Belief dynamics#
Phenomenon. Beliefs, preferences and trust change over time and with evidence, and asking for a judgement can change later judgements. Quantum and Markov dynamics make different predictions about this (Busemeyer, Kvam and Pleskac, 2019; Kvam et al., 2015).
Use it for: confidence over time in perception or diagnosis, trust in automation and AI assistants, customer satisfaction over a service episode, opinion change during deliberation.
Models#
Class |
Parameters |
Intermediate judgement changes later ones |
Notes |
|---|---|---|---|
|
mu (drift), gamma (rate) |
no (on average) |
N ordered states, K response bins |
|
mu, sigma |
yes |
H_jj = μ x_j, H_{j,j±1} = σ |
|
mu, sigma, lam (dephasing) |
yes, less with larger lam |
Lindblad master equation |
|
p0, up, down |
no |
Yes/no belief over discrete events |
|
phi0, a_pos, a_neg, gamma |
yes for gamma < 1 |
Qubit with dephasing |
Options for walks: n_states (default 21), n_categories (3), initial_width (0.15).
Data format#
walk_design = {'t2_only': ('single', 1.5), 'both': ('joint', 0.5, 1.5)} # K or K*K outcome cells
belief_design = {'end_only': ((1, 1, 0, 1), (3,)), 'twice': ((1, 1, 0, 1), (1, 3))} # events, query indices
Outcome order for beliefs: answer sequences in itertools.product((1, 0), repeat=k) order (yes = 1).
Quick start#
from quantum_mind.families.dynamics import QuantumWalk, MarkovWalk, OpenSystemBelief, MarkovBelief, question_effect
question_effect(OpenSystemBelief(gamma=0.3), (1, 1, 0, 1, 0, 1), last=5, intermediate=2) # -0.076
Circuits#
walk_circuit(model, t) (state preparation and exp(−iHt) as a unitary gate; single-time
distributions) and belief_circuit(model, events, queries, form) (rotations, ancilla-controlled
dephasing, mid-circuit or deferred measurement).
Limitations#
Walk circuits measure a single time point; two-time judgements on hardware need coarse-grained (category) measurements, which are implemented analytically only.
References#
Busemeyer, Wang and Townsend (2006) J. Math. Psych. 50. Kvam, Pleskac, Yu and Busemeyer (2015) PNAS 112(34). Busemeyer, Kvam and Pleskac (2019) Scientific Reports 9.