## 3 Integrated Quantum Photonics Systems
[43] realized a programmable nanophotonic chip. A rendering of the photonic processor is presented in Figure 2d. Four micro-ring resonators generated two-mode squeezed states, achieving large-photon-number event rates: with the four squeezers activated, the 4-photon detection rate reached, on average, 10,000 events per second, and the 19-photon an average rate of 0.3 events per second. An external computer ran custom-developed control software to operate the chip, which was programmable by means of a classical computer and python libraries, allowing dummy users to run remotely quantum algorithms directly on the device. To prove the quantum advantage of using this photonic hardware, the authors performed the boson-sampling algorithm, which was mapped to the calculation of molecular spectra. The chip was used for a proof-of-principle demonstration of the evaluation of the Franck-Condon spectra of ethylene and (E)-phenylvinylacetylene, without the need to evaluate the usual Franck-Condon factors, which represented a computational hard task [54]. A photonic quantum chip with 95 phase shifters and 355 optical components was realized by [PERSON] et al. [55]. This chip represented a platform on which to study the quantum superposition of coherent multimode states--in particular, a generalized multipath wave-particle duality. The transition between the full-particle nature and full-wave nature was obtained for a classical mixture and a quantum superposition. One year later, the same  
Figure 2: (**a**) Scheme of the universal linear-optical processor realized by [PERSON] et al. [39]. From [39], reprinted with permission from AAAS. (**b**) Programmable nanophotonic processor realized by [PERSON] et al. [52]. From [52], Springer Nature. (**c**) Photograph of the quantum photonic chip realized by [PERSON] et al. [42]. From [42], reprinted with permission from AAAS. (**d**) Rendering of the chip realized by [PERSON] et al. in Ref. [43], showing fiber-optical inputs and outputs and on-chip modules for coherent pump-power distribution, squeezing, pump filtering and programmable linear-optical transformations. From [43], Springer Nature. (**e**) A microscopy image of the d-QPU chip realized by [PERSON] et al. [45]. It monolithically integrated 451 optical components. From [45], under a Creative Commons license ([[https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/)]([https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/)), accessed on 8 August 2023). group presented an advanced chip a quantum processing unit [45], that integrated all the necessary components to initialize, manipulate, and measure quantum-quart (ququart) states. It was composed of 451 photonic components, including 116 reconfigurable phase shifters, which could be directly addressed and controlled by using the co-integration technology of photonic and electronic circuits in silicon [see Figure 2e]. The authors proved that quantum computation based on a qudit of dimension \(d\), together with integrated photonics, can increase quantum parallelism with reference to computational accuracy, capacity, and efficiency, compared to its counterpart of quantum computing based on qubits. Specifically, the computational capacity of a four-qubit processor can be equivalently achieved by a two-ququart quantum processor. Encoding each qudit in a dimension \(d\), keeping the same number of photons, improves the detection rate of photons. Furthermore, computational efficiency and speed-up are enhanced by multiple-path interference. One of the most complicated quantum-photonics devices, in terms of circuitry complexity and functionality, was realized in 2023 by [PERSON] et al. [46]. A multi-chip multi-dimensional quantum-entanglement network with retrievability was demonstrated by using silicon-photonic-hybrid-multiplexing technologies. The full spectrum of hybrid encoding and multiplexing devices was monolithically integrated on chips.