Trust as a qubit

Robotics / HRI: a person’s trust in a robot as a qubit (quantum_mind OpenSystemBelief, simulated parameters). Successes rotate the belief towards |0> (‘I trust the robot’), failures away from it, and dephasing pulls it towards the z axis. The animation shows the belief over the event sequence; the printout compares P(trust) read from the Bloch vector with the model’s prediction.

import pathlib
from quantum_mind.families.dynamics import OpenSystemBelief, final_yes
from quantum_mind.applications.robotics import TRUST_EVENTS
from quantum_mind.viz import belief_trajectory

The belief trajectory

P(trust) read from the final Bloch vector equals the model’s prediction.

m = OpenSystemBelief(phi0=1.6, a_pos=0.8, a_neg=1.2, gamma=0.3)
traj = belief_trajectory(m, TRUST_EVENTS, steps=10)
p_sphere = (1 + traj.vectors[-1, 0, 2]) / 2
print('events %s: P(trust) from the Bloch vector %.4f, model %.4f' % (TRUST_EVENTS, p_sphere, final_yes(m, TRUST_EVENTS, (5,))))
print('Bloch-vector length (coherence lost to dephasing): start %.3f, end %.3f' % (traj.purity()[0, 0], traj.purity()[-1, 0]))

events (1, 1, 0, 1, 0, 1): P(trust) from the Bloch vector 0.7247, model 0.7247
Bloch-vector length (coherence lost to dephasing): start 1.000, end 0.466

Interactive animation

try:
    from quantum_mind.viz import animate_bloch, save_html
    out = pathlib.Path(sys.argv[0]).resolve().parent / 'output'; out.mkdir(exist_ok=True)
    save_html(animate_bloch(traj, title='Trust belief (simulated person)'), out / 'trust_belief.html')
    print('interactive figure:', out / 'trust_belief.html')
except ImportError:
    print('install plotly for the interactive figure')

interactive figure: /home/runner/work/Quantum-mind/Quantum-mind/examples/output/trust_belief.html