In recent years Gottesman-Kitaev-Preskill (GKP) codes have witnessed an increasing amount of interest for both their theoretically interesting features and as a possible route towards scalable hardware-efficient error correction.
In this talk, I would like to dive deeper into the theoretical understanding of GKP codes from a lattice theoretic perspective, which highlights how the GKP code bridges aspects of classical error correction, quantum error correction as well as post-quantum cryptography and presents an accessible framework to investigate the computational complexity of decoding these codes.
On this basis, I describe a new class of random GKP codes derived from the cryptanalysis of the so-called NTRU cryptosystem. The derived codes are good in that they exhibit constant rate and average distance scaling comparable to that of a GKP code obtained by concatenating single mode GKP codes into a qubit-quantum error correcting code with linear distance.
The derived class of NTRU-GKP codes has the additional property that decoding for a stochastic displacement noise model is equivalent to the decryption process of the NTRU cryptosystem, such that every random instance of the code naturally comes with an efficient decoder. As an application, I discuss how these codes can be used to set up a private quantum channel under the security assumption of the NTRU cryptosystem and provide an outlook on interesting questions that may be tackled at the intersection of GKP quantum error correction and cryptography.