Robust quantum computational advantage with programmable 3050-photon Gaussian boson sampling

The creation of large-scale, high-fidelity quantum computers is not only a fundamental scientific endeavour in itself, but also provides increasingly robust proofs of quantum computational advantage (QCA) in the presence of unavoidable noise and the dynamic competition with classical algorithm improvements. To overcome the biggest challenge of photon-based QCA experiments, photon loss, we report new Gaussian boson sampling (GBS) experiments with 1024 high-efficiency squeezed states injected into a hybrid spatial-temporal encoded, 8176-mode, programmable photonic quantum processor, Jiuzhang 4.0, which produces up to 3050 photon detection events. Our experimental results outperform all classical spoofing algorithms, particularly the matrix product state (MPS) method, which was recently proposed to utilise photon loss to reduce the classical simulation complexity of GBS. Using the state-of-the-art MPS algorithm on the most powerful supercomputer EI Capitan, it would take > $10^{42}$ years to construct the required tensor network for simulation, while our Jiuzhang 4.0 quantum computer takes 25.6 $\mu$s to produce a sample. This work establishes a new frontier of QCA and paves the way to fault-tolerant photonic quantum computing hardware.