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Silicon-based quantum logic is a promising technology to implement universalquantum computing. It is widely believed that a millikelvin cryogenicenvironment will be necessary to accommodate silicon-based qubits. This promptsa question of the ultimate scalability of the technology due to finite coolingcapacity of refrigeration systems. In this work, we answer this question bystudying energy dissipation due to interactions between nuclear spin impuritiesand qubit control pulses. We demonstrate that this interaction constrains thesustainable number of single-qubit operations per second for a given coolingcapacity. Our results indicate that a state-of-the-art dilution refrigeratorcan, in principle, accommodate operations on millions of qubits before thermalenergy dissipation becomes a problem.

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