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 random cluster states, which are at the heart of measurement-based computing, up to a size of 4 x 4 qubits. Moreover, 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：量子计算机目前正处于超越经典计算机的前沿。展示量子计算优势的一种方式是通过量子计算设备执行量子随机采样。然而，现有用于验证量子设备确实执行了经典难以处理的采样任务的工具，要么不切实际，要么无法扩展到量子优势区域。因此，验证问题仍是一个突出的挑战。在此，我们在基于测量型量子计算的离子阱量子处理器上，实验演示了可高效验证的量子随机采样。我们创建了随机簇态（测量型计算的核心），其规模达4×4量子比特。此外，通过利用这些态的结构，我们能够在计算过程中回收量子比特，从比量子比特寄存器更大的纠缠簇态中进行采样。然后，我们高效估计保真度以验证所制备的态（包括单实例和平均情况），并将结果与交叉熵基准测试进行比较。最后，我们研究实验噪声对验证证书的影响。我们的结果和技术为实现可验证的量子优势演示提供了一条可行路径。