## 3 The Q1 Synth System  
Q1 Synth works with one qubit. Figure 1 shows a screenshot of the system in 'Simple' mode. It shows an artistic representation of a Bloch sphere and its respective axes: \(z\), \(y\), and \(x\). Note the labels \(\ket{0}\) on the north and \(\ket{1}\) on the south of the vertical \(z\) axis. The labels \(\ket{+}\) and \(\ket{-}\) mark the opposing ends of the \(x\) axis, as \(\ket{i}\) and \(\ket{-i}\) denote \(y\). The meaning of \(\ket{+}\) and  
The angle \(\theta\) will determine the inclination (or latitude) of the vector, whereas \(\varphi\) is responsible for its azimuth (or longitude). The angle \(\lambda\) does not change the position of the red dot, but it will influence the orientation of the sphere. We refer to \(\lambda\) as the _phase_ of the vector. Once the button 'rotate' is pressed, the instrument begins to make a sound. Rotating the sphere (e.g., by clicking and dragging the mouse) moves the state vector and modifies the sound continuously. The red dot indicates where the state vector is pointing. When the'measure' button is activated, the system takes control from the user, and moves the vector to either north or south, depending on the result of the measurement. The vector moves in slow motion and is accompanied by a respective sound. Once the vector reaches the destination the sound ends. Activating the 'rotate' button again recommences the process, and so on. This is how the instrument is played. When the measuring command is detected, the system builds a quantum circuit that implements a **U** gate and sends it to a quantum computer over the cloud (Figure 4). The coordinates of the sphere at the moment the'measure' button is activated define the angles for the **U** gate. Then, the quantum computer returns the measurement result (\(c_{0}\)), which defines whether the vector moves north or south. Currently, Q1 Synth connects to an IBM Quantum processor located in the USA. At the time of writing, Q1 Synth uses three types of sound synthesis techniques [14]: frequency modulation (FM), additive synthesis, and granular synthesis. This paper focuses on the method for controlling FM. The methods for controlling the other two techniques are identical to the FM one. FM synthesis is based upon the same principles used for FM radio transmission: the frequency of a waveform (referred to as the _carrier_) is altered with a modulating signal (referred to as the _modulator_) [15]. There are a number of variations in FM synthesiser design. The most basic comprises two sine wave oscillators: one acting as the modulator and the other as the carrier signal, respectively (Figure 5). In FM sound synthesis, the carrier is the signal that we hear directly. By contrast, the modulator is heard only indirectly, because its output is added to the base frequency of the carrier (Figure 5). When the frequency of the modulator is in the audio range, numerous additional partials, or sidebands, are added to the spectrum of the carrier's wave. Let us consider the vibrato effect as a starting point example to illustrate the FM technique. Vibrato is a tremulous effect imparted to vocal or instrumental notes. It is often used to add expressivity to musical notes. It is caused by variations in pitch. The fundamental difference, however, is that vibrato uses a sub-audio signal to modulate the pitch of a sound. A sub-audio signal is a low-frequency signal, well below the human hearing threshold, which is approximately 20 Hz. The resulting sound, in this case, has a perceptibly slow variation in its pitch. If the modulator's frequency is set to a value above the human  
Figure 4: For measurement, Q1 Synth builds a quantum circuit and sends it to a quantum computer over the cloud. hearing threshold, then new components are added to the sound spectrum of the carrier. The frequency and amplitudes of these new components influence our perception of timbre. The QISynth implementation of FM requires values for seven parameters:  
* Frequency (_freq_): defines the pitch of the sound.