Notes on Quantum Soundscapes and Music

TL;DR

This work investigates turning quantum experimental data into audio (quantum soundscapes) and music to reveal signals and test foundational ideas. It presents two projects: quantum soundscapes derived from mesoscopic oscillators and quantum measurements, and quantum music based on Leggett-Garg inequality tests implemented on an IBM quantum computer, with outcomes mapped to musical notes. Audio synthesis uses inverse Fourier transforms with randomized phase handling to produce time-domain signals, with a tunable sampling rate shaping timbre. Notably, audible signals were discovered that were not evident in visual representations, and the quantum music composition encodes four correlation-based movements with LG-violating and LG-respecting values $K_{\mathrm{exp}}$ of $-2.824$, $-0.96$, $0.709$, and $1.339$, including a maximal violation near $\Delta t=\pi/(3\Omega)$. This approach offers a novel, accessible window into quantum phenomena and motivates listener-based validation and cross-modal explorations, including potential multi-qubit LG tests.

Abstract

We describe our investigations involving the sonification of data from experiments involving various mesoscopic mechanical oscillator systems cooled to close to their quantum ground states, as well as the sonification of measured data from a single qubit subject to various unitary rotations designed to test the Leggett-Garg inequality. "Listening" to data via their resulting sonifications facilitates the discovery of signals that might otherwise be hard to detect in common graphic (i.e., visual) representations, and for the qubit experiment provides a complementary way to discern when the data violates macroscopic realism with some prior listening training. The resulting soundscapes and music also provide a complementary window into the quantum realm that is accessible to non-experts with open ears.

Figures (4)

• Figure 1: Scanning electron microscope image of the drum-shaped, aluminium mechanical oscillator with diameter $15~\mu{\mathrm{m}}$ and thickness $100~{\mathrm{nm}}$ that was investigated in Ref. cattiaux2021. (Figure courtesy of L. Mercier de Lépinay and M. Sillanpää.)
• Figure 2: Spectrogram of the full data set sonification. The vertical axis gives the sound frequency spectrum in Hertz and the horizontal axis gives the time elapsed in seconds. The colour represents sound amplitude, with deep purple to black denoting "very loud" and light yellow denoting "very quiet".
• Figure 3: Plot of the theoretical prediction for $K_{\mathrm{theor}}=C_{12}+C_{23}-C_{13}=2 \cos\left(\Omega\Delta t\right)-\cos\left(2\Omega\Delta t\right)$ versus $\Delta t$ (solid black line) for a qubit evolving according to the Hamiltonian $H=\frac{1}{2}\hbar \Omega \sigma_x$ and subject to measurements of the observable $\sigma_z$. The experimental $K_{\mathrm{exp}}$ results (black dots) for an actual qubit (realized through one of IBM's quantum computers), are evaluated at the selected time intervals $\Delta t=\pi/(3\Omega),\, \pi/(2\Omega),\, 0.712\pi/\Omega,\, \pi/\Omega$. Data points above the horizontal dashed line violate the LG inequality (\ref{['keq']}).
• Figure 4: Plot of the experimental correlation value $K_{\mathrm{exp}}$ for the time interval $\Delta t=\pi/(3\Omega)$ versus the accumulated number of repeated state preparation and measurements (i.e., "shots") over which the correlation value is calculated. When the number of shots is $500$, we have $K_{\mathrm{exp}}=1.339$. The horizontal dashed line indicates the predicted theoretical value $K_{\mathrm{theor}}=1.5$.