Quantum Guitar

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)

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

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

# Guitar string as quantum type
string = Ty('string')
quantum_string = qubit

# Quantisation functor
def quantise_string(classical_note):
    """Map classical guitar note to qubit state."""
    # Frequency → phase
    phase = frequency_to_phase(classical_note)
    return Ket(0) >> Rx(phase)

# Foot controller rotation
def foot_rotation(axis, angle):
    if axis == 'X':
        return Rx(angle)
    elif axis == 'Z':
        return Rz(angle)
    else:
        return Ry(angle)

# Measurement
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]  # |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

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

Conservation: (-1) + (0) + (+1) = 0 ✓

References

1. Coecke, B. (2025). A Quantum Guitar. arXiv:2509.04526
2. Miranda, E.R. (2022). Quantum Computer Music. Springer
3. Coecke, B. (2023). Basic ZX-calculus. arXiv:2303.03163
4. 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:

1. Prime Path: No state revisited in skill invocation chain
2. Möbius Filter: Composite paths (backtracking) cancel via μ-inversion
3. GF(3) Conservation: Trit sum ≡ 0 (mod 3) across skill triplets
4. 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)