Quantum Computing: Foundations and Applications

Ivan Pasev

Quantum Computing: Foundations and Applications

Scientific Status

This document presents research within an active scientific investigation program. The theorems, formalisms, and systems described herein are subject to continuous validation and rigorous logical verification by the Global Institute of Logic & Cybernetics (GILC) and are not automatically peer-validated unless explicitly stated.

Executive Abstract

This whitepaper details the Sovereign Quantum Computing Architecture (SQCA) designed for the Stitchia Protocol and wider digital fabrics. We establish a post-quantum cryptographic layer secured by high-dimensional Lattice-Based Cryptography, resisting polynomial-time quantum adversaries such as Shor's and Grover's algorithm families. Furthermore, we formulate a highly optimized Quantum Execution Queue scheduling algorithm that leverages Fractal Quantum Field Theory (FQFT) spatial-temporal metrics to coordinate quantum execution gates. This document presents the mathematical definitions of our lattice-based constructs, state decoherence prevention protocols, and the sovereign validation pipeline.

Strategic Impact: SQCA guarantees permanent cryptographic immunity and high-performance quantum co-processing for sovereign ledger networks, preventing future state-level decryption.

1. Post-Quantum Lattice Security Layer

Modern cryptographic systems relying on RSA or Elliptic Curve signatures are compromised under Shor's algorithm. To secure the long-term integrity of the digital fabric, SQCA implements the Ring Learning With Errors (R-LWE) hardness problem as its primary security invariant.

Hardness Formulation

Let $R_{q} = z_{q} [x] / (x^{n} + 1)$ be a cyclotomic polynomial ring where $n$ is a power of 2, and $q$ is a prime number. The secret key is $s \in R_{q}$ with small coefficients. The R-LWE distribution over $R_{q} \times R_{q}$ is generated by:

(a, b = a \cdot s + e) \in R_{q} \times R_{q}

Where:

$a$ is chosen uniformly at random from $R_{q}$ .
$e$ is an error polynomial sampled from a discrete Gaussian distribution $χ^{n}$ over the ring.
Decryption is computationally infeasible without the knowledge of the secret vector $s$ , even under complete quantum search configurations.

By mapping all Stitchia Protocol credentials onto this lattice invariant, we secure the transactional state space from quantum decryption.

2. FQFT-Driven Quantum Queue Scheduling

Coordinating quantum-classical co-processors requires high-speed scheduler models that prevent premature qubit decoherence. SQCA leverages FQFT spatial layout dynamics to schedule quantum execution gates in real-time.

Scheduling Formulations

The priority vector $P_{j}$ of a quantum computational queue $j$ is calculated as a function of the local coherence lifetime $τ_{coh}$ , the computational weight $W_{j}$ , and the FQFT field density $D (x, y)$ :

P_{j} = \int_{0}^{τ_{coh}} (W_{j} \cdot e^{- λ t} + α \cdot D (r_{j}, t)) d t

Where:

$λ$ is the decoherence decay parameter.
$r_{j}$ is the coordinate vector of the quantum gate.
$α$ is a scaling multiplier balancing FQFT attractive forces.

This equation guarantees that highly sensitive quantum operations are executed in regions of high field density and before the qubit state degrades.

System Architecture Diagram

graph TD
  A[Classical Request Queue] --> B[Lattice-Based Verification R-LWE]
  B --> C[FQFT Queue Scheduler]
  C -->|Optimal State| D[Quantum Execution Core]
  C -->|High Decoherence Risk| E[Coherent Reserve Buffer]
  D --> F[Quantum State Measurement]
  F --> G[Sovereign State Commitment]
  E --> B
  
  style C fill:#ff9800
  style D fill:#4caf50
  style F fill:#2196f3

3. Quantum State Protection Protocols

To shield physical superconducting loops and ion traps from electromagnetic interference, the Stitchia Protocol incorporates Topological Braiding Protection:

Braid Stability Invariant: $B (ψ) = \oint_{Σ} Tr (F \land F) = N_{invariant}$
Any external perturbation that does not alter the global topological genus of the braid has exactly zero influence on the computational state, ensuring high-fidelity operation without massive error-correction overhead.

References

Pasev, I. (2024). Quantum Co-Processing and Lattice Sovereignty. fabrica Quantum Studies.
Regev, O. (2005). On lattices, learning with errors, and cryptography. ACM Symposium on Theory of Computing.
Global Institute of Logic & Cybernetics. (2025). Post-Quantum Cryptographic Frameworks v6.0.4.

CANONICAL SYNTHESIS PATH

01

The Foundations

Science of Fabric Reality (SFR).

->

02

The Systems

Digital Fabrica Theory (DFT).

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03

The Research

Active inquiry and scientific mapping.