## 3 Integrated Quantum Photonics Systems
Moreover, the scalability of integrated quantum devices, networking architecture, multi-mode fiber channels, and entanglement retrieving techniques was demonstrated and verified. Three pairs of three-dimensional entangled photons were distributed from the server chip to three node chips through three few-mode fibers. Then, a quantum-entanglement-retrieving algorithm was used to retrieve entanglement, and quantum tomography was performed. An average fidelity of 89.0% was obtained. A 12-mode programmable photonic chip implementing arbitrary linear-optical transformations on 12 waveguides was used to simulate the unitary evolution of a global isolated system and to demonstrate that the initial state of a local subsystem evolves towards a state of maximum entropy--that is, to a thermal ensemble, due to entanglement with the other modes of the global system [56]. _Boson sampling_--Photonics systems have also been studied to achieve boson sampling, which is a good candidate for quantum supremacy. Since 2013, [PERSON] et al. [57] reported on the first experimental observation of three-photon interference in an integrated three-port directional coupler (tritter) realized by ultrafast-laser-writing waveguides in a borosilicate-glass substrate. The tritter made three photons interact simultaneously without having to decompose the process into cascaded two-mode interactions and phase shifters. In Ref. [38], a quantum-boson-sampling machine with a silica-on-silicon waveguide was reported. The integrated photonic circuit sampled the output distribution resulting from the nonclassical interference of three and four photons. A larger photonic chip for boson-sampling experiments was realized and reported in Ref. [58]. The authors reported on photonic-boson-sampling experiments in randomly designed integrated chips with 5, 7, 9, and 13 modes, which corresponded to 10, 35, 84, and 286 different no-collisions outputs. The waveguides were directly fabricated in the glass chip. In 2022, [PERSON] et al. [59] realized a programmable photonic processor, named Borealis, showing a quantum-computational advantage by carrying out Gaussian boson sampling on 216 squeezed entangled modes. By using the best classical resources available, it would take more than 9000 years, on average, to get a single sample output, whereas Borealis required only 36 us. Among all the photonic demonstrations of quantum computational advantage, photonic or otherwise, Borealis uses the largest number of independent quantum systems. Recently, [PERSON] et al. experimentally realized a universal bosonic quantum classifier of classical data [47]. Quantum classification has three main steps: encoding data into a quantum state, processing the state, and measuring. Then, a classification model is built, with the parameters characterizing the classifier. A bosonic system consisting of a three-layer two-mode circuit and a two-photon input state was fabricated. By training a part of the circuit, it was possible to classify points inside an elliptical boundary, with a success probability of (\(94\pm 0.8\))%. Boson sampling, by its very nature, is a quantum algorithm, whose solution might not be efficiently verifiable. Indeed, any experimental instance approaching the regime of quantum advantage must be necessarily accompanied by appropriate evidence that the employed device is correctly performing the sampling process [20, 60]. Quantum Key DistributionNowadays, security in exchanging encrypted messages is a crucial issue. QKD is a corroborated approach to generating a secret key at a distance in a secure way, because QKD relies on quantum mechanics laws and not on computational complexity. A fundamental step, in order to industrialize QKD systems, is miniaturization, with advantages in terms of mass production, low cost, simple stabilization in temperature, scalability, and compatibility with CMOS production. [PERSON] et al. [61] realized an integrated QKD system at 2.5 GHz, which featured a polarization-independent receiver and precise state preparation.