We present the first detailed simulation of a measurement based quantum computation based on Gottesman-Kitaev-Preskill (GKP) qubits within a quad-rail lattice (QRL) cluster state involving over 100 GKP modes. This was enabled by the recently developed functional matrix product states (FMPS) framework, with which we simulate continuous-variable (CV) quantum circuits while explicitly modelling intrinsic coherent error sources due to finite squeezing. We perform simulated randomised benchmarking across squeezing levels between 5 and 15 dB and find strong agreement with analytical estimates for high quality GKP qubits. As a demonstration of practical computation, we simulate a three-qubit Grover's algorithm within the QRL and identify a fundamental squeezing threshold -- approximately 10 dB -- beyond which the algorithm outperforms classical probability bounds.
@article{arxiv.2507.15955,
title = {Impact of finite squeezing on near-term quantum computations using GKP qubits},
author = {Frederik K. Marqversen and Andreas B. Michelsen and Janus H. Wesenberg and Nikolaj T. Zinner},
journal= {arXiv preprint arXiv:2507.15955},
year = {2025}
}