Modular-Assembly-of-High-Performance-Logical-Blocks

Innovative coding strategies for quantum computing challenges.

Pitch

This project explores advanced strategies for Quantum LDPC codes using geometric scaling and algebraic techniques. It introduces the Augmented-Seed Code Family, which significantly enhances performance by breaking previous distance limits, making it highly applicable for near-term quantum computing solutions.

Description

Modular Assembly of High-Performance Logical Blocks utilizes advanced quantum error correction strategies derived from the Lorentzian causal diamond framework. This repository contains vital resources for researchers and practitioners in the field of quantum information theory and coding.

Overview

This project delves into innovative geometric scaling strategies for Quantum Low-Density Parity-Check (LDPC) codes, inspired by the discrete Lorentzian causal diamond (\mathcal{D}). Key methods explored include:

Algebraic amplification through the Hypergraph Product.
Geometric tessellation using one-dimensional chains and two-dimensional tori.
Lattice enrichment involving (E_8) Lorentzian structures.

The primary achievement is the introduction of the Augmented-Seed Code Family. This breakthrough allows for an increase in the classical seed distance from 4 to 6, breaking previous limitations and developing a Pareto-optimal frontier of finite-block CSS codes tailored for near-term quantum devices operating within the range of 100 to 200 qubits.

Key Codes & Results

This repository includes exemplary codes with their respective performance metrics as follows:

Code	(N)	(k)	(d)	Rate	Highlights
Augmented F₆	112	4	(6, 6)	0.036	Best figure of merit at (N \sim 100) (\left(\frac{kd^2}{N} \approx 1.29\right))
Augmented Z-Bias	176	32	(3, 6)	0.182	Optimized for Z-biased noise, promoting asymmetric distances.
Augmented Self-HGP	208	16	(6, 6)	0.077	Proven algebraically with (d=6) and (\frac{kd^2}{N} \approx 2.77).
D4 HGP (Corrected)	193	25	(4, 6)	0.130	Accurate integer linear programming (ILP) distance achieved.

Methodological Discoveries

The provided script verification_modular_assembly.py offers tools for verifying the methods and structures discussed in the paper:

Sampling Blindness Warning: Highlights challenges faced in finding minimum-weight coset representatives in high-dimensional kernels, retracting earlier distance bounds.
Integer Linear Program Distance Oracle: Implements a precise method for calculating logical weights, interfacing between GF(2) and ILP arithmetic efficiently.
(E_8) Lorentzian Obstruction: Explores the structural failures within the (E_8) lattice, impacting distance calculations post row eliminations.
Naïve CSS Lift Obstruction: Discusses how the condition (H_X = \ker(H_Z)) inherently leads to a zero-rate result independently of topology.

Execution of the Verification Script

To utilize the computational insights provided in this project, run the verification suite with:

python3 script/verification_modular_assembly.py

This will initiate a sequence of calculations to verify various geometric constructions based on the findings detailed in the accompanying paper.

Dependencies

Installation of standard scientific Python libraries is required:

pip install numpy scipy

Citation

For any usage of the methodologies or findings, please cite as follows:

@misc{schmitt2026modular,
  author    = {Yannick Schmitt},
  title     = {Modular Assembly of High-Performance Logical Blocks from the 
               Lorentzian Causal Diamond: Pareto-Optimal Finite-Block Codes, 
               Asymmetric Distance Families, and an E8 Structural Obstruction},
  year      = {2026},
  doi       = {10.5281/zenodo.19484043},
  url       = {https://doi.org/10.5281/zenodo.19484043}
}

Explore the innovative strategies featured in this project to advance the frontier of quantum coding by leveraging the potential of modular assembly derived from the Lorentzian causal diamond framework.

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