Mode 1 (Stochastic Note Generation Model)

In Mode 1, each musical note is encoded using a single qubit. The quantum state of the qubit is measured along a time-varying axis on the Bloch sphere, with the measurement angle around the Y-axis (in x-z plane) specified by the user through the GUI.

The measurement outcome determines which note is played:

• If the result is 0, the note corresponds to one of the following: G, G, D, or E.

• If the result is 1, it corresponds to F♯, D♭, A♭, or E♭, which are tritone pairs to the former on the circle of fifths.

Transitions between notes are mediated by CNOT gates, linking each note to the next. This design allows for entangled and superposed quantum states along the timeline, depending on the chosen measurement axes.

Upon measurement, one of the superposed possibilities is realized and played as sound. When increasing the number of shots, the sequence of non-equivalent measurement outcomes is played serially, producing a probabilistically-generated melody.

Mode 2 (Stochastic Note name/Note value Generation Model)

In Mode 2, each musical note is encoded using two qubits. 

The first qubit corresponds to the note duration (note value). If the measurement result of this second qubit is:

• 0, the note is assigned a quarter note (♩)

• 1, the note is assigned a half note (𝅗𝅥)

The second qubit determines the pitch of the note in the same way as in Mode 1—by measuring the qubit state along a time-varying axis on the Bloch sphere (around the Y-axis), resulting in one of two complementary notes related by a tritone interval.

As in Mode 1, transitions between qubits are mediated by CNOT gates, but in this case the sequence is structured as follows:
Duration of note 1 → Pitch of note 1 → Duration of note 2 → Pitch of note 2 → ..., with a chain of CNOTs connecting them in time.

This arrangement creates quantum entanglement not only between pitches but also between pitch and duration, resulting in complex quantum correlations between musical parameters.

Upon measurement, one of the superposed possibilities is realized and played as sound. When increasing the number of shots, the sequence of non-equivalent measurement outcomes is played serially, producing a probabilistically-generated melody.

Mode 3 (Chord generation)

In Mode 3, each musical note is represented using three qubits. The quantum states |000⟩ to |111⟩ are mapped respectively to a rest (|000⟩) and to the notes F, C, G, D, A, E, and B, in ascending order of perfect fifths (e.g., |001>=|F>, |010>=|C>, |011>=|G>, |100>=|D>, |101>=|A>, |110>=|E>, |111>=|B>). This assignment is based on the circle-of-fifths concept in music theory. Each of the three qubits contributes additively to the pitch identity: the least significant bit corresponds to a fifth shift (V degree), the second to a second upward shift (II degree), and the most significant to a third upward shift (III degree). In this way, the seven diatonic chords (from I_M7 to VII♭5_m7) can be implemented by applying appropriate quantum gates that shape the superposition to include only the pitches belonging to a given chord. Upon measurement, one of the constituent notes of the chord is probabilistically realized and played. By extending this approach, it becomes possible to represent not only individual chords but also transitions between them, using quantum entanglement to encode harmonic correlations. This opens up a novel paradigm in which musical progressions are generated through the interplay between quantum coherence and tonal logic.

Mode 4 (Quantum "Phrase" modulation model)

Mode 4 also uses three qubits to represent pitch information through a mapping onto the circle of fifths, as in Mode 3. However, instead of associating notes with chord names, Mode 4 allows users to directly input the desired pitch names. For each note in the temporal sequence, a dedicated quantum circuit is prepared such that, when measured, it deterministically yields the specified pitch. This ensures that, initially, each note collapses to the user-defined value upon measurement. Then, between each successive pair of notes, phase modulation is applied via quantum gates. This introduces meaningful interactions between adjacent notes, allowing the pitch of a given note to be influenced by the preceding one. As a result, the actual outcome of the later notes may differ from the originally assigned pitch, despite being initialized to those values. The modulation is not random or classically perturbed, but rather introduced coherently at the quantum state level. Upon measurement, a variety of melodic outcomes may be generated probabilistically. This kind of inter-note modulation corresponds to transformations within the space of superposed possibilities prior to measurement—what can be thought of as a meta-space—and offers a novel approach to musical modulation, understood as transformations in musical context and key. 

Mode 5 (Two Players Model Based on Quantum Game Theory)

In Mode 5, as in Modes 1 and 2, each note is represented by a single qubit. That is, the user specifies the measurement axis on the circle of fifths, thereby shaping the flow of musical possibilities as an act of composition, while the actual sounding notes are determined probabilistically through measurement. What distinguishes Mode 5 from Modes 1 and 2 is the introduction of two players. Each player generates a tone, but before the note is measured and heard, the two players' quantum states are entangled in the quantum space. This entanglement process—an inherent feature of the system rather than something directly manipulated by the user—creates a shared quantum state between the two performers. After this entanglement, each player independently chooses a measurement strategy, which ultimately determines the observed note. However, the strategy chosen by one player not only affects their own note, but may also influence the outcome of the other player’s measurement. The same applies symmetrically, so the two players mutually affect each other's sonic output. This is not to say that their choices distort the intended sounds; rather, their strategic interactions serve as a creative process that collaboratively shapes the musical output. As a result, the music that emerges may transcend the individual intentions of either player. This system can be likened to a jazz session, where mutual inspiration leads to spontaneous, co-created expression. Thus, Mode 5 offers a novel paradigm in which composition and performance are unified, while also enabling a new interpretation of ensemble or polyphonic interaction from the perspective of quantum entanglement.