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For more than three centuries, classical optics has thrived on fundamental principles like refraction, lenses, and interference. These principles have facilitated the creation of sophisticated optical systems without the necessity of solving Maxwell's equations, thereby propelling the advancement of modern optical technology. The infinite-dimensional Fock space associated with bosonic resonators is a pivotal resource for quantum computing, communication, simulation, and precision measurement. However, the manipulation of high-dimensional quantum states has been lacking an intuitive design methodology comparable to that of classical optics. As the number of photons increases, the computational cost of traditional numerical optimization methods escalates dramatically, posing a significant barrier to the deterministic control of quantum states with a large number of photons.
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