The supplementary document provides additional information about the quantum generative adversarial learning (QGAN) experiments in photonics. The document starts by explaining the structure of the photonic chip used in the experiments. The chip contains on-chip photon pair sources, universal linear optical circuits, and measurement circuits. The on-chip photon pair sources generate two-photon entangled states using the spontaneous four-wave mixing (SFWM) effect. The universal linear optical circuits implement arbitrary unitary operations on each ququarts, which are the quantum states being manipulated. The measurement circuits perform arbitrary projections on each ququarts, allowing for the measurement of quantum states.

The document then explains the working principle of each component of the chip in more detail. It describes how the photon pair sources generate entangled states using SFWM and beam splitters. It explains the design of the universal linear optical circuits, which are based on the use of multi-mode interferometers (MMIs) and phase shifters. The phase shifters are used to induce phase differences between different paths of the photons, allowing for the implementation of arbitrary unitary operations. The document also discusses the calibration of the phase shifters and the effects of phase noise on the performance of the chip.

The document also addresses the issue of shot noise, which arises from the discrete nature of photons. In the experiments, low count levels can lead to intense shot noise, which can degrade the precision of the obtained probability distributions and affect the performance of the QGAN. The document provides examples demonstrating the effects of shot noise on the quality of generated quantum states and the learning performance of the QGAN.

Furthermore, the document discusses the effect of circuit defects on the QGAN. Numerical simulations were performed to investigate the impact of having a defective phase shifter in the circuit. The results showed that a single defective phase shifter did not have a significant impact on the fidelity of the generated quantum states. However, as the number of defective phase shifters increased, the fidelity gradually decreased, indicating that there are limitations to the adaptability of the circuit in the presence of defects.

Overall, the supplementary document provides additional technical details about the photonic chip structure, the working principles of its components, and the impact of shot noise and circuit defects on the QGAN experiments in photonics. These details shed light on the performance characteristics and limitations of the quantum generative adversarial learning approach in photonics.

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