子算法在理论上能够比经典算法更快地解决它们。但是纠缠在实现量子计算加速中的作用尚未完全了解。通过四个实际用例的理论分析和数值计算，我们研究了量子相位估计算法和量子计数算法中采用的量子态的纠缠特征。结果表明，这两种算法是否产生纠缠取决于第二个寄存器的输入量子态是否是本征态的叠加态。