We study random constant-depth quantum circuits in a two-dimensional architecture. While these circuits only produce entanglement between nearby qubits on the lattice, long-range entanglement can be generated by measuring a subset of the qubits of the output state. It is conjectured that this long-range measurement-induced entanglement (MIE) proliferates when the circuit depth is at least a constant critical value. For circuits composed of Haar-random two-qubit gates, it is also believed that this coincides with a quantum advantage phase transition in the classical hardness of sampling from the output distribution. Here we provide evidence for a quantum advantage phase transition in the setting of random Clifford circuits. Our work extends the scope of recent separations between the computational power of constant-depth quantum and classical circuits, demonstrating that this kind of advantage is present in canonical random circuit sampling tasks. In particular, we show that in any architecture of random shallow Clifford circuits, the presence of long-range MIE gives rise to an unconditional quantum advantage. In contrast, any depth-d 2D quantum circuit that satisfies a short-range MIE property can be classically simulated efficiently and with depth O(d). Finally, we introduce a two-dimensional, depth-2, "coarse-grained" circuit architecture, composed of random Clifford gates acting on O(log n) qubits, for which we prove the existence of long-range MIE and establish an unconditional quantum advantage.

翻译：我们研究二维架构中的随机常数深度量子电路。虽然这些电路仅在晶格上相邻量子比特之间产生纠缠，但通过对输出态的部分量子比特进行测量，可以生成长程纠缠。据推测，当电路深度至少达到一个常数临界值时，这种长程测量诱导纠缠（MIE）会大量涌现。对于由Haar随机双量子比特门构成的电路，人们还认为这与从输出分布中采样的经典计算难度所对应的量子优势相变点重合。本文为随机Clifford电路场景中的量子优势相变提供了证据。我们的工作拓展了近期关于常数深度量子电路与经典电路计算能力分离的研究范畴，证明此类优势存在于典型的随机电路采样任务中。具体而言，我们证明在任意随机浅层Clifford电路架构中，长程MIE的存在会引发无条件量子优势。相比之下，任何满足短程MIE特性的深度d二维量子电路都可以在O(d)深度内被经典计算机高效模拟。最后，我们提出一种由作用于O(log n)个量子比特的随机Clifford门构成的二维深度2“粗粒度”电路架构，并证明了该架构中存在长程MIE且具有无条件量子优势。