Computational Simulation of Geometric Orientation Codes

In the paper's words

Fault-tolerant quantum computing requires robust error correction traditionally met using planar topologies that assume noise is perfectly isotropic. However, recent astrophysical measurements suggest the universe possesses fundamental anisotropic properties. This paper challenges the isotropic assumption in quantum error correction by proposing geometric orientation codes.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. Profiles The d=3 surface code performs optimally under isotropic noise, achieving its standard ~1% threshold.

   from 3.3 Surface Code Degradation

2. Analysis In the isotropic regime, the surface code threshold is confirmed at ~1%, while the orientation code fails to exhibit a useful threshold.

   from 3.4 Comparative Threshold

3. Conversely, in the highly anisotropic regime, the surface code threshold drops below 0.1% and effectively registers as NaN due to total lattice failure.

   from 3.4 Comparative Threshold

4. Remarkably, the N=4 orientation code threshold rises to a massive ~10% under this high anisotropy.

   from 3.4 Comparative Threshold

5. A mere 10-degree misalignment degrades the logical threshold by over 40%, as orthogonal isolation breaks down.

   from 3.6 Sensitivity

6. Standard errors for the overhead ratios are bounded tightly within 2%.

   from 3.7 Statistical

How it is done

1. Therefore, an in silico computational approach is strictly required to test this theoretical paradigm.

   from 2.1 Epistemic

2. We define a tetrahedral code (N=4) where qubits are aligned at 109.5-degree intervals.

   from 2.3 Formalizing the

3. Definition: The Isotropic Surface Code A distance-3 surface code serves as the baseline control group for our experiment (Debroy, 2025).

   from 2.5 Baseline

4. Protocol The fault-tolerance pseudothreshold is defined as the physical error rate where the logical error rate exactly equals the physical error rate.

   from 2.6 Threshold Calculation

What would falsify it

1. This variation is not random but forms a distinct dipole across the observable sky.

   from 1.3 Astrophysical

2. The Webb dipole and CMB anomalies indicate that the observable universe possesses a preferred spatial direction (Webb, 2011).

   from 4.7 Alignment with

Where the claim stops

1. Isotropic Assumptions in Quantum Error Correction Author: Rowan Brad Quni-Gudzinas Contact: rowan.quni@outlook.com ORCID: 0009-0002-4317-5604 ISNI: 0000000526456062 DOI: https://papers.qnfo.org/papers/computational-simulation-of-geometric-orientation-codes/ Date: 2026-04-09 Version: 1.0 Abstract : Fault-tolerant quantum computing requires robust error correction traditionally met using planar topologies that assume noise is perfectly isotropic.

   from Addressing

2. However, recent astrophysical measurements suggest the universe possesses fundamental anisotropic properties.

   from Addressing

3. This paper challenges the isotropic assumption in quantum error correction by proposing geometric orientation codes.

   from Addressing

Where to read

1. Addressing255 words · 1 min
2. 1.0 Introduction830 words · 4 min
3. 2.0 Methodology827 words · 4 min
4. 3.0 Results877 words · 4 min
5. 4.0 Discussion833 words · 4 min
6. 5.0 Conclusion770 words · 3 min
7. Appendices425 words · 2 min