Glossary#

Terms used across the documentation, in alphabetical order. The mathematics pages give the equations.

Adjoint method#: A way to compute the gradient of a circuit’s output with respect to every angle in about three simulations, by running the circuit forward and a co-state backward. Used by the simulator to train circuits with many angles.
AIC, BIC#: Akaike and Bayesian information criteria: \(2k - 2\log L\) and \(k\log n - 2\log L\). Lower is better; both penalise the number of parameters \(k\), BIC more strongly for large samples \(n\).
Amplitude#: A (possibly complex) number \(\psi_i\) whose squared magnitude \(\lvert\psi_i\rvert^2\) is a probability. Amplitudes add before squaring, which is the source of interference.
Anchoring model#: Classical baseline for order effects: the second answer is pulled towards the first.
Ask or act#: The robot’s decision rule: ask when the expected cost of acting, error cost times \((1 - p)\), is larger than the cost of asking, or when its models of the person disagree.
Atom interferometer#: A sensor that splits and recombines a cloud of cold atoms with laser pulses; it reads acceleration as a phase \(\varphi = k_{\mathrm{eff}} a T^2\) and is very sensitive and almost drift-free, but slow.
Baseline#: The classical model a quantum-like model is compared with on the same data. Every model in the library has at least one.
Bloch sphere#: The picture of a qubit’s state as a point on (pure) or inside (mixed) a unit sphere.
Born rule#: The probability of an outcome is the squared length of the state’s projection onto that outcome: \(p = \lVert P\psi\rVert^2\).
Calibration#: A confidence is calibrated when events reported with confidence \(c\) happen with frequency \(c\).
Clopper-Pearson interval#: Exact binomial confidence interval for a success rate; its lower end is a safe confidence for risky actions.
COBRA#: Context-rotated density-matrix belief filter: the previous sensor frame rotates the basis in which the next frame is measured, so what a reading means depends on what came before it.
Coherence#: The off-diagonal part of a density matrix. COBRA reports its l1 value (the sum of the moduli of the off-diagonal entries) as a diagnostic.
Concurrence#: A measure of two-qubit entanglement between 0 (product state) and 1 (maximally entangled).
Conformal prediction#: A method that turns any classifier’s scores into prediction sets containing the true label with a chosen probability, for exchangeable data.
Decoherence, dephasing#: Loss of the off-diagonal terms of a density matrix; a quantum-like belief then behaves more and more like a classical one.
Dempster-Shafer theory#: Evidence theory in which mass can be assigned to “any hypothesis” (ignorance) as well as to single hypotheses.
Density matrix#: \(\rho\), a positive matrix with trace 1 that describes pure and mixed states.
Dephasing#: Loss of coherence: the off-diagonal entries shrink while the diagonal is unchanged.
ECE#: Expected calibration error: the bin-weighted average gap between accuracy and confidence.
Empirical Bayes#: Estimating a prior from data, for example the typical confidence bias of a module from earlier tasks.
Entanglement#: Correlation between qubits that no product of single-qubit states can describe.
Generalised measurement#: An update \(\rho \to M\rho M^\dagger/\mathrm{tr}(M\rho M^\dagger)\) with a positive operator \(M\); with a diagonal \(M\) it is Bayes’ rule, with a rotated \(M\) it reads the evidence in a different basis.
Gymnasium#: The standard Python interface for reinforcement-learning environments (reset, step).
Incompatible questions#: Questions whose projectors do not commute, \(P_AP_B \neq P_BP_A\); the order of asking them then matters.
Interference term#: The extra term \(2\sqrt{\cdot}\cos\theta\) in a quantum-like probability that makes it differ from the classical law of total probability.
Kalman filter#: The optimal linear estimator of a state from noisy measurements; the multi-rate version here fuses sensors that report at different rates.
Kraus operator#: A matrix \(K\) that updates a state as \(\psi \mapsto K\psi/\lVert K\psi\rVert\); used for quantum-like cue fusion.
Lindblad equation#: The equation of motion of an open quantum system: unitary evolution plus dissipation and dephasing.
Lüders rule#: After a “yes”, the state becomes its normalised projection \(P\psi/\lVert P\psi\rVert\).
MAP estimate#: Maximum a posteriori: the parameters that maximise likelihood times prior.
Model recovery#: Simulating data from each candidate model and checking that model comparison picks the true one.
Order effect#: The answer to a question depends on which question was asked before it.
Partial pooling#: Estimating each person’s parameters with a prior learnt from the population, so estimates are shrunk towards the population when data are few.
Projector#: A matrix \(P\) with \(P^2 = P = P^\dagger\); it represents the “yes” answer to a question.
QAOA#: Quantum Approximate Optimisation Algorithm: alternating cost and mixer layers that prepare a state concentrated on good solutions of a binary optimisation problem. Here it runs through Qiskit on an exact simulator.
QQ equality#: A parameter-free prediction of every projective model of two questions: the probability of giving different answers is the same in both orders.
Quantum Zeno effect#: Frequent observation slows the evolution of a quantum system; used to model bistable perception.
Quantum-like#: A model of human judgement that uses quantum probability; it assumes nothing quantum in the brain.
Qubit#: A two-level quantum system, \(\alpha\lvert 0\rangle + \beta\lvert 1\rangle\) with \(\lvert\alpha\rvert^2 + \lvert\beta\rvert^2 = 1\).
QUBO#: Quadratic unconstrained binary optimisation: minimise \(x^TQx\) over bit strings. Robot allocation, grasp selection and scheduling are encoded this way with penalty terms.
REINFORCE#: Policy-gradient method that increases the log-probability of actions that led to better than average returns.
Standard quantum limit#: The best phase resolution, \(1/\sqrt{N}\) for \(N\) independent probes; entangled probes can in principle reach the Heisenberg limit \(1/N\).
Temperature scaling#: Recalibration of a classifier by dividing its logits by one fitted temperature \(T\).
Value of information (VOI)#: How much a question is expected to reduce the cost of the final decision.
Variational circuit#: A parameterised circuit whose angles are trained by a classical optimiser.