Frozen-Tree Sampling Refutes Quantum Advantage of Random Circuit Sampling

• URL: http://arxiv.org/abs/2607.04054v1
• Date: Sat, 04 Jul 2026 23:24:43 GMT
• Title: Frozen-Tree Sampling Refutes Quantum Advantage of Random Circuit Sampling
• Abstract summary: Random circuit sampling of bitstrings from a Haar-random quantum state is widely believed to be intractable.<n>We propose an efficient classical frozen-tree sampling algorithm that exploits the conditional scale invariance of Haar-random quantum states.<n>No statistical test acting on samples alone can distinguish the classical frozen-tree sampler from a quantum random circuit.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Random circuit sampling of bitstrings from a Haar-random quantum state is widely believed to be classically intractable, and has therefore been implemented as a primary benchmark for demonstrating quantum advantage. Here, we challenge this premise by proposing an efficient classical frozen-tree sampling algorithm that exploits the conditional scale invariance of Haar-random quantum states [Oh, arXiv:2602.19448]. The frozen-tree sampler draws bitstrings of $n$ qubits in $O(n)$ time per sample. Moreover, its output probability $p_F(x)$ is statistically identical to the probability $p_C(x)$ of a random quantum circuit, since both are independent instances of the same Dirichlet distribution. Consequently, no statistical test acting on samples alone can distinguish the classical frozen-tree sampler from a quantum random circuit. The claimed quantum advantage of random circuit sampling therefore does not withstand scrutiny: its hardness lies not in sampling from the Dirichlet distribution, which is classically efficient, but in identifying a specific circuit realization.

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