We show how to construct simulation secure one-time memories, and thus one-time programs, without computational assumptions in the presence of constraints on quantum hardware. Specifically, we build one-time memories from random linear codes and quantum random access codes (QRACs) when constrained to non-adaptive, constant depth, and -dimensional geometrically-local quantum circuit for some constant . We place no restrictions on the adversary's classical computational power, number of qubits it can use, or the coherence time of its qubits. Notably, our construction can still be secure even in the presence of fault tolerant quantum computation as long as the input qubits are encoded in a non-fault tolerant manner (e.g. encoded as high energy states in non-ideal hardware). Unfortunately though, our construction requires decoding random linear codes and thus does not run in polynomial time. We leave open the question of whether one can construct a polynomial time information theoretically secure one-time memory from geometrically local quantum circuits.
View on arXiv@article{stambler2025_2503.22016,
title={ Information Theoretic One-Time Programs from Geometrically Local $\text{QNC}_0$ Adversaries },
author={ Lev Stambler },
journal={arXiv preprint arXiv:2503.22016},
year={ 2025 }
}