Fig. 1: A VLSI graph-theoretical quantum photonic device.

a–c, Diagrams of a graph-based quantum device with 4 × 4 nonlinear photon-pair sources in bulk optics (a) and integrated optics (b), which can directly encode and process a complex-weighted undirected graph (c). An example to illustrate the correspondence of graph theory and quantum device: one pair of single photon created at the source (3,2) and separately routed along the orange and purple pathways corresponds to an edge linked to two vertices in c. The device is fully programmable, consisting of switchable nonlinear photon-pair sources and reconfigurable linear optical waveguide circuits. The device in b monolithically integrates 2,446 components, including 32 spontaneous four-wave mixing degenerate photon-pair sources, 216 phase shifters and 432 transmission lines, 351 low-loss beamsplitters, 463 ultralow-loss waveguide crossers, 420 length-matching delay lines, 100 optical optical inputs/optical outputs (OIs/OOs) and 432 electronic inputs (EIs). Each source can be turned on or off or a state in between using the Mach–Zehnder interferometer keys to alter the edge amplitudes, whereas each phase shifter before the erasers can be addressed to alter the edge phases. By coherently erasing the which-source information using an array of pathway erasers, genuine quantum interference of indistinguishable processes of photon generation takes place. d, Photograph for the ‘Boya’-graph-based quantum device in a 200 mm silicon-on-insulator (SOI) wafer, fabricated by complementary metal–oxide–semiconductor processes. The white dashed box refers to a single copy of the device. e, Characterizations of waveguide crossers with a measured loss of 0.038(4) dB each. f, Classical characterizations (associated with the real part of the graph’s edges) of four eight-mode reconfigurable linear optical circuits. The colour in each grid represents the measured classical statistical fidelity and a mean value of 0.925(32) is obtained from all the 256 measured fidelities. The losses are corrected by normalizing the outcomes. g, Histogram of the measured contrast (C) of all the RHOM quantum interference fringes between two adjacent sources. h, Heralded RHOM quantum interference fringe. It quantifies the indistinguishability of separate quantum processes that create pairs of single photons. A number of 5,600 fourfold coincidence counts (CC) were collected. The error bars (±1σ) in e are given by characterizing five copies of chips in different dies; the error bars (±1σ) in g and h are estimated from Poissonian photon statistics.