论文标题
使用量子幅度估计来估算PI的量子电路
Quantum circuit to estimate pi using quantum amplitude estimation
论文作者
论文摘要
这项研究提出了一个量子电路，用于使用算术电路和量子幅度估计来估计PI值。我们回顾两种类型的量子乘数，并根据乘数作为执行量子计算所需的基本算术电路提出量子平方电路。量子加法器实现的平方尺寸为$ O（n）$需要$ o（n^2）$门和至少一个辅助量子尺，而使用量子傅立叶变换（qft）实现的，则需要$ O（n^3）$ GATES $ GATES $ GATES $ GATES，而无需辅助Qubit。提出的量子电路估计PI基于蒙特卡洛方法，量子振幅估计和量子平方。通过使用QFT应用量子平方，该电路以$ 4N + 1 $ QUBITS实现，价格为$ 2^{2n} $采样。使用$ n $从2到6变化的量子计算机模拟器证明了所提出的方法，并将获得的结果与通过执行经典计算获得的结果进行了比较。
This study presents a quantum circuit for estimating the pi value using arithmetic circuits and by quantum amplitude estimation. We review two types of quantum multipliers and propose quantum squaring circuits based on the multiplier as basic arithmetic circuits required for performing quantum computations. The squarer realized by a quantum adder with the gate size of $ O(n) $ requires $ O(n^2) $ gates and at least one ancillary qubits, while that realized by using quantum Fourier transform (QFT) requires $ O(n^3) $ gates without ancillary qubit. The proposed quantum circuit to estimate pi is based on the Monte Carlo method, quantum amplitude estimation, and quantum squarer. By applying the quantum squarer using QFT, the circuit was implemented in $ 4n + 1 $ qubits at $ 2^{2n} $ sampling. The proposed method was demonstrated using a quantum computer simulator with $ n $ being varied from 2 to 6, and the obtained result was compared with the one obtained by performing a classical calculation.
