Upper bounds for the clock speeds of fault-tolerant distributed quantum computation using satellites to supply entangled photon pairs

Despite recent advances in quantum repeater networks, entanglement distribution on a continental scale remains prohibitively difficult and resource intensive. Using satellites to distribute maximally entangled photons (Bell pairs) between distant stations is an intriguing alternative. Quantum satellite networks are known to be viable for quantum key distribution, but the question of if such a network is feasible for fault tolerant distributed quantum computation (FTDQC) has so far been unaddressed. In this paper we determine a closed form expression for the rate at which logical Bell pairs can be produced between distant surface code encoded qubits using a satellite network to supply imperfect physical Bell pairs. With generous parameter assumptions, our results show that FTDQC with satellite networks over statewide distances (500–999 km) is possible up to a collective clock rate on the order of 1 MHz, while continental (1000–4999 km) and transcontinental (5000+ km) distances run on the order of 10 kHz and 100 Hz, respectively.