# Got QUALMS?

Physical modeling has always been among my favorite forms of synthesis. DSP technology is now powerful enough to solve the equations that describe the behavior of various acoustical systems, such as musical instruments, in real time.

**FIG. 1: In this image from a scanning tunneling microscope, electron-density waves diffract around atom-sized pimples on the surface of a copper crystal, demonstrating the wave nature of these particles. **

A bold new step has been taken in this direction. Fu Ling Yu, a Chinese graduate student in both physics and music at the Beijing School of Heisenbergian Technology (www.bsht.edu), recently realized that acoustic-wave equations are not the only ones that can be used to model sound. He wondered if the equations of quantum mechanics, which describe the wave nature of subatomic particles (see **Fig. 1**), might be used in a modeling engine to reproduce the “sound” of the quantum realm.

From his studies in physics, Fu knew that quantum particles are described as sums of many separate wave functions, much as complex musical timbres can be described as the sum of many separate sine waves. These mathematical functions are combined to form one of the most important equations in all of physics: Schrödinger's Equation. Fu wondered what would happen if he plugged that equation into a modeling engine. What would it sound like?

Unfortunately, conventional computer horsepower is insufficient to render Schrödinger's Equation in real time. Fu, however, had a way around that problem: a prototype quantum computer sitting on his lab bench. He had built it as part of a project to see just how fast such a computer could search through huge tables of data, one of the most promising potential applications of quantum computing. That was precisely what Fu needed to process the data from Schrödinger's Equation in real time as if it described an acoustical system.

He decided to call his idea Quantum Linear Modeling Synthesis (QUALMS). After programming the quantum computer to spit out numbers based on Schrödinger's Equation, including octave transpositions to account for the fact that quantum waves are typically in the terahertz range of frequencies, Fu cobbled together a MIDI interface for note entry and a D/A converter to hear the resulting audio. To drive the QUALMS engine, he created a simple MIDI sequencer that can accommodate 127 billion tracks. (Quantum computers are *very* fast!)

The first time Fu tried the new synth, he heard bright, otherworldly timbres that seemed to reflect his excitement and anticipation. But when he played it for others, he was amazed to discover that their descriptions of what they heard were completely different from his; some described dark, somber tones, while others heard calm, serene textures. Over time, he also noticed that his perception of the same music was different depending on his state of mind.

Fu realized that QUALMS was behaving just like other quantum systems, which are affected by the presence of an observer. In conventional quantum experiments, the state of a particle (energy, position, spin, and so on) is indeterminate until it is observed or measured; in fact, before observation, it exists in a condition called superposition, which embodies all possible states simultaneously. The superposition “collapses” as soon as the particle is observed or measured, and the intent of the observer helps determine which state it ultimately manifests.

Similarly, the timbres generated by QUALMS exist in a kind of aural superposition, which collapses into well-defined harmonic structures depending on the listener's state of mind. In this case, however, Fu discovered that the collapse occurs in the mind of each listener independently, meaning that everyone hears timbres coming from the same audio output differently. The implications of this discovery for the future of music technology are staggering, so it seems certain that Fu Ling Yu will continue his work for years to come.