Gaussian boson sampling with 1,024 squeezed states in 8,176 modes

The development of large-scale, high-fidelity quantum processors is a fundamental scientific challenge, essential for exploring the boundaries of classical computation and advancing towards fault-tolerant systems. Gaussian boson sampling not only serves as a prominent model for demonstrating quantum computational advantage^1-3 but can also generate bosonic error-correcting codes for fault-tolerant quantum computing^4-6. However, its scalability has been hindered by significant photon loss in increasingly large and complex encoding circuits. Here we show a programmable photonic quantum processor, Jiuzhang 4.0, which incorporates 1,024 high-efficiency squeezed states into a hybrid spatial-temporal encoded 8,176-mode circuit. By achieving 92% source efficiency and 51% overall system efficiency, the processor produces samples with detection events up to 3,050 photons, representing an order-of-magnitude increase in scale over previous demonstrations^7-10. This architecture realizes a cubic scaling of connectivity (16³ = 4, 096), enabling sampling within a Hilbert space of dimension approximately 10^2,461. The experimental results are rigorously validated against all current classical simulation methods, especially the matrix product state algorithms recently designed to exploit photon loss¹¹. The ability to control thousands of photons in programmable low-loss quantum processors pushes the experimental frontier into a regime far beyond classical tractability and opens a pathway to trillion-qumode three-dimensional cluster states and fault-tolerant photonic quantum hardware.