Design of Tunable Quantum Thermal Diodes and Dissipative Quantum Gates Based on Positive Overflow Algebraic Anchors

Based on the discrete algebraic congruence laws of the positive overflow spectrum, this paper proposes a "look-up table control" parameter design method for non-Hermitian quantum thermodynamic engineering. By mapping pure algebraic anchors to physical dissipation space, this paper reveals the "miracle of algebraic dimensionality reduction" within the Q(√5) domain: the dissipative retention rates and coupling conditions of specific anchors (such as Γ = φ³ and √5) can not only be analytically simplified perfectly, but also naturally lock the degeneracy conditions of non-Hermitian Exceptional Points (EPs) mathematically. Based on this, three parameter formulations for dissipative quantum gates (Modes A/B/C) are designed, and a theoretical model of a quantum thermal diode based on the positive overflow dual-channel intersection is constructed. Using the Lindblad master equation, an idealized rectification ratio (approximately 4.25) is derived. Furthermore, an engineering scheme for a zero-overshoot thermal transistor is proposed utilizing topological short-circuiting (4 + 4/φ³ = 8/φ). Combining dual physical platforms—superconducting quantum circuits and graphene near-field radiation (Rytov theory)—this paper provides a complete engineering implementation guide encompassing process tolerances, material selection, and FPGA look-up table microsecond-level closed-loop feedback, offering a paradigm-shifting solution for high-performance quantum thermal management chips.