Collapse-Induced Excitation Redistribution and Entropy Structuring in Fully Connected Qubit Networks

Author: Nicholas Panek
Affiliation: PatternRipple Labs
Date: October 2025
License: MIT (code) / CC BY-4.0 (paper, figures)

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Abstract

We study a 16-qubit system prepared as a uniform superposition over all computational basis states with total Hamming weight ≥ 8.
An all-to-all controlled-Z (CZ) layer, being diagonal in the computational basis, leaves Z-basis populations unchanged.
Measurement of eight qubits in the Z basis and post-selection by their Hamming weight r produces a strict excitation–entropy trade-off on the remaining eight qubits:

• r = 0 deterministically yields |11111111⟩ (Eq = 1, zero entropy).
• r = 8 yields a maximally mixed distribution (Eq = 0.5, eight bits of entropy).

A complementary interference variant—adding Hadamard gates on the unmeasured qubits before readout—reveals phase-sensitive deviations from the classical curve, confirming the quantum origin of the correlations.
The supplied data and figures reproduce both regimes exactly.

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Repository Structure

collapse-redistribution-benchmark/ ├── paper/

│ ├── Collapse-Induced Excitation Redistribution and Entropy Structuring in Fully Connected Qubit Networks.pdf

│ ├── fig_z_only.png

│ ├── fig_interfere.png

│

├── data/

│ ├── table_z_only.csv

│ ├── table_interfere.csv

│

├── code/

│ ├── v4cg.py

│ ├── v4cg.ipynb

│

├── requirements.txt

└── LICENSE

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Reproduction Guide

1. Environment

python3 -m venv venv
source venv/bin/activate
pip install -r requirements.txt

2. Generate Tables and Figures

python code/v4cg.py --z-only
python code/v4cg.py --interfere

Outputs are written to data/ and paper/ as CSV and PNG files.

3. Notebook Version

v4cg.ipynb reproduces both modes interactively using the same combinatorial model.

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Contents

File	Description
table_z_only.csv	Exact combinatorial Z-basis statistics for r = 0 … 8.
table_interfere.csv	Phase-sensitive results after applying H on the unmeasured qubits.
fig_z_only.png	Eq vs r (Z-only).
fig_interfere.png	Eq vs r (after interference).
Collapse-Induced … Networks.pdf	Final formatted paper summarizing results.

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Method Summary

1. State preparation: uniform superposition of all 16-bit strings with Hamming weight ≥ 8.
2. Entangling layer: all-to-all CZ (120 gates, diagonal).
3. Measurement: first 8 qubits in Z, conditioned by Hamming weight r.
4. Metrics: excitation E, per-qubit Eq, marginal entropy Hₘₐᵣg, joint entropy Hⱼₒᵢₙₜ, multi-information I = Hₘₐᵣg − Hⱼₒᵢₙₜ.
5. Interference extension: apply H^{⊗8} on unmeasured qubits before readout to expose CZ-phase effects.

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Acknowledgments

Computation and visualization by PatternRipple Labs.
Figures and tables generated using NumPy, Pandas, Matplotlib, and ReportLab.

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Reuse

• Code: MIT License
• Paper, images, and tables: CC BY 4.0
  Please cite the work when reusing data or figures.