Gaussian boson sampling, a computational model that is widely believed to admit quantum supremacy, has already been experimentally demonstrated to surpasses the classical simulation capabilities of even with the most powerful supercomputers today. However, whether the current approach limited by photon loss and noise in such experiments prescribes a scalable path to quantum advantage is an open question. For example, random circuit sampling with constant noise per gate was recently shown not to be a scalable approach to achieve quantum supremacy, although simulating intermediate scale systems is still difficult. To understand the effect of photon loss on the scability of Gaussian boson sampling, we use a tensor network algorithm with $U(1)$ symmetry to examine the asymptotic operator entanglement entropy scaling, which relates to the simulation complexity. We develop a custom-built algorithm that significantly reduces the computational time with state-of-the-art hardware accelerators, enabling simulations of much larger systems. With this capability, we observe, for Gaussian boson sampling, the crucial $N_\text{out}\propto\sqrt{N}$ scaling of the number of surviving photons in the number of input photons that marks the boundary between efficient and inefficient classical simulation. We further theoretically show that this should be general for other input states.
翻译:摘要:高斯玻色子采样是一个广泛认为具有量子优势的计算模型,即使是目前最强大的超级计算机也无法经典模拟。然而,在实验中受光子损失和噪声的限制下,当前的方法是否规定了一条可扩展的取得量子优势的路径是一个开放的问题。例如,最近显示随机电路采样在噪声门限下不是一种可扩展的取得量子优势的方法,虽然模拟中间尺度系统仍然很困难。为了理解光子损失对高斯玻色子采样可扩展性的影响,我们使用具有 $U(1)$ 对称性的张量网络算法来研究渐近算子纠缠熵缩放,这与模拟复杂度相关。我们开发了一种定制的算法,使用最先进的硬件加速器显著缩短了计算时间,使得能够模拟更大的系统。利用这种能力,我们观察到,在高斯玻色子采样中,输出光子数和输入光子数的关键比例 $N_\text{out}\propto \sqrt{N}$ 将模拟复杂度划分为有效和无效的经典模拟。我们进一步理论证明,这对于其他输入状态应该是通用的。