Thermodynamic Effects of Single-Qubit Operations in Silicon-Based Quantum Computing

Silicon-based quantum logic is a promising technology to implement universal quantum computing. It is widely believed that a millikelvin cryogenic environment will be necessary to accommodate silicon-based qubits. This prompts a question of the ultimate scalability of the technology due to finite cooling capacity of refrigeration systems. In this work, we answer this question by studying energy dissipation due to interactions between nuclear spin impurities and qubit control pulses. We demonstrate that this interaction constrains the sustainable number of single-qubit operations per second for a given cooling capacity. Our results indicate that a state-of-the-art dilution refrigerator can, in principle, accommodate operations on millions of qubits before thermal energy dissipation becomes a problem.