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Graphs have provided an expressive mathematical tool to model quantum-mechanical devices and systems. In particular, it has been recently discovered that graph theory can be used to describe and design quantum components, devices, setups and systems, based on the two-dimensional lattice of parametric nonlinear optical crystals and linear optical circuits, different to the standard quantum photonic framework. Realizing such graph-theoretical quantum photonic hardware, however, remains extremely challenging experimentally using conventional technologies. Here we demonstrate a graph-theoretical programmable quantum photonic device in very-large-scale integrated nanophotonic circuits. The device monolithically integrates about 2,500 components, constructing a synthetic lattice of nonlinear photon-pair waveguide sources and linear optical waveguide circuits, and it is fabricated on an eight-inch silicon-on-insulator wafer by complementary metal-oxide-semiconductor processes. We reconfigure the quantum device to realize and process complex-weighted graphs with different topologies and to implement different tasks associated with the perfect matching property of graphs. As two non-trivial examples, we show the generation of genuine multipartite multidimensional quantum entanglement with different entanglement structures, and the measurement of probability distributions proportional to the modulus-squared hafnian (permanent) of the graph's adjacency matrices. This work realizes a prototype of graph-theoretical quantum photonic devices manufactured by very-large-scale integration technologies, featuring arbitrary programmability, high architectural modularity and massive manufacturing scalability.A graph-theoretical programmable quantum photonic device composed of about 2,500 components is fabricated on a silicon substrate within a 12 mm x 15 mm footprint. It shows the generation, manipulation and certification of genuine multiphoton multidimensional entanglement

Graphs have provided an expressive mathematical tool to model quantum-mechanical devices and systems. In particular, it has been recently discovered that graph theory can be used to describe and design quantum components, devices, setups and systems, based on the two-dimensional lattice of parametric nonlinear optical crystals and linear optical circuits, different to the standard quantum photonic framework. Realizing such graph-theoretical quantum photonic hardware, however, remains extremely challenging experimentally using conventional technologies. Here we demonstrate a graph-theoretical programmable quantum photonic device in very-large-scale integrated nanophotonic circuits. The device monolithically integrates about 2,500 components, constructing a synthetic lattice of nonlinear photon-pair waveguide sources and linear optical waveguide circuits, and it is fabricated on an eight-inch silicon-on-insulator wafer by complementary metal–oxide–semiconductor processes. We reconfigure the quantum device to realize and process complex-weighted graphs with different topologies and to implement different tasks associated with the perfect matching property of graphs. As two non-trivial examples, we show the generation of genuine multipartite multidimensional quantum entanglement with different entanglement structures, and the measurement of probability distributions proportional to the modulus-squared hafnian (permanent) of the graph’s adjacency matrices. This work realizes a prototype of graph-theoretical quantum photonic devices manufactured by very-large-scale integration technologies, featuring arbitrary programmability, high architectural modularity and massive manufacturing scalability.

A high-efficiency single photon source (SPS) emitting photons at the telecom O-band or C-band has minimum transmission loss in the silica-based optical fibres, thus is essential in applications such as quantum communication and quantum teleportation. This thesis explores the possibilities of developing such a SPS based on quantum dots (QDs). First, Tamm-based photonic cavities are designed and optimised for extracting the telecom-wavelength photons emitted by the QDs from the high-refractive-index matrix materials using electromagnetic modelling techniques. The optimal confined Tamm structure has been found to have an extraction efficiency of 18\%, and is potentially robust against fabrication errors and suitable for scalable production. In addition, a novel confined Tamm structure with an aperture has been proposed, which is predicted to further improve the extraction efficiency by a factor of 2. Second, a potential QD-SPS, InGaAs-capped InAs QD, which can emit photons at the telecom O-band are investigated experimentally by optical measurements. The wavelength and linewidth distribution of the QD emission lines are characterised, and the exciton and biexciton lines are successfully isolated. In addition, the effects of photonic cavities, such as microcavities and confined Tamm structures, on these QD emissions are studied. The measured mode wavelength, photoluminescence intensity, and quality factor are in broad agreement with the simulation results. Remarkably, we observed single emission lines from the QDs emitting at telecom O-band coupled to confined Tamm mode. Finally, a new promising QD platform, the bismuth-incorporated InAs QD, which can potentially further extend the emission wavelength to the telecom C-band, is also investigated. The emission lines from these QDs are observed and characterised for the first time. We find that with 1\% Bi incorporated, the emission wavelength is close to the telecom window, and the linewidth is