        |0⟩ (North pole)
         │
         │  θ = polar angle
         │
    ─────┼───── φ = azimuthal angle
         │
         │
        |1⟩ (South pole)

|ψ⟩ = cos(θ/2)|0⟩ + e^{iφ}sin(θ/2)|1⟩

Audio Mapping

Parameter	Bloch Coordinate	Sound Effect
θ (theta)	Polar angle	Timbre blend
φ (phi)	Azimuthal angle	Phase/detune
r	Radius (purity)	Amplitude/reverb

MIDI Control

CC Mappings

CC	Controller	Rotation
1	Expression 1	X-axis (orange)
2	Expression 2	Z-axis (blue)
3	Expression 3	Y-axis (green)
64	Sustain/Switch	Measurement

Note Input

# MIDI note → qubit initialization
def note_to_qubit(note, velocity):
    """
    Map MIDI note to initial qubit state.
    
    note: 0-127 → θ = note * π / 127
    velocity: 0-127 → φ = velocity * 2π / 127
    """
    theta = note * np.pi / 127
    phi = velocity * 2 * np.pi / 127
    return cos(theta/2), exp(1j * phi) * sin(theta/2)

Integration with Quantum Guitar

┌─────────────┐     MIDI      ┌─────────────┐
│   Fishman   │──────────────▶│   Actias    │
│  MIDI Pickup│               │   Synth     │
└─────────────┘               └──────┬──────┘
                                     │
┌─────────────┐     MIDI             │ Audio
│ Boss EV-1-WL│──────────────────────┤
│ Foot Pedals │                      │
└─────────────┘                      ▼
                              ┌─────────────┐
┌─────────────┐               │    Mix      │
│  Boss FS-6  │───Measure────▶│   Output    │
│ Foot Switch │               └─────────────┘
└─────────────┘

Web Interface

Actias runs as web application with:

Real-time Bloch sphere visualization
MIDI device selection
Audio output configuration
Preset management

Note: Web MIDI requires secure context (HTTPS/localhost)

Known Issues & Workarounds

From Coecke's tech notes:

Issue	Workaround
Preset loss on MIDI reconnect	Re-add device in settings
Tablet web MIDI	Use desktop only
Two laptops needed	Separate Actias + DAW hosts
Only Z-measurement	Rotate before measure for X

SuperCollider Alternative

// Actias-like qubit sonification
SynthDef(\actias, { |theta=0, phi=0, gate=1|
    var sig, prob0, prob1, env;
    
    prob0 = cos(theta/2).squared;
    prob1 = sin(theta/2).squared;
    
    // Blend two timbres based on |0⟩/|1⟩ probability
    sig = (SinOsc.ar(440) * prob0) + 
          (Saw.ar(440 * 1.5) * prob1);
    
    // Phase modulation from φ
    sig = sig * (1 + (0.5 * cos(phi)));
    
    env = EnvGen.kr(Env.asr(0.01, 1, 0.1), gate);
    
    Out.ar(0, sig * env ! 2);
}).add;

GF(3) Triad

Component	Trit	Role
zx-calculus	-1	Notation
quantum-guitar	0	Interface
moth-actias	+1	Sonification

Conservation: (-1) + (0) + (+1) = 0 ✓

References

Miranda, Thomas & Itaboraí (2023). Q1Synth. Applied Sciences
Coecke (2025). A Quantum Guitar. arXiv:2509.04526
Moth. Actias documentation (web)

Skill Name: moth-actias Type: Quantum Synthesizer / MIDI Trit: +1 (PLUS)

Non-Backtracking Geodesic Qualification

Condition: μ(n) ≠ 0 (Möbius squarefree)

This skill is qualified for non-backtracking geodesic traversal.

moth-actias

Moth Actias Quantum Synth

Overview

Bloch Sphere Sonification