Applies tensor network renormalization to analyze entanglement structure across multiple length scales simultaneously — revealing how quantum correlations organize at different scales in ways that single-scale analysis cannot detect.
Many important quantum systems — materials near phase transitions, entangled networks in quantum error correction, complex molecular systems — have significant structure at multiple length scales simultaneously. A small-scale view misses the large-scale organization; a large-scale view loses the local detail. Multi-scale entanglement renormalization analysis (MERA) captures both by systematically coarsening the system layer by layer, preserving long-range correlations at each step.
The φCoherent MERA renormalization engine uses N-nacci coarsening ratios — the degree to which each renormalization step compresses the system follows Fibonacci, tribonacci, or tetranacci proportions depending on the dimensionality chosen. This gives renormalization trajectories that align with the natural self-similar structure of the systems being analyzed. The adjustable N parameter allows the same engine to cover a wide range of system types without re-parameterization.
Computes entanglement structure at every scale simultaneously, revealing long-range correlations that would be invisible to single-scale analysis.
The compression factor at each renormalization step follows the chosen N-nacci sequence, aligning coarsening with the system's natural self-similar structure.
The N parameter selects Fibonacci (N=2), tribonacci (N=3), or tetranacci (N=4) coarsening, covering different dimensionalities and system types without re-engineering the analysis.
The MERA tensor network structure explicitly tracks how entanglement at small scales generates correlations at large scales, making previously opaque long-range effects interpretable.
Analysis tool — used in research settings to understand the entanglement structure of quantum many-body systems and to diagnose entanglement patterns in QEC code states. Pairs with the MPS engine (which represents states the renormalization engine analyzes) and with the entanglement fabric (whose Fibonacci-word cluster states have multi-scale structure that MERA analysis can characterize).
Published under the GNU AGPLv3 with whitepaper and reference implementation. Commercial licensing is available for closed-source deployments.