Reduction of Processor-Nonlocal Gates in Distributed Quantum Computing by Distributed Quantum Error Correction

The paradigm of distributed quantum computing is growing in popularity as an effective way of scaling beyond the limits of monolithic architectures. By networking small, modular processors with fewer qubits, one can reduce qubit cross-talk while still scaling to a large number of qubits. However, this cross-talk is replaced by the need to perform gates between error-corrected modules to utilize the full quantum computing system. We show how building error correction codes across modules, rather than within them, can decrease the number of processor-nonlocal gates required to execute a logical circuit by over 80% by making transversal gates processor local, even after accounting for distributed syndrome extraction cost. Furthermore, we mathematically show that the error correction capabilities of distributed codes are strictly equal to or better than those of local codes, assuming no correlations in noise across processors. Finally, we discuss distribution of approximate error correcting codes as a potential way to solve the issue of executing non-transversal gates in such a distributed architecture.