| name | quantum-guitar |
| description | Coecke's Quantum Guitar: quantising guitar strings via qubit association, ZX-calculus notation, Moth Actias synth integration |
| trit | 0 |
| geodesic | true |
| moebius | μ(n) ≠ 0 |
| arxiv | 2509.04526 |
Quantum Guitar
Trit: 0 (ERGODIC - coordinator between classical and quantum)
Author: Bob Coecke (Quantum Brain Art Ltd / Oxford / Perimeter)
arXiv: 2509.04526v1 [quant-ph] 3 Sep 2025
Core Principle
"A guitar string represents a wave, and by associating a qubit to each of its playable states we get a quantum wave."
Quantisation: Each playable state of a guitar string → qubit
Control: Four limbs like a drummer (hands: guitar, feet: qubit)
Transition: Smooth classical ↔ quantum sound continuum
Architecture
┌─────────────────────────────────────────────────────────────────────┐
│ QUANTUM GUITAR │
├─────────────────────────────────────────────────────────────────────┤
│ │
│ GUITAR (hands) QUBIT CONTROL (feet) │
│ ┌──────────────┐ ┌──────────────────────────────┐ │
│ │ Fishman MIDI │───────▶│ Moth Actias Quantum Synth │ │
│ │ Pickup │ │ ┌────────────────────────┐ │ │
│ └──────────────┘ │ │ Bloch Sphere │ │ │
│ │ │ |ψ⟩ │ │ │
│ Fernandes │ │ / \ │ │ │
│ Sustainer ──────────────│ │ |0⟩ |1⟩ │ │ │
│ (continuous) │ └────────────────────────┘ │ │
│ │ │ │
│ │ FOOT CONTROLLERS: │ │
│ │ • Boss EV-1-WL (X rotation) │ │
│ │ • Boss EV-1-WL (Z rotation) │ │
│ │ • Boss FS-6 (measurement) │ │
│ └──────────────────────────────┘ │
│ │
│ VOLUME PEDALS │
│ ┌────────────┐ ┌────────────┐ │
│ │ Classical │ │ Quantum │ │
│ │ FV500L/H │ │ FV500L/H │ │
│ └────────────┘ └────────────┘ │
│ ↓ ↓ │
│ └────────┬───────┘ │
│ ▼ │
│ FINAL MIX │
│ │
└─────────────────────────────────────────────────────────────────────┘
Qubit Operations
Rotations (Foot Controllers)
| Controller | Color | Rotation | Pauli Gate |
|---|
| Pedal 1 | Orange | X-axis | σₓ |
| Pedal 2 | Blue | Z-axis | σᵤ |
| (Internal) | Green | Y-axis | σᵧ |
Measurement (Foot Switch)
- Boss FS-6 in momentary mode
- Z-measurement (computational basis)
- Suggestion: Add X-measurement primitive
ZX-Calculus Notation
From "Bell" composition [Abdyssagin & Coecke]:
┌───┐
────┤ Z ├──── Z-spider (phase)
└───┘
┌───┐
────┤ X ├──── X-spider (phase)
└───┘
╲ ╱
╲ ╱
╳ Hadamard edge
╱ ╲
╱ ╲
Musical ZX notation: Augmented score for quantum music
GF(3) Mapping
| State | Trit | Sound Character |
|---|
| 0⟩ | -1 |
| +⟩ | 0 |
| 1⟩ | +1 |
Conservation: Classical-Quantum-Classical transitions preserve Σ = 0
Implementation
DisCoPy Integration
from discopy import Ty, Box, Diagram
from discopy.quantum import qubit, Ket, Bra, H, Rx, Rz, Measure
string = Ty('string')
quantum_string = qubit
def quantise_string(classical_note):
"""Map classical guitar note to qubit state."""
phase = frequency_to_phase(classical_note)
return Ket(0) >> Rx(phase)
def foot_rotation(axis, angle):
if axis == 'X':
return Rx(angle)
elif axis == 'Z':
return Rz(angle)
else:
return Ry(angle)
def measure_qubit():
return Measure()
Moth Actias Interface
import mido
class ActiasController:
"""Control Moth Actias quantum synth via MIDI."""
def __init__(self, port_name='Actias'):
self.port = mido.open_output(port_name)
self.qubit_state = [1, 0]
def rotate_x(self, angle):
"""X-rotation via expression pedal CC."""
