A quantum Fourier transform (QFT) based note detection algorithm
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.
Shlomo Kashani Maryam Alqasemi Jacob Hammond