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This research advances quantum computing by introducing a novel Riemannian optimization framework specifically tailored for linear optical interferometers. The method significantly accelerates the search for optimal state preparations, such as NOON states, enabling more complex photonic experiments with higher success probabilities. By deriving closed-form analytical gradients, this work removes computational bottlenecks that previously limited the scale of linear optical problems solvable in quantum science.
Riemannian optimization for linear optical problems
arXiv:2609.07890v1 Announce Type: new Abstract: Many applications of linear optics in quantum science involve searching for some optimal configuration of a multiport interferometer. For example, to find heralded state preparations, one can optimize the interferometer to maximize the fidelity and success probability of the state preparation. In this paper, we derive a closed analytical formula for the Riemannian gradient of any differentiable function defined over the interferometer unitaries. We use this gradient in Riemannian optimization algorithms, such as gradient descent or BFGS, to find the optimal setup of the interferometer. As an interesting use case, we search for linear optical state preparations, improving some of the success probabilities reported in the literature for NOON or photon catalysis preparations. Finally, we show that our optimizer is orders of magnitude faster than other methods in the literature, opening the door for solving linear optical problems involving more modes and photons.
Abstract:Many applications of linear optics in quantum science involve searching for some optimal configuration of a multiport interferometer. For example, to find heralded state preparations, one can optimize the interferometer to maximize the fidelity and success probability of the state preparation. In this paper, we derive a closed analytical formula for the Riemannian gradient of any differentiable function defined over the interferometer unitaries. We use this gradient in Riemannian optimization algorithms, such as gradient descent or BFGS, to find the optimal setup of the interferometer. As an interesting use case, we search for linear optical state preparations, improving some of the success probabilities reported in the literature for NOON or photon catalysis preparations. Finally, we show that our optimizer is orders of magnitude faster than other methods in the literature, opening the door for solving linear optical problems involving more modes and photons.
16 pages, 2 figures, 5 tables. Comments welcome!!
arXiv:2609.07890 [quant-ph]
(or arXiv:2609.07890v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2609.07890 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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