Optimal linear-optical interferometers for unitary t-designs in a multi-photon Fock space
Abstract
We investigate the construction of unitary 1-designs and two-photon designs on programmable linear-optical interferometers. Using the frame-potential loss as the optimization objective, we identify architectures that reproduce the relevant Haar moments with considerably fewer programmable phase shifters than required for universal linear optics. For unitary 1-designs, we provide an exact construction and prove that the minimum number of programmable phase shifters within the considered layered architecture is 2(d−1), where d is the number of optical modes. Numerical optimization confirms this parameter count over the tested range of dimensions. For two-photon designs, defined by first-moment matching in the symmetric two-photon representation of U(d), we numerically investigate the resources required to achieve prescribed approximation thresholds. We benchmark the resulting ensembles using single- and two-photon transition probabilities and average channel fidelities. Furthermore, we develop a protocol for estimating the total photon number of a multiphoton Fock state using a single monitored output mode and derive the corresponding Haar-averaged photon-count moments. Our findings demonstrate that shallow interferometers can reproduce Haar-averaged observables with reduced hardware resources, while photon-number fluctuations provide a more stringent test of approximate two-photon designs.
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BibTeX
@misc{grinshtein2026optimal,
title = {{Optimal linear-optical interferometers for unitary t-designs in a multi-photon Fock space}},
author = {Robert A. Grinshtein and Ivan V. Dyakonov and Stanislav S. Straupe},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12646},
eprint = {2610.12646},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12646},
}
RIS
TY - UNPB
TI - Optimal linear-optical interferometers for unitary t-designs in a multi-photon Fock space
AU - Robert A. Grinshtein
AU - Ivan V. Dyakonov
AU - Stanislav S. Straupe
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12646
UR - https://arxiv.org/abs/2610.12646
AB - We investigate the construction of unitary 1-designs and two-photon designs on programmable linear-optical interferometers. Using the frame-potential loss as the optimization objective, we identify architectures that reproduce the relevant Haar moments with considerably fewer programmable phase shifters than required for universal linear optics. For unitary 1-designs, we provide an exact construction and prove that the minimum number of programmable phase shifters within the considered layered architecture is 2(d−1), where d is the number of optical modes. Numerical optimization confirms this parameter count over the tested range of dimensions. For two-photon designs, defined by first-moment matching in the symmetric two-photon representation of U(d), we numerically investigate the resources required to achieve prescribed approximation thresholds. We benchmark the resulting ensembles using single- and two-photon transition probabilities and average channel fidelities. Furthermore, we develop a protocol for estimating the total photon number of a multiphoton Fock state using a single monitored output mode and derive the corresponding Haar-averaged photon-count moments. Our findings demonstrate that shallow interferometers can reproduce Haar-averaged observables with reduced hardware resources, while photon-number fluctuations provide a more stringent test of approximate two-photon designs.
ER -