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Paper 1

Lattice: A Post-Quantum Settlement Layer

David Alejandro Trejo Pizzo

Year

2026

Journal

arXiv preprint

DOI

arXiv:2603.07947

arXiv

2603.07947

We present Lattice (L, ticker: LAT), a peer-to-peer electronic cash system designed as a post-quantum settlement layer for the era of quantum computing. Lattice combines three independent defense vectors: hardware resilience through RandomX CPU-only proof-of-work, network resilience through LWMA-1 per-block difficulty adjustment (mitigating the Flash Hash Rate vulnerability that affects fixed-interval retarget protocols), and cryptographic resilience through ML-DSA-44 post-quantum digital signatures (NIST FIPS 204, lattice-based), enforced exclusively from the genesis block with no classical signature fallback. The protocol uses a brief warm-up period of 5,670 fast blocks (53-second target, 25 LAT reduced reward) for network bootstrap, then transitions permanently to 240-second blocks, following a 295,000-block halving schedule with a perpetual tail emission floor of 0.15 LAT per block. Block weight capacity grows in stages (11M to 28M to 56M) as the network matures. The smallest unit of LAT is the shor, named after Peter Shor, where 1 LAT = 10^8 shors.

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Paper 2

Qubit-oscillator concatenated codes: decoding formalism & code comparison

Yijia Xu, Yixu Wang, En-Jui Kuo, Victor V. Albert

Year

2022

Journal

arXiv preprint

DOI

arXiv:2209.04573

arXiv

2209.04573

Concatenating bosonic error-correcting codes with qubit codes can substantially boost the error-correcting power of the original qubit codes. It is not clear how to concatenate optimally, given there are several bosonic codes and concatenation schemes to choose from, including the recently discovered GKP-stabilizer codes [Phys. Rev. Lett. 125, 080503 (2020)}] that allow protection of a logical bosonic mode from fluctuations of the mode's conjugate variables. We develop efficient maximum-likelihood decoders for and analyze the performance of three different concatenations of codes taken from the following set: qubit stabilizer codes, analog/Gaussian stabilizer codes, GKP codes, and GKP-stabilizer codes. We benchmark decoder performance against additive Gaussian white noise, corroborating our numerics with analytical calculations. We observe that the concatenation involving GKP-stabilizer codes outperforms the more conventional concatenation of a qubit stabilizer code with a GKP code in some cases. We also propose a GKP-stabilizer code that suppresses fluctuations in both conjugate variables without extra quadrature squeezing, and formulate qudit versions of GKP-stabilizer codes.

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