A quantum error-correcting code is a central piece of fault-tolerant quantum computation that is required to realise large-scale quantum algorithms. Unfortunately, the state-of-the-art codes with the best parameters that require the least overheads do not yet admit experimentally feasible implementations. Therefore, exploring codes that are both high-performing and practical on proposed quantum computing architectures is essential. Recently, modular system architectures – comprised of equivalent units (modules) that are interconnected in some network – have been at the centre of advances towards scalable fault-tolerant quantum computation.
In our work [1], we take a crucial first step of closing the gap between physical system architectures and error-correcting code constructions. We give a novel way to view and construct quantum codes “tailored” for modular architectures. More specifically, we show how one can see both the inter modular qubit connectivity and the modular network as two separate graphs corresponding to representations of classical or quantum error-correcting codes. With this knowledge, we show how to construct a new quantum code that fully respects the qubit connectivity given by the architecture.
On the one hand, our work opens a new realm of research of constructing high-performance quantum error-correcting codes for physically realisable architectures. On the other, we demonstrate an important connection between physical architectures and theorised code families. With these insights, we expect to lower the overheads necessary for error correction, enable code constructions that can be implemented on physically realisable devices and thus bring fault-tolerant quantum computation closer to fruition.
[1] A. Strikis, L. Berent, “Quantum LDPC Codes for Modular Architectures”, (2022), arXiv:2209.14329.
