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WORLD SCIENTIFIC eBooks

An Introduction to Quantum Probability Amplitude Modulation (QPAM) from a Compositional Perspective

Eren Utku

Published Jan 1, 2025• 0 citations
Publisher
DOI
10.1142/9789819800186_0005

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•Oct 28, 2025•1 citation
Quantum Probability Amplitude Modulation (QPAM) was implemented on a real quantum computer, ibm_brisbane, one of IBM’s 127-qubit devices from the Eagle r3 family. To evaluate the errors, advantages, and limitations of such a real-world implementation, four experiments were conducted. Three of them encoded different signals: a ramp signal, a jagged signal, and a custom signal constructed from a sequence of five quantum gates. The first two signals were prepared using a built-in function from IBM’s Qiskit library, which includes an optimization step. Despite the relatively high root-mean-square errors normalized to the signal range (RMSEN) observed in the measurements, the encoding of NSanalog samples with only log2NSqubits was successfully demonstrated for NS= 8 using three qubits. The maximum RMSEN error obtained from the real quantum hardware was 8.7%. However, the need for a disproportionately large number of measurement shots to extract classical information significantly limits the practical applicability of the QPAM method, unless further quantum signal processing is performed within the quantum system.
In this paper we describe methods for mapping the information contained in a spline model of one cycle of an audio signal to the quantum information setting. We use this mapping to describe methods of sonification of quantum algorithms which use spline models to describe and generate timbre, melody, and rhythm. We show how a musical state vector given by n B-spline coefficients, which represent one cycle of a waveform, can produce these three musical elements simultaneously. We present two modes of correspondence between quantum and musical states. The first mode is derived from proposed signal processing of quantum audio, such as QPAM (Quantum Probability Amplitude Modulation), and the second mode works with superposition states achievable through quantum algorithms. Musical states are initialized using approximate timbres derived from instrument samples or synthesized timbres. Melodic contours are derived from spline models of these timbres, using continuous pitch and duration spaces. Musical examples are discussed, and larger compositional works are currently in production.
In this paper we describe methods for mapping the information contained in a spline model of one cycle of an audio signal to the quantum information setting. We use this mapping to describe methods of sonification of quantum algorithms which use spline models to describe and generate timbre, melody, and rhythm. We show how a musical state vector given by n B-spline coefficients, which represent one cycle of a waveform, can produce these three musical elements simultaneously. We present two modes of correspondence between quantum and musical states. The first mode is derived from proposed signal processing of quantum audio, such as QPAM (Quantum Probability Amplitude Modulation), and the second mode is more abstract, modeling the evolution of musical states through unitary evolution of intermediate states in quantum algorithms. Musical states are initialized using approximate timbres derived from instrument sam- ples or synthesized timbres. Melodic contours are derived from spline models of these timbres, using continuous pitch and duration spaces. Musical examples are discussed, and larger compositional works are currently under development.