# SPDCinv: Inverse Quantum-Optical Design of High-Dimensional Qudits

arXiv: https://arxiv.org/abs/2112.05934 · HTML: https://mlsanity.com/paper/2112.05934/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 110 references that are in the map.
- First posted on arXiv 11 Dec 2021.

## Builds on (most cited first, 10 of 10)

- [Discovering physical concepts with neural networks](https://mlsanity.com/paper/1807.10300/) (2018)
- [Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledge](https://mlsanity.com/paper/1711.07970/) (2017)
- [Active learning machine learns to create new quantum experiments](https://mlsanity.com/paper/1706.00868/) (2017)
- [DPM: A deep learning PDE augmentation method (with application to large-eddy simulation)](https://mlsanity.com/paper/1911.09145/) (2019)
- [Solving inverse-PDE problems with physics-aware neural networks](https://mlsanity.com/paper/2001.03608/) (2020)
- [Computer-inspired Quantum Experiments](https://mlsanity.com/paper/2002.09970/) (2020)
- [Learning models of quantum systems from experiments](https://mlsanity.com/paper/2002.06169/) (2020)
- [Inverse design of photonic crystals through automatic differentiation](https://mlsanity.com/paper/2003.00379/) (2020)
- [Physics-Based Deep Learning for Fiber-Optic Communication Systems](https://mlsanity.com/paper/2010.14258/) (2020)
- [Inverse Design of Quantum Holograms in Three-Dimensional Nonlinear Photonic Crystals](https://mlsanity.com/paper/2102.10344/) (2021)

## Abstract (arXiv)

Spontaneous parametric down-conversion in quantum optics is an invaluable resource for the realization of high-dimensional qudits with spatial modes of light. One of the main open challenges is how to directly generate a desirable qudit state in the SPDC process. This problem can be addressed through advanced computational learning methods; however, due to difficulties in modeling the SPDC process by a fully differentiable algorithm that takes into account all interaction effects, progress has been limited. Here, we overcome these limitations and introduce a physically-constrained and differentiable model, validated against experimental results for shaped pump beams and structured crystals, capable of learning every interaction parameter in the process. We avoid any restrictions induced by the stochastic nature of our physical model and integrate the dynamic equations governing the evolution under the SPDC Hamiltonian. We solve the inverse problem of designing a nonlinear quantum optical system that achieves the desired quantum state of down-converted photon pairs. The desired states are defined using either the second-order correlations between different spatial modes or by specifying the required density matrix. By learning nonlinear volume holograms as well as different pump shapes, we successfully show how to generate maximally entangled states. Furthermore, we simulate all-optical coherent control over the generated quantum state by actively changing the profile of the pump beam. Our work can be useful for applications such as novel designs of high-dimensional quantum key distribution and quantum information processing protocols. In addition, our method can be readily applied for controlling other degrees of freedom of light in the SPDC process, such as the spectral and temporal properties, and may even be used in condensed-matter systems having a similar interaction Hamiltonian.