A quantum Fourier transform (QFT) based note detection algorithm

TL;DR

This paper introduces a quantum Fourier transform-based algorithm for detecting musical notes, implemented on both simulated and real quantum computers, demonstrating its potential for quantum signal processing.

Contribution

It presents a novel quantum note detection algorithm utilizing QFT, validated through symbolic and circuit-based implementations on IBM's quantum platform.

Findings

Successful implementation on simulated quantum computers.

Effective note detection on real quantum hardware.

Demonstrates feasibility of quantum algorithms for audio analysis.

Abstract

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.