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Fock states are a fundamental resource for many quantum technologies such as quantum metrology. While much progress has been made in single-photon source technologies, preparing Fock states with a large photon number remains challenging. We present and analyze a bootstrapped approach for nondeterministically preparing large photon-number Fock states by iteratively fusing smaller Fock states on a beamsplitter. We show that by employing state recycling we are able to exponentially improve the preparation rate over conventional schemes, allowing the efficient preparation of large Fock states. The scheme requires single-photon sources, beamsplitters, number-resolved photodetectors, fast-feedforward, and an optical quantum memory.
Motes et al. (Wed,) studied this question.