Quantum computers are now on the brink of outperforming their classical counterparts. One way to demonstrate the advantage of quantum computation is through quantum random sampling performed on quantum computing devices. However, existing tools for verifying that a quantum device indeed performed the classically intractable sampling task are either impractical or not scalable to the quantum advantage regime. The verification problem thus remains an outstanding challenge. Here, we experimentally demonstrate efficiently verifiable quantum random sampling in the measurement-based model of quantum computation on a trapped-ion quantum processor. We create and sample from random cluster states, which are at the heart of measurement-based computing, up to a size of 4 x 4 qubits. By exploiting the structure of these states, we are able to recycle qubits during the computation to sample from entangled cluster states that are larger than the qubit register. We then efficiently estimate the fidelity to verify the prepared states -- in single instances and on average -- and compare our results to cross-entropy benchmarking. Finally, we study the effect of experimental noise on the certificates. Our results and techniques provide a feasible path toward a verified demonstration of a quantum advantage.

翻译：量子计算机现已处于超越经典计算机的关键节点。展示量子计算优势的途径之一是在量子计算设备上执行量子随机采样。然而，现有用于验证量子设备确实执行了经典难解采样任务的工具，要么不切实际，要么无法扩展至量子优势所需规模。因此，验证问题仍是亟待解决的关键挑战。本研究在离子阱量子处理器上，基于测量量子计算模型，实验演示了高效可验证的量子随机采样。我们制备并采样了随机簇态——这是测量计算的核心资源——其规模达到4×4量子比特。通过利用这些态的结构特性，我们能够在计算过程中循环利用量子比特，从而对大于量子比特寄存器规模的纠缠簇态进行采样。随后，我们通过高效保真度估计对制备的量子态进行验证（包括单次实例与平均情况），并将结果与交叉熵基准测试进行对比。最后，我们研究了实验噪声对验证证书的影响。本研究成果及相关技术为可验证量子优势演示提供了可行路径。