Quantum-like families#

Models of human judgement, decision, memory and trust written in quantum probability, each with the classical baselines it must beat. The equations are on the mathematics page.

Legend: blue inputs, violet internal steps, green outputs, coral people, dashed grey classical baselines. Each entry is labelled by origin: Unique to Quantum Mind designed in this library; it builds on the methods cited with it, Published model, extended implements the cited model as published; Quantum Mind adds the capabilities listed, Published method implements the cited method as published, Software tool infrastructure rather than a model; and by category: Quantum-like quantum probability used to model people; runs on an ordinary computer, Quantum computing quantum circuits; run on the simulator or sent to quantum hardware, Classical classical statistics, decision theory or baselines, Mixed combines parts from more than one of these categories.

Question order: quantum-like model#

Published model, extended Quantum-like

Belief and “yes” subspaces in a 3D or 4D real space; answering projects the belief, so order matters.

        flowchart LR
    accTitle: Block diagram of Question order: quantum-like model
    accDescr: Belief and "yes" subspaces in a 3D or 4D real space; answering projects the belief, so order matters.
    psi["belief ψ (angle g)"]:::hum --> A["subspace A (angle a)"]:::op & B["subspace B (angle b)"]:::op
    A --> AB["A then B<br/>‖P_B P_A ψ‖²"]:::op
    B --> BA["B then A<br/>‖P_A P_B ψ‖²"]:::op
    AB & BA --> out["joint answers in both orders"]:::out
    out --> qq["QQ test: same-answer rate equal"]:::out
    base1["Bayes · anchoring · saturated"]:::base -.-> out
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  • API: QuantumOrderModel, QuantumOrderModel4D

  • Compared with: BayesOrderModel (no order effect), AnchoringOrderModel, SaturatedOrderModel

  • Tutorial: Question-order effects

  • Origin: Published model, extended: implements the cited model as published; Quantum Mind adds the capabilities listed.

  • Category: Quantum-like: quantum probability used to model people; runs on an ordinary computer.

  • Quantum Mind adds: bootstrap intervals, a per-person posterior updated after every answer, and the choice of the most informative condition (what Quantum Mind adds).

  • Reference: Wang, Z., & Busemeyer, J. R. (2013). Topics in Cognitive Science, 5(4), 689-710.

Question order: classical baselines#

Published model, extended Classical

Bayes: a fixed joint distribution; anchoring: the second answer is pulled towards the first; saturated: one free probability per cell (upper bound on fit).

        flowchart LR
    accTitle: Block diagram of Question order: classical baselines
    accDescr: Bayes: a fixed joint distribution; anchoring: the second answer is pulled towards the first; saturated: one free probability per cell (upper bound on fit).
    pA["P(A) · P(B) · correlation"]:::in --> J["fixed joint table"]:::base --> o1["same in both orders"]:::out
    w["anchoring weights wA, wB"]:::in --> AN["second answer pulled<br/>towards the first"]:::base --> o2["order effect"]:::out
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  • API: BayesOrderModel, AnchoringOrderModel, SaturatedOrderModel

  • Tutorial: Question-order effects

  • Origin: Published model, extended: implements the cited model as published; Quantum Mind adds the capabilities listed.

  • Category: Classical: classical statistics, decision theory or baselines.

  • Quantum Mind adds: bootstrap intervals, a per-person posterior updated after every answer, and the choice of the most informative condition (what Quantum Mind adds).

  • Reference: Hogarth, R. M., & Einhorn, H. J. (1992). Cognitive Psychology, 24, 1-55.

Quantum-like Bayesian network#

Published model, extended Quantum-like

A Bayesian network whose unobserved nodes are summed as amplitudes, giving interference terms.

        flowchart LR
    accTitle: Block diagram of Quantum-like Bayesian network
    accDescr: A Bayesian network whose unobserved nodes are summed as amplitudes, giving interference terms.
    G["network graph<br/>CPTs"]:::in --> H["hidden configurations"]:::op --> A["sum amplitudes<br/>with phases"]:::op --> m["marginal of the query"]:::out
    G --> C["classical BN<br/>sum probabilities"]:::base -.-> m
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  • API: QLBNModel

  • Compared with: ClassicalBNModel

  • Origin: Published model, extended: implements the cited model as published; Quantum Mind adds the capabilities listed.

  • Category: Quantum-like: quantum probability used to model people; runs on an ordinary computer.

