Quaternary Quantum Dynamics and SRM Algorithms: A Middle-Path Framework Beyond Qubits
Description
Quantum computation and theory have historically been dominated by the binary logic of qubits. Yet, the natural expansion to higher-dimensional qudits opens doors to symmetries, correction codes, and previously underexplored algorithmic structures. This work introduces the concept of Quantum Quaternary (QQ), based on four-level qudits, quaternary POVM measures, and four-step evolution cycles. We propose that QQ offers not only a technical generalization of the qubit but also a conceptual architecture that resonates with fundamental patterns of mathematical organization. The originality of this proposal lies in its mirroring of Infinite Series with Multiple Ratios (SRMs), a novel structure already developed and applied in thirteen previous works. In the studies collected in the Trilogy (P10–P12), SRMs have shown themselves capable of interacting with quantum computing, demonstrating properties intermediate between determinism and probabilism. In P4, this framework provided closed-form solutions for trajectories in gravitational fields—a hybrid problem where classical methods fail. In P13, we demonstrated that SRMs can be seen as an operational path between Relativity and Quantum Mechanics. This new paper advances in the same direction, articulating how SRM algorithms can mirror the QQ formalism to propose a novel path to compactness, robustness, and algorithmic control in a quaternary basis. The framework outlined here establishes an operational dictionary: SRM ratios correspond to elementary QQ operators; SRM products to quaternary propagators; trapezoidal corrections to discrete action accumulations. This mapping allows us to construct base-4 words as quantum control programs, exploiting noncommutative order as a resource, not a limitation. The result is a mathematics of local determinism combined with controllable randomness, offering an alternative to the deterministic/probabilistic dualism that separates Relativity and Quantum Mechanics.
Technical info (En)
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8 – Citation CAP 10 – LIVRO FUCAP NO ZENODO
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