Adaptive Error Correction for Entanglement Distillation

Abstract: Quantum network applications impose a variety of requirements on entanglement resources in terms of rate, fidelity, latency, and more. The repeaters in the quantum network must combine good methods for entanglement generation, effective entanglement distillation, and smart routing protocols to satisfy these application requirements. In this work, we focus on quantum error correction-based entanglement distillation in a linear chain of quantum repeaters. While conventional approaches reuse the same distillation scheme over multiple hop lengths after entanglement swaps, we propose a novel adaptive error correction scheme that boosts end-to-end metrics. Specifically, depending on the network operation point, we adapt the code used in distillation over successive rounds to monotonically increase the rate while also improving fidelity. We demonstrate the effectiveness of this strategy using three codes: [[9,1,3]], [[9,2,3]], [[9,3,3]]. We compare the performance of four different protocols that combine the codes in different ways, where we define a new performance metric, efficiency, that incorporates both overall rate and fidelity. While we highlight our innovation under minimal assumptions on noise, the method can be easily generalized to realistic network settings. By combining our approach with good entanglement generation methods and smart routing protocols, we can achieve application requirements in a systematic, resource-efficient, way.