Modular decoding: parallelizable real-time decoding for quantum computers

Abstract: Universal fault-tolerant quantum computation will require real-time decoding algorithms capable of quickly extracting logical outcomes from the stream of data generated by noisy quantum hardware. We propose modular decoding, an approach capable of addressing this challenge with minimal additional communication and without sacrificing decoding accuracy. We introduce the edge-vertex decomposition, a concrete instance of modular decoding for lattice-surgery style fault-tolerant blocks which is remarkably effective. This decomposition of the global decoding problem into sub-tasks mirrors the logical-block-network structure of a fault-tolerant quantum circuit. We identify the buffering condition as a key requirement controlling decoder quality; it demands a sufficiently large separation (buffer) between a correction committed by a decoding sub-task and the data unavailable to it. We prove that the fault distance of the protocol is preserved if the buffering condition is satisfied. Finally, we implement edge-vertex modular decoding and apply it on a variety of quantum circuits, including the Clifford component of the 15-to-1 magic-state distillation protocol. Monte Carlo simulations on a range of buffer sizes provide quantitative evidence that buffers are both necessary and sufficient to guarantee decoder accuracy. Our results show that modular decoding meets all the practical requirements necessary to support real-world fault-tolerant quantum computers.