Thermodynamic and Quantum Constraints on Scalable Quantum Computing: A Consilience of Modeling, Experiment, and Theory

The central tension in scalable quantum computing lies between the exponential growth of quantum information density and the polynomial limits of cryogenic heat extraction. This thermodynamic bottleneck motivates an architectural inversion, where high-power control and readout electronics are offloaded to the 4 Kelvin stage to leverage its vastly greater cooling capacity. However, the physical viability of this paradigm is contingent upon qubits maintaining high-fidelity operation in this more energetic environment. This work validates this architectural solution through a consilience of a physically-grounded numerical model and established thermodynamic theory. Moving beyond simplistic temperature-centric models, we construct a Lindblad framework grounded in the measurable physics of two-level system (TLS) loss and intrinsic 1/f noise. We demonstrate that the systematic engineering of dielectric material quality—specifically the reduction of the effective TLS loss tangent—is the key enabling factor for thermal robustness. The numerical analysis shows that by transitioning from standard amorphous dielectrics ($\tan\delta \approx 10^{-5}$) to state-of-the-art low-loss material systems ($\tan\delta < 10^{-7}$), the decoherence-limited single-qubit gate fidelity at 4 Kelvin can exceed 99.96%, becoming statistically indistinguishable from the ideal performance at 10 millikelvin. This provides a quantitative, materials-driven roadmap for overcoming the thermodynamic constraints on scalable quantum information systems.