Investigation of Heat Transfer in 3D Packaging for Practical-Scale Quantum Annealing Machines

A Qubit-chip/Interposer/Package substrate (QUIP) structure based on the 3D packaging technology is proposed to realize scalable quantum annealing machines. We investigate the thermal conduction of the QUIP structure with finite element method. The effect of the TSV diameter and number, the thickness of interposer and substrate, and the pitch of bumps on thermal conduction is discussed. We reveal the reduction of the maximum temperature of the qubit chips from 40.2 mK to 18.8 mK by optimizing the heat transfer to the heat sink. A cryogenic environment at 20 mK level is successfully achieved for qubit chip operation in QUIP structure.