Network-Integrated Decoding System for Real-Time Quantum Error Correction with Lattice Surgery

Abstract

Existing real-time decoders for surface codes are limited to isolated logical qubits and do not support logical operations involving multiple logical qubits. We present Deconet, a first-of-its-kind decoding system that scales to thousands of logical qubits and supports logical operations implemented through lattice surgery. Deconet organizes compute resources in a network-integrated hybrid tree-grid structure, which results in minimal latency increase and no throughput degradation as the system grows. Specifically, Deconet can be scaled to any arbitrary number of $l$ logical qubits by increasing the compute resources by $O(l \times \log (l))$, which provides the required $O(l)$ growth in I/O resources while incurring only an $O(\log (l))$ increase in latency-a modest growth that is sufficient for thousands of logical qubits. Moreover, we analytically show that the scaling approach preserves throughput, keeping Deconet backlog-free for any number of logical qubits We report an exploratory prototype of Deconet, called Deconet/Helios, built with five VMK-180 FPGAs, that successfully decodes 100 logical qubits of distance five. For 100 logical qubits, under a phenomenological noise rate of $\mathbf{0. 1 \%}$, the Deconet/Helios has an average latency of $2.40 \mu ~\mathrm{s}$ and an inverse throughput of 0.84 $\mu$ s per measurement round.