论文标题
基于量子傅立叶变换（QFT）的音符检测算法
A quantum Fourier transform (QFT) based note detection algorithm
论文作者
论文摘要
在量子信息处理（QIP）中，量子傅立叶变换（QFT）具有大量应用[1] [2] [3]：Shor的算法和相位估计只是一些众所周知的示例。 Shor的量子分解算法是最广泛引用的量子算法之一[4] [5] [6]在很大程度上取决于QFT，并有效地在量子计算机上找到了大数量的整数素数[4]。这种针对量子算法的开创性开创性设计引发了一系列可行的替代方案，用于在经典计算机上以前无法解决的问题的可行替代方案，这些问题可能会出色，并且可以在多项式时间内运行。在这项工作中，我们检查了QFT的结构和实现，以在模拟和真实的量子计算机上创建量子音乐检测算法。尽管存在形式的方法[7] [1] [8] [9]用于验证量子算法，但在本研究中，我们将自己限制为一种更简单的符号表示，我们使用符号sympy [10] [11]包装来验证，象征性地复制量子计算过程。然后，使用IBM的Qiskit [12]库将算法作为量子电路实现，最后在实际的单个音乐音调上使用不同数量的量子器来体现周期检测。
In quantum information processing (QIP), the quantum Fourier transform (QFT) has a plethora of applications [1] [2] [3]: Shor's algorithm and phase estimation are just a few well-known examples. Shor's quantum factorization algorithm, one of the most widely quoted quantum algorithms [4] [5] [6] relies heavily on the QFT and efficiently finds integer prime factors of large numbers on quantum computers [4]. This seminal ground-breaking design for quantum algorithms has triggered a cascade of viable alternatives to previously unsolvable problems on a classical computer that are potentially superior and can run in polynomial time. In this work we examine the QFT's structure and implementation for the creation of a quantum music note detection algorithm both on a simulated and a real quantum computer. Though formal approaches [7] [1] [8] [9] exist for the verification of quantum algorithms, in this study we limit ourselves to a simpler, symbolic representation which we validate using the symbolic SymPy [10] [11] package which symbolically replicates quantum computing processes. The algorithm is then implemented as a quantum circuit, using IBM's qiskit [12] library and finally period detection is exemplified on an actual single musical tone using a varying number of qubits.
