Good Gottesman-Kitaev-Preskill Codes from the NTRU Cryptosystem

Explore the theoretical foundations and practical applications of Gottesman-Kitaev-Preskill (GKP) codes in this 57-minute QuICS talk. Delve into the lattice theoretic perspective of GKP codes, highlighting their connections to classical error correction, quantum error correction, and post-quantum cryptography. Discover a new class of random GKP codes derived from the NTRU cryptosystem, featuring constant rate and average distance scaling comparable to concatenated single-mode GKP codes. Learn how these NTRU-GKP codes offer efficient decoding for stochastic displacement noise models, equivalent to the NTRU cryptosystem's decryption process. Investigate the potential of NTRU-GKP codes in establishing private quantum channels under NTRU cryptosystem security assumptions. Gain insights into the intersection of GKP quantum error correction and cryptography, and explore future research directions in this fascinating field.

Intro
A brief (incomplete) history of Gottesman-Kitaev-Preskill Codes
GKP codes →→ Lattice theory
GKP Code constructions
Random GKP Codes
The NTRU Cryptosystem as R-Lattice
NTRU Lattice is q-symplectic!
Distance of NTRU-GKP
The Decoding Problem
Basis dependency
Decoding NTRU-GKP
CVP-decoding on NTRU lattices
NTRU-GKP Private Quantum Channel
Summary + Future?