Quantum-like models and what they are not

The word “quantum” is used in several senses. This library uses exactly one of them, and keeps it apart from the others, because each makes a different claim and needs a different test.

	Quantum-like (this library)	Quantum computing	Quantum-inspired algorithms
What is modelled	Human judgement, decision and trust; a robot’s belief about a person	Any task posed as a quantum computation	Any optimisation or learning task
Mathematics	Quantum probability: state vectors and density matrices, projectors, generalised measurements, interference, open-system dynamics	Gate-model circuits: unitaries, measurement, parameterised ansatz	Classical algorithms that borrow a quantum idea
Runs on	Any computer (microseconds); optionally as a circuit	A quantum computer or a simulator of one	Any computer
The claim	People’s answers violate classical probability in ways quantum probability predicts	A circuit solves or learns the task (advantage is open and problem-specific)	The quantum idea gives a useful heuristic
How to test it	Against classical cognitive models on human data: BIC, QQ equality, total-probability bounds	Against the exact answer and classical baselines; on hardware, against noise	Against classical heuristics with equal budgets
In this library	quantum_mind.families, quantum_mind.belief, quantum_mind.applications	quantum_mind.computing (robot QUBOs, QAOA adapter), quantum_mind.sensing (quantum sensors), the simulator and circuit exports	Not included

Quantum robotics has three threads: quantum computing for robot algorithms, quantum sensing for robots and quantum-probability models of the beliefs a robot holds about people. This library covers all three: the second column through quantum_mind.computing (robot problems and a Qiskit QAOA adapter, never a re-implementation of Qiskit), quantum sensing through quantum_mind.sensing (simulated sensor models and their fusion with classical sensors), and the first column through the families, COBRA and the decision layer. Quantum-inspired optimisers are left to dedicated libraries.

How the parts connect

        flowchart LR
    subgraph QL[Quantum-like cognition]
      F[4 model families<br/>order effects, QLBN,<br/>trust dynamics, bistable perception]
      B[COBRA belief filter<br/>context-rotated measurement]
      R[robot decision layer<br/>questioning, trust, ensemble, ask or act]
    end
    C[quantum_mind.circuits<br/>circuits of the families]
    V{{quantum_mind.viz<br/>Bloch-sphere viewer}}
    F --> R
    B --> R
    F --> C
    C --> H[run: Aer, IBM Quantum, Amazon Braket]
    C --> V
    F --> V
    

• A quantum-like model is a set of vectors and projectors; quantum_mind.circuits turns it into a quantum circuit, so the same model can be executed on quantum hardware (a representation, not a speed-up).

• COBRA applies the same mathematics to the robot’s own belief: a density matrix updated by generalised measurements whose basis depends on the previous frame.

• quantum_mind.viz draws any of them on Bloch spheres: circuit trajectories, the trust qubit of the open-system belief model, and states measured on real backends.

Choosing

• Modelling people (answers, trust, perception) for a robot? Start with the quantum-like families and always fit the classical baselines next to them.

• A robot reading a stream of sensor frames whose meaning depends on context? Try COBRA next to the Gaussian Bayes filter, and look at the ablations before believing a gain.

• Asking whether a quantum computer could help a robot team? Use quantum_mind.computing to pose the problem, run the classical baselines and the QAOA adapter, and compare them honestly; use Qiskit or PennyLane directly for the algorithms.

• Asking whether a quantum sensor would help a robot navigate? Use quantum_mind.sensing with your sensor’s numbers.