IEQ – Measurement & Simulation

IEQ makes interaction energy in the field quantifiable. It bridges XQM (substance logic) via VQM (relation/topology) to XDM (ethics): we measure resonance, empathy, and stability in coupled systems — and translate them into simulation and practice.

The IEQ approach combines measurement & simulation to reveal coherence and stability as optimizable objectives.

The core idea is an application-dependent functional that logs coherence contributions of the field and makes them optimizable. IEQ is formally grounded in the Hilbert space model (XQM) with operators, uses relations from VQM, and yields measurable targets for XDM.

Objectives & Metrics

Typical IEQ metrics:

IEQ score: aggregated interaction energy as a measure of effective coupling.
Resonance rate: share of links that reinforce coherence rather than damp it.
Stability window: parameter ranges in which patterns are robust to perturbations.
Dephasing index: loss of coherent contributions due to noise (cf. Lindblad).
Coupling coherence: alignment between planned and actually effective relations.

The IEQ Functional

Central is a functional IEQ[∙] that combines coherence and resonance terms with weights and — per application — adds constraints (e.g., fairness, safety, energy use). The result is a multi-objective, comparable and optimizable quantity that is empirically testable.

We start from XQM-style functionals and add application-proximate terms:

$$ \mathcal{K}(\rho) \;=\; \sum_{\alpha\neq\beta} w_{\alpha\beta}\,|\rho_{\alpha\beta}|,\qquad \mathcal{R}(\rho) \;=\; \mathrm{Tr}(\rho R). $$

Additional targets (e.g., de-escalation $D$, fairness $F$, stability $S$) yield

$$ \mathsf{IEQ}(\rho) \;=\; a\,\mathcal{K}(\rho) \;+\; b\,\mathcal{R}(\rho) \;+\; c\,D(\rho) \;+\; d\,F(\rho) \;+\; e\,S(\rho), \quad a,\dots,e \ge 0. $$

Interpretation

$\mathcal{K}$: “How much superposition/resonance is present?”
$\mathcal{R}$: “How strong are the desired couplings?”
Extra terms: tailored to use case (e.g., de-escalation in social media; stability in multi-agent AI).

Basics: Hilbert space, operator, CPTP channel.

Measurement Design & Data

IEQ is tech-agnostic and applies across data worlds:

Simulation: agent-based models, networks, dynamical systems, Monte-Carlo experiments.
Lab/experiment: controlled couplings, perturbations, logging of response patterns.
Process data: interaction logs, comms networks, control and sensor data.

A pre-defined protocol is key: which couplings vary? what counts as “resonance”? which perturbations are realistic?

IEQ in practice

Average IEQ over windows; contrast against a baseline (noise model).
Attribute contributions per relation (interpretability) and feed into XDM.
Document parameters and data paths (reproducibility).

Simulation: From Theory to Numbers

Typical pipeline:

Fix topology (from VQM): ring, grid, small-world, scale-free …
Parametrize couplings: strengths, directions, temporal modulations.
Inject disturbances: noise, outages, delays.
Evaluate trajectories: aggregate coherence contributions over time windows.
Optimize IEQ score: grid/Bayes search or gradient-based heuristics.

First experiments (sketch)

2–4 carriers: XY/XXZ couplings, dephasing; maximize $\mathcal{K}$, $\mathcal{R}$.
“Social toy”: cluster/bridge graph; damp polarizing edges, promote deliberative subgraphs.
Multi-agent AI: reward shaping with IEQ term; aim for de-escalation & stability.

Optimization (formal)

Consider a time-dependent dynamic $ \rho(t) $ (open, Lindblad) and optimize parameters $ \theta $:

$$ \max_{\theta}\ \mathsf{IEQ}\!\big(\rho_\theta(T)\big) \quad\text{s.t.}\quad \dot{\rho}_\theta(t) \;=\; -\,i\,[H_\theta,\rho_\theta(t)] \;+\; \mathcal{L}_\theta\!\big(\rho_\theta(t)\big),\qquad \rho_\theta(0)=\rho_0. $$

Numerics: time discretization, adjoint gradients, regularization (sparsity/robustness).

Validation & Transparency

Baselines (e.g., random couplings) for comparison.
Ablations: which relations truly matter?
Reproducibility: version data/models with CIDs (IPFS); report format with $\rho_0$, $H$, $\mathcal{L}$, time grid, targets, IEQ.

From IEQ to XDM

IEQ yields measurable criteria for XDM: “good” if $ \Delta \mathsf{IEQ} \ge 0 $ (locally or over windows). The weights $a,\dots,e$ make norms transparent and debatable — policy, not dogma.

Why IEQ?

IEQ turns “coherence” into a measurable, steerable quantity — in AI architectures, social systems, or technical networks. Whether de-escalation, fairness, or resilience: with IEQ, desired field effects become explicit objectives — and systematically achievable.

In short: IEQ operationalizes the Theory of Quantum Monads — it delivers numbers we can design with.

Further publication on IEQ

Quantum Monads IV: The Evolution of Interaction Intelligence (2025-02-23)

Introduction of the Interaction-Energy Quotient (IEQ) as a measure for the quality and stability of communication between autonomous quantum monads.

DOI: 10.5281/zenodo.14913679 · Zenodo

Historical references

For state dynamics and projection see Erwin Schrödinger.

IEQ – FAQ

What is IEQ formally based on?

On XQM (Hilbert space, operators) with open dynamics (cf. Lindblad, CPTP channels).

How does IEQ relate to VQM?

VQM provides relations/topologies which IEQ measures and compares.

And the link to XDM?

XDM uses IEQ as criterion: “good” when $ \Delta \mathsf{IEQ} \ge 0 $.

Is there a glossary?

Yes: Glossary: IEQ, plus Hilbert space, operator, and entanglement.