Optimal linear-optical interferometers for unitary t-designs in a multi-photon Fock space

Abstract:We investigate the construction of unitary $t$-designs in a multi-photon Fock space on programmable linear-optical interferometers. Using the frame potential as the optimization objective, we identify architectures that realize approximate unitary 1- and 2-designs with considerably fewer controllable parameters than required for universal linear optics. For example, we find numerical evidence suggesting that for unitary 1-designs, the required number of programmable parameters scales empirically as $2d$ with the number of modes $d$, instead of $O(d^2)$. We benchmark the resulting ensembles using single-photon transition probabilities and average channel fidelities. Furthermore, as a practical result, we develop a photon-number estimation protocol for multi-photon Fock states that leverages these optimized 1- and 2-designs. Our findings demonstrate that shallow interferometers can accurately reproduce Haar-averaged first moments, while second-moment-sensitive observables provide a considerably stricter test for approximate unitary 2-designs.

Quantum Physics (quant-ph); Optics (physics.optics)

arXiv:2610.12646 [quant-ph]

(or arXiv:2610.12646v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.12646 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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