Frozen-Tree Sampling Refutes Quantum Advantage of Random Circuit Sampling

2026-07-04

AI Summary

This work challenges the assumption of classical intractability underlying random quantum circuit sampling as evidence for quantum advantage. The authors propose an efficient classical algorithm—termed “frozen-tree sampling”—that exploits the conditional scale invariance of Haar-random quantum states to demonstrate that this sampling task is equivalent to drawing samples from a Dirichlet distribution. Their method generates bitstrings in O(n) time whose statistics are indistinguishable from those produced by the quantum circuit. This result implies that agreement in output distributions alone is insufficient to verify quantum advantage, thereby raising fundamental doubts about current experimental claims of quantum supremacy based on random circuit sampling.

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.

Problem

• quantum advantage
• random circuit sampling
• classical intractability
• Haar-random quantum states
• Dirichlet distribution

Innovation

• frozen-tree sampling
• random circuit sampling
• classical simulation
• Haar-random quantum states
• quantum advantage