Network Requirements for Distributed Quantum Computation

Abstract: Physical constraints and engineering challenges, including wafer dimensions, classical control cabling, and refrigeration volumes, impose significant limitations on the scalability of quantum computing units. As a result, a modular quantum computing architecture, comprising small processors interconnected by quantum links, is emerging as a promising approach to fault-tolerant quantum computing. However, the requirements that the network must fulfill to enable distributed quantum computation remain largely unexplored. We consider an architecture tailored for qubits with nearest-neighbor physical connectivity, leveraging the surface code for error correction and enabling fault-tolerant operations through lattice surgery and magic state distillation. We propose measurement teleportation as a tool to extend lattice surgery techniques to qubits located on different computing units interconnected via Bell pairs. Through memory simulations, we build an error model for logical operations and deduce an end-to-end resource estimation of Shor's algorithm over a minimalist distributed architecture. Concretely, for a characteristic physical gate error rate of 1e-3, a processor cycle time of 1 microsecond, factoring a 2048-bit RSA integer is shown to be possible with 379 computing processors, each made with 89781 qubits, with negligible space and time overhead with respect to a monolithic approach without parallelization, if 70 Bell pairs are available per cycle time between each processor with a fidelity exceeding 98.4 percent.