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 $\mathcal{O}(\log n)$ 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.

翻译：随机电路采样（RCS）是实现量子优势的主要途径，其经典难解性被认为源于输出分布的反集中化与概率估计的平均情况难度。本文证明这种关联并非本质。我们引入全息随机电路采样（HRCS）——一种将随机幺正演化与电路中间测量交织的时空协议。我们证明仅需$\mathcal{O}(\log n)$个物理量子比特和线性深度，即可生成具有Haar随机态$ε$近似反集中化特征的$n$个经典比特，揭示了精确的时空权衡关系，并表明存在高效经典模拟方案。我们的分析基于碰撞概率与高阶幂和的精确公式。在IBM量子设备上的实验验证表明，仅用20个量子比特即可实现对多达200个经典比特的采样。