Anticoncentrated $n$-bit distribution from $\log(n)$ qubits

Bingzhi Zhang; Quntao Zhuang

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arXiv · 2511.05433

Anticoncentrated $n$-bit distribution from $\log(n)$ qubits

Bingzhi Zhang·Quntao Zhuang

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Abstract

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 $\epsilon$-approximate anticoncentration of Haar random states can be generated using only $\mathcal{O}(\log n)$ 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.

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Bingzhi Zhang, Quntao Zhuang. 2025-11-07. Anticoncentrated $n$-bit distribution from $\log(n)$ qubits. https://arxiv.org/abs/2511.05433

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