A quantum Fourier transform (QFT) based note detection algorithm

A quantum Fourier transform (QFT) based note detection algorithm. Kashani, S., Alqasemi, M., & Hammond, J. arXiv:2204.11775 [quant-ph], April, 2022. arXiv: 2204.11775

Paper abstract bibtex

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.

@article{kashani_quantum_2022,
	title = {A quantum {Fourier} transform ({QFT}) based note detection algorithm},
	url = {http://arxiv.org/abs/2204.11775},
	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.},
	urldate = {2022-04-30},
	journal = {arXiv:2204.11775 [quant-ph]},
	author = {Kashani, Shlomo and Alqasemi, Maryam and Hammond, Jacob},
	month = apr,
	year = {2022},
	note = {arXiv: 2204.11775},
	keywords = {audio speech and processing, quantum physics, uses sympy},
}

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