论文标题
与局部相互作用的浅高斯量子光电电路的有效采样
Efficient sampling from shallow Gaussian quantum-optical circuits with local interactions
论文作者
论文摘要
我们证明，经典的计算机可以通过使用浅层和局部的光电路制备的高斯状态的光子数概率分布有效地采样。我们的工作将Qubits的先前已知结果推广到连续变化的域。我们证明的关键是观察到的，即表征浅层和当地电路产生的高斯状态的邻接矩阵的带宽很小。为了利用这种结构，我们设计了快速算法来计算带状矩阵的循环hafnians。由于在经典上可以从具有指数尺度的光子损失的深度光电电路中进行采样，因此我们的结果对在具有局部相互作用的光子平台上证明量子至上的可行性构成了挑战。
We prove that a classical computer can efficiently sample from the photon-number probability distribution of a Gaussian state prepared by using an optical circuit that is shallow and local. Our work generalizes previous known results for qubits to the continuous-variable domain. The key to our proof is the observation that the adjacency matrices characterizing the Gaussian states generated by shallow and local circuits have small bandwidth. To exploit this structure, we devise fast algorithms to calculate loop hafnians of banded matrices. Since sampling from deep optical circuits with exponential-scaling photon loss is classically simulable, our results pose a challenge to the feasibility of demonstrating quantum supremacy on photonic platforms with local interactions.
