Computational Simulation Approach to Non-Archimedean Quantum Architectures

In the paper's words

The prevailing quantum computing paradigm is fundamentally constrained by the continuous analog fragility inherent to Archimedean spaces, resulting in uncontrolled linear error accumulation that demands massive active correction overheads. To address this structural bottleneck, we propose a transition to a non-Archimedean state space modeled on the p-adic numbers and their graph-theoretic realization, the Bruhat-Tits tree. To validate this non-Archimedean architecture without physical p-adic hardware substrates, we developed a comprehensive software emulation utilizing Bounded Algorithmic Number (BAN) arithmetic logic units to process exact ultrametric valuations.

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

Numbers it reports

1. Pulses registering below the 98% energy threshold yielded zero state transition, resulting in a 0% execution fidelity and leaving the qubit safely moored to its original node.

   from 4.3 Threshold Gate Execution

2. Conversely, pulses impacting between 100% and 150% of the threshold yielded exactly 1.0 logic fidelity within the strict Boolean parameters of the simulation, snapping the state to the target vertex.

   from 4.3 Threshold Gate Execution

3. Pulses recklessly exceeding the 150% threshold successfully initiated defined leakage, blasting the qubit into non-computational branches and forcing an error flag.

   from 4.3 Threshold Gate Execution

4. When subjected to simulated random gauge transformations (relabeling the nodes without altering topology), the algorithm yielded exactly 0% variance in the measured cross-ratio.

   from 4.6 Cross-Ratio Measurement

5. This relentless signal degradation decisively breached the vital 99% operational fidelity threshold within just $10^3$ uncorrected emulation cycles.

   from 5.1 Archimedean

6. Gate fidelity remained spectacularly flat, maintaining >99.9% integrity over $10^5$ uncorrected simulation cycles without a single active intervention.

   from 5.2 Non-Archimedean Noise

How it is done

1. Computational Simulation Approach to Non-Archimedean Quantum Architectures

   from A

2. Continuous Analog Fragility through Ultrametric Geometric Robustness 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-approach-to-non-archimedean-quantum-architectures/ Date: 2026-04-16 Version: 1.0 Abstract : The prevailing quantum computing paradigm is fundamentally constrained by the continuous analog fragility inherent to Archimedean spaces, resulting in uncontrolled linear error accumulation that demands massive active correction overheads.

   from Addressing

3. This continuous degradation directly drives the thermodynamic limits of active correction frameworks, mandating an entirely new geometric approach to hardware state spaces.

   from 1.1 The

4. We simulate these gates strictly as discrete automorphisms: implementing branch swaps, targeted vertex shifts, and synchronized cyclic permutations along the graph edges.

   from 3.4

What would falsify it

1. Observables and Gauge Invariance The fundamental observable extracted in this non-Archimedean framework is the projective cross-ratio, entirely replacing standard Hermitian eigenvalue extraction.

   from 2.7 Cross-Ratio

Where the claim stops

1. Archimedean Limitation in Conventional Systems Continuous analog fragility represents the fundamental barrier to scalable quantum hardware, deeply rooted in the continuous metrics of Euclidean and Archimedean spaces.

   from 1.1 The

2. However, a natively fabricated physical p-adic quantum substrate remains absent from current laboratory capabilities, stalling direct empirical hardware testing.

   from 1.5 Literature Landscape and

3. Consequently, current empirical work relies heavily on classical FPGA emulations, utilizing software approximations to model discrete state isolation.

   from 1.5 Literature Landscape and

Where to read

1. Addressing248 words · 1 min
2. 1.0 Introduction and1,051 words · 5 min
3. 2.01,076 words · 5 min
4. 3.01,051 words · 5 min
5. 4.01,115 words · 5 min
6. 5.0 Simulated1,011 words · 4 min
7. 6.01,028 words · 4 min
8. 7.0 Conclusions and929 words · 4 min