What this is
The E8 lattice is the densest known sphere packing in 8 dimensions, a mathematical object so symmetric it was used to prove the solution to the 8-dimensional sphere-packing problem (Viazovska, 2016, Fields Medal). Our codec implements a nearest-vector decoder: given a received point in ℝ⁸, it finds the closest E8 lattice point exactly. This is the building block for error-correcting codes and post-quantum key encapsulation schemes that use lattice hard problems as their security foundation.
Why it matters
Lattice-based cryptography is the dominant family of NIST-standardized PQC algorithms: ML-KEM (CRYSTALS-Kyber), ML-DSA (CRYSTALS-Dilithium), and SLH-DSA all rely on lattice hardness assumptions. Understanding the geometry of the lattices underpinning these schemes is prerequisite to evaluating their security parameters honestly. The E8 codec is our baseline implementation for lattice geometry work.
Technical Specification
- -Dimension: 8
- -Kissing number: 240, all 240 minimal vectors enumerated and verified
- -Coding gain: 1.46 dB (4-QAM baseline) → 2.19 dB (E8 shaping)
- -Decoder: nearest-vector via Gosset polytope projection
- -Status: internal, not published; IP Claim filed
IBM Quantum Job IDs
60 jobs total across Build 41 (coupling sweep) + 6 across Build 40 (gauge decomposition) · IBM ibm_fez · 156-qubit Heron r2