cc_value = int((angle / (2 * np.pi)) * 127)
self.port.send(mido.Message('control_change',
control=1, value=cc_value))
def rotate_z(self, angle):
"""Z-rotation via expression pedal CC."""
cc_value = int((angle / (2 * np.pi)) * 127)
self.port.send(mido.Message('control_change',
control=2, value=cc_value))
def measure(self):
"""Trigger measurement via foot switch."""
self.port.send(mido.Message('control_change',
control=64, value=127))
OSC Protocol (SuperCollider)
// Quantum Guitar SynthDef
SynthDef(\quantumString, { |freq=440, theta=0, phi=0, amp=0.5|
var classical, quantum, mix;
var prob0, prob1;
// Classical component
classical = Saw.ar(freq) * EnvGen.kr(Env.perc);
// Qubit probabilities from Bloch sphere
prob0 = cos(theta/2).squared;
prob1 = sin(theta/2).squared;
// Quantum superposition sound
quantum = (SinOsc.ar(freq) * prob0) +
(SinOsc.ar(freq * 1.5) * prob1);
// Phase modulation from phi
quantum = quantum * cos(phi);
// Mix via volume pedals
mix = XFade2.ar(classical, quantum, \qMix.kr(0));
Out.ar(0, mix * amp ! 2);
}).add;
Performances
| Date | Venue | Configuration |
|---|
| 2024 | Edinburgh Science Festival | First Quantum Guitar |
| 2024 | Wacken Open Air | With Black Tish |
| 2024 | Lowlands Festival | Industrial Metal |
| 2025 | Vienna World Quantum Day | "Bell" with Grand Piano |
| 2025 | Berlin UdK Medienhaus | Quantum Guitar + Piano |
| 2025 | Merton College Oxford | + Cathedral Organ |
| 2026 | St Giles' Edinburgh | "Quantum Universe" Symphony |
Industrial Music Connection
"Industrial Music is the Musique Concrète 'of the people'."
Pioneers using guitar:
- Throbbing Gristle
- Cabaret Voltaire
- Einstürzende Neubauten
- Nine Inch Nails
Black Tish: Recording full album with Quantum Guitar
Tech Rider
quantum_guitar_rider:
audio:
- 2x XLR outputs (classical + quantum mix)
- Quality PA with stage monitor
visual:
- Large screen (HDMI) for Actias Bloch sphere
seating:
- Armless semi-high chair (adjustable)
- Foot access to pedal board
refreshments:
- "Good quality drinks"
Future Instruments
The hands-free quantum enhancement pattern extends to:
- Quantum Violin: Bow + feet
- Quantum Wind: Breath + feet
- Quantum Percussion: Sticks + additional feet
GF(3) Triad
| Component | Trit | Role |
|---|
| zx-calculus | -1 | Notation (classical diagrams) |
| quantum-guitar | 0 | Performance (superposition) |
| discopy | +1 | Computation (quantum circuits) |
Conservation: (-1) + (0) + (+1) = 0 ✓
References
- Coecke, B. (2025). A Quantum Guitar. arXiv:2509.04526
- Miranda, E.R. (2022). Quantum Computer Music. Springer
- Coecke, B. (2023). Basic ZX-calculus. arXiv:2303.03163
- Abdyssagin & Coecke (2025). Quantum concept music score
Demo
Video: https://www.youtube.com/watch?v=Pr4Wr8fdsL0
Skill Name: quantum-guitar
Type: Quantum Music / Industrial / ZX-Calculus
Trit: 0 (ERGODIC)
GF(3): Classical ↔ Quantum transitions conserve
Non-Backtracking Geodesic Qualification
Condition: μ(n) ≠ 0 (Möbius squarefree)
This skill is qualified for non-backtracking geodesic traversal:
- Prime Path: No state revisited in skill invocation chain
- Möbius Filter: Composite paths (backtracking) cancel via μ-inversion
- GF(3) Conservation: Trit sum ≡ 0 (mod 3) across skill triplets
- Spectral Gap: Ramanujan bound λ₂ ≤ 2√(k-1) for k-regular expansion
Geodesic Invariant:
∀ path P: backtrack(P) = ∅ ⟹ μ(|P|) ≠ 0
Möbius Inversion:
f(n) = Σ_{d|n} g(d) ⟹ g(n) = Σ_{d|n} μ(n/d) f(d)