  • Quantum Mind adds: bootstrap intervals, a per-person posterior updated after every answer, and the choice of the most informative condition (what Quantum Mind adds).

  • Reference: Moreira, C., & Wichert, A. (2016). Frontiers in Psychology, 7, 11.

Belief dynamics: quantum and Markov walks#

Published model, extended Mixed

Evidence accumulation as a walk over confidence levels: unitary (quantum), with decoherence (open system) or stochastic (Markov).

        flowchart LR
    accTitle: Block diagram of Belief dynamics: quantum and Markov walks
    accDescr: Evidence accumulation as a walk over confidence levels: unitary (quantum), with decoherence (open system) or stochastic (Markov).
    s0["initial confidence"]:::hum --> U["Hamiltonian walk<br/>drift · diffusion"]:::op --> D["dephasing γ"]:::op --> j["confidence at time t"]:::out
    s0 --> MK["Markov walk"]:::base -.-> j
    j --> Q["asking changes later answers"]:::out
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  • API: QuantumWalk, OpenSystemWalk

  • Compared with: MarkovWalk

  • Origin: Published model, extended: implements the cited model as published; Quantum Mind adds the capabilities listed.

  • Category: Mixed: combines parts from more than one of these categories.

  • Quantum Mind adds: bootstrap intervals, a per-person posterior updated after every answer, and the choice of the most informative condition (what Quantum Mind adds).

  • Reference: Kvam, P. D., Pleskac, T. J., Yu, S., & Busemeyer, J. R. (2015). PNAS, 112(34), 10645-10650.

Trust belief (open system)#

Published model, extended Quantum-like

Trust as a qubit: outcomes rotate it, time dephases it, a trust question projects it.

        flowchart LR
    accTitle: Block diagram of Trust belief (open system)
    accDescr: Trust as a qubit: outcomes rotate it, time dephases it, a trust question projects it.
    t0["trust state ρ₀"]:::hum --> ev{"hand-over outcome"}:::in
    ev -->|good| up["rotate by a₊"]:::op
    ev -->|bad| dn["rotate by −a₋"]:::op
    up & dn --> deph["dephase γ"]:::op --> q{"asked?"}:::op
    q -->|yes| proj["project · answer"]:::out
    q -->|no| nxt["next interaction"]:::op
    mk["Markov belief"]:::base -.-> proj
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  • API: OpenSystemBelief

  • Compared with: MarkovBelief

  • Tutorial: Trust on a qubit

  • Origin: Published model, extended: implements the cited model as published; Quantum Mind adds the capabilities listed.

  • Category: Quantum-like: quantum probability used to model people; runs on an ordinary computer.

  • Quantum Mind adds: bootstrap intervals, a per-person posterior updated after every answer, and the choice of the most informative condition (what Quantum Mind adds); used for robot hand-over decisions.

  • Reference: Busemeyer, J. R., & Bruza, P. D. (2024). Quantum Models of Cognition and Decision (2nd ed.); Roeder, L., et al. (2023). A quantum model of trust calibration in human-AI interactions. Entropy, 25(9), 1362.

Bistable perception (quantum Zeno)#

Published model, extended Quantum-like

A percept rotating between two interpretations, re-projected every Δt; dwell time ∝ Δt/sin²(gΔt).

        flowchart LR
    accTitle: Block diagram of Bistable perception (quantum Zeno)
    accDescr: A percept rotating between two interpretations, re-projected every Δt; dwell time ∝ Δt/sin²(gΔt).
    p0["percept: interpretation 1"]:::hum --> R["rotate by gΔt"]:::op --> C{"check every Δt"}:::op
    C -->|stays| R
    C -->|flips| f["dwell time ends"]:::out
    f --> d["dwell-time distribution"]:::out
    mk["Markov switching · gamma renewal"]:::base -.-> d
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  • API: QuantumZenoBistableModel

  • Compared with: MarkovSwitchingModel, GammaRenewalModel

  • Tutorial: Bistable perception and the quantum Zeno effect

  • Origin: Published model, extended: implements the cited model as published; Quantum Mind adds the capabilities listed.

  • Category: Quantum-like: quantum probability used to model people; runs on an ordinary computer.

  • Quantum Mind adds: bootstrap intervals, a per-person posterior updated after every answer, and the choice of the most informative condition (what Quantum Mind adds).

  • Reference: Atmanspacher, H., Filk, T., & Römer, H. (2004). Biological Cybernetics, 90, 33-40.