Simulating lossy Gaussian boson sampling with matrix product operators

• DOI: 10.48550/arxiv.2301.12814
• Publication Date: 2023-11-13
• Authors: Minzhao Liu; Changhun Oh; Junyu Liu; Liang Jiang; Yuri Alexeev
• Keywords: FOS: Computer and information sciences; Quantum Physics; Computer Science - Computational Complexity; 0103 physical sciences; FOS: Physical sciences; Computational Complexity (cs.CC); Computational Physics (physics.comp-ph); Quantum Physics (quant-ph); Physics - Computational Physics; 01 natural sciences

16 pages, 11 figures. To appear in PRA. This article supersedes arXiv:2303.11409<br/>Gaussian boson sampling, a computational model that is widely believed to admit quantum supremacy, has already been experimentally demonstrated and is claimed to surpass the classical simulation capabilities of even 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. To understand the effect of photon loss on the scalability of Gaussian boson sampling, we analytically derive the asymptotic operator entanglement entropy scaling, which relates to the simulation complexity. As a result, we observe that efficient tensor network simulations are likely possible under the $N_\text{out}\propto\sqrt{N}$ scaling of the number of surviving photons orange$N_\text{out}$ in the number of input photons $N$. We numerically verify this result using a tensor network algorithm with $U(1)$ symmetry, and overcome previous challenges due to the large local Hilbert space dimensions in Gaussian boson sampling with hardware acceleration. Additionally, we observe that increasing the photon number through larger squeezing does not increase the entanglement entropy significantly. Finally, we numerically find the bond dimension necessary for fixed accuracy simulations, providing more direct evidence for the complexity of tensor networks.<br/>