The Refrigeration Multiplier: What Cold Computing Really Costs at the Wall

Removing one watt at cryogenic temperature T costs at least (300-T)/T watts at the wall, and more in a real refrigerator. This paper computes the ideal and realistic refrigeration multiplier at 77 K, 4 K, 1 K, 100 mK and 15 mK, derives the break-even condition for cold computing, and applies it to superconducting single-flux-quantum logic (conventional RSFQ and ERSFQ, including static bias dissipation) and to a published cryo-CMOS control processor at 4 K (23 mW per qubit). On the cited numbers, under assumptions favourable to the cold technologies, no complete cold technology examined is a net wall-plug winner today: conventional RSFQ loses by about a factor of 66 per operation at the wall, ERSFQ reaches approximate parity per switching event, and the cryo-CMOS controller costs 17.0 W per qubit at the wall. Model calculations, simulated not measured; computation script and full results are included.