Matrix Holography on an Optical Lattice
Abstract
We propose an analog quantum-simulation protocol based on a lattice of atomic ensembles and time-averaged Floquet dynamics to construct the four-body potentials that typically appear in bosonic BFSS-like matrix quantum mechanics. In contrast to gate-based digital implementations requiring deep circuits, our approach generates the target model through a fixed set of control stages per Floquet cycle, keeping the number of consecutive unitaries constant with respect to the matrix size N. The principal scaling cost in our construction is given by the frequency range required to control the growing lattice. We show that this cost grows at most as 𝒪(N3), giving a polynomial scaling route to large−N, attractive to experimental implementation. Additionally, we demonstrate that the coupling parameter can be tuned beyond 𝒪(1), enabling the simulation of strong-coupling physics necessary for holographic phases.
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BibTeX
@misc{lowenberg2026matrix,
title = {{Matrix Holography on an Optical Lattice}},
author = {Robin Löwenberg and Julian Sonner},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05613},
eprint = {2609.05613},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05613},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Matrix Holography on an Optical Lattice
AU - Robin Löwenberg
AU - Julian Sonner
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.05613
UR - https://arxiv.org/abs/2609.05613
AB - We propose an analog quantum-simulation protocol based on a lattice of atomic ensembles and time-averaged Floquet dynamics to construct the four-body potentials that typically appear in bosonic BFSS-like matrix quantum mechanics. In contrast to gate-based digital implementations requiring deep circuits, our approach generates the target model through a fixed set of control stages per Floquet cycle, keeping the number of consecutive unitaries constant with respect to the matrix size N. The principal scaling cost in our construction is given by the frequency range required to control the growing lattice. We show that this cost grows at most as 𝒪(N^3), giving a polynomial scaling route to large−N, attractive to experimental implementation. Additionally, we demonstrate that the coupling parameter can be tuned beyond 𝒪(1), enabling the simulation of strong-coupling physics necessary for holographic phases.
ER -