The Belief Genome Project · Cognitive Qubit

The Cognitive Qubit^™

The cognitive qubit is a proposed model of one belief dimension. Amplitude sets its position between true and false. Phase represents framing, and coherence changes how the model responds to phase.

Move the sliders to see these properties represented by the sphere's position, size, and appearance. Lower coherence breaks the inner sphere into particles. The presets show contrasting example states. They are not diagnoses of a person's beliefs, certainty, or experiences.

State on the Bloch sphere

θ (polar)90.0°

φ (azimuth)0.0°

state(|true⟩ + |false⟩)/√2

|false⟩ — score 1

uncommitted · 5

|true⟩ — score 9

absolute true

deeply true

true

leaning true

uncommitted

leaning false

false

deeply false

absolute false

Predicted answer · by framing

|false⟩ · 1 disagree

5 · uncommitted uncertain

|true⟩ · 9 agree

direct framing (σ_z · phase-invariant) complementary framing (σ_x · phase-dependent)

Drag inside the sphere to rotate the view. The orange ring is the equator: every point on it is an equal-amplitude superposition (score 5).

Probability Density Wave

In this model, position sets the peak, phase changes the oscillation, and coherence controls the spread. Move the sliders to explore the result.

Probe wave (foreground) over probability density (faint fill)

Controls

Amplitude: BGP score (θ)

5.0

1 · |false⟩ 3 5 · uncommitted 7 9 · |true⟩

Phase: framing orientation (φ)

0°

0°90°180°270°360°

Coherence (r)

1.00

0 · noise 0.5 · mixed 1 · coherent

Presets: four example states i

Readouts

Single-probe Likert readout i

amplitude only

5.0

score on 1–9 substantive range

Score = 5 + 4·cos θ, set by amplitude alone. Invariant under phase and coherence. Slide φ or r and this number stays still.

Paired-framing QQ signature i

phase-dependent

+0.000

order-effect magnitude (q)

q ∝ sin θ · cos φ. Changes with φ even when amplitude is fixed — this is the signature the single probe cannot see. Wang et al. (2014) derive a parameter-free constraint of this form from quantum probability.

Depth of conviction i

effective resolution

0.00

|⟨σ_z⟩| · 0 to 1

Locked-in scar (extreme amplitude, full coherence): 1.00. Faded belief (extreme amplitude, low coherence): about 0.25. Neutral or fully decohered states sit near 0. Depth is highest where a strong position and high coherence meet.

How to read this. The inner sphere shows all three dimensions at once: amplitude as its size, coherence as its substance, and the two together as its colour. Three things to try, in order:

1. Click Locked-in scar. The sphere grows to full size at the |true⟩ pole. Sweep phase and the direct answer stays at 9. This is a property of the model, not evidence that a real belief is permanent.

2. Click Faded belief. The direct score stays at 9 and the sphere keeps its size and direction. Lower coherence changes its appearance to a cloud of particles and reduces the complementary readout's sensitivity to phase.

3. Compare Active superposition (amplitude 5, coherence 1) with No opinion (amplitude 5, coherence 0). A direct survey writes down 5 for both. Here they look different. The first is a small solid blue sphere, a genuinely balanced belief held steadily. The second scatters into blue noise, with no settled belief underneath. The geometry tells apart two states a single question cannot.

Formalism follows the quantum-cognitive tradition of Busemeyer & Bruza (2024) and Wang et al. (2014), extended to mixed states with the density-matrix formalism. The state is ρ = ½(I + r·(sin θ cos φ σ_x + sin θ sin φ σ_y + cos θ σ_z)) with coherence 0 ≤ r ≤ 1. The paired-framing order effect q ∝ r·sin θ·cos φ decays as coherence falls, the signature a single probe cannot see. For clarity the direct readout here tracks raw amplitude (score = 5 + 4·cos θ), so a resolved belief keeps its score whatever the coherence, while coherence drives the sphere's substance, its colour, and its framing sensitivity. beliefgenomeproject.org.