Random circuit sampling (RCS) is a leading approach to demonstrate quantum advantage, with its believed classical hardness rooted in anticoncentration of output distributions and average-case hardness of probability estimation. Here we show that this association is not fundamental. We introduce holographic random circuit sampling (HRCS), a spatiotemporal protocol that interleaves random unitary evolution with mid-circuit measurements. We prove that n classical bits exhibiting ϵ-approximate anticoncentration of Haar random states can be generated using only O(logn) physical qubits and linear depth, establishing a precise space-time trade-off and indicating efficient classical simulation. Our analyses is built upon exact formulas for collision probability and higher-order power sums. Our experimental validation on IBM Quantum devices demonstrates sampling up to 200 classical bits using only 20 qubits.
@article{arxiv.2511.05433,
title = {Anticoncentrated $n$-bit distribution from $\log(n)$ qubits},
author = {Bingzhi Zhang and Quntao Zhuang},
journal= {arXiv preprint arXiv:2511.05433},
year = {2026}
}