Kaustav Chatterjee, Niklas Budinger, Kian Latifi Yaghin, Lucas Borg Clausen, Ulrik Lund Andersen

Reliable quantum memory is essential for scalable quantum networks and fault-tolerant photonic quantum computing. We present a quantitative analysis of an all-optical quantum memory architecture in which a Gottesman-Kitaev-Preskill (GKP) encoded qubit is stored in a fibre loop and periodically stabilized using teleportation-based error correction. By modelling fibre propagation as a pure-loss channel and representing each correction round as an effective logical map acting on the Bloch vector, we obtain a compact description of the full multi-round memory channel. We show that syndrome decoder optimization plays a crucial role in the experimentally relevant finite-squeezing regime. The optimal decoder deviates from standard square-grid GKP decoder in both tile-size and tile-shape, leading to significant improved logical performance. Using this optimized decoding strategy, we identify a squeezing-dependent optimal spacing between correction nodes that maximizes the memory lifetime. Remarkably, this optimal segment length is largely independent of the desired storage time, providing a simple and practical design rule for fibre-loop quantum memory. We further find a squeezing threshold of approximately 6.7 dB below which intermediate error correction becomes counterproductive, while above threshold the achievable storage time increases approximately exponentially with squeezing. For example, at 17 dB squeezing, storage times exceeding 400 ms can be achieved with logical infidelity below 1%. These results establish clear performance benchmarks and reveal the fundamental trade-off between photon loss, squeezing, and correction frequency in continuous-variable architectures. Our findings provide actionable design principles for near-term photonic quantum memory and clarify the path toward scalable all-optical fault-tolerant quantum storage.