Analog photonic simulator for large-scale transport

Mengyu Zhao; Xuezhi Zhu; Nikita Guseynov; Yewei Yuan; Na Wang; Meihong Wang; Yunyun Cao; Shi Jin; Nana Liu; Changde Xie; Kunchi Peng; Xiaolong Su

arXiv · 2606.00581

Analog photonic simulator for large-scale transport

Mengyu Zhao·Xuezhi Zhu·Nikita Guseynov·Yewei Yuan·Na Wang·Meihong Wang·Yunyun Cao·Shi Jin·Nana Liu·Changde Xie·Kunchi Peng·Xiaolong Su

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Abstract

Transport equations describe how physical quantities -- such as mass, energy, momentum, concentration, probability, or fields -- are carried, propagated, or redistributed through space and time, forming a foundational class of partial differential equations across science and engineering. However, high-dimensional partial differential equations are difficult to represent on digital grids because the number of degrees of freedom grows exponentially with dimension. Continuous-variable quantum photonics on the other hand can represent and evolve these large-scale fields without first discretizing space into a discrete grid. We demonstrate a large-scale analog photonic simulator for the constant-coefficient advection equation, a transport equation that is a fundamental benchmark for scientific computing. The solution of a $d$-variable advection equation is encoded into $d$ optical modes, so that the partial differential equation evolution maps directly to programmable phase-space displacements generated by optical quadrature momenta. Using a time-domain continuous-variable quantum photonic platform, we validate programmable control with $20,000$ single-mode squeezed states and $20,000$ two-mode squeezed states, and implement transport dynamics on a $20,000$-mode cluster-state resource. Homodyne measurements then verifies mode-resolved displacement control, which can provide first and second-order moment information of the solution to the advection equation, with final achievable relative error as low as $0.8\%$ and $0.92\%$ for first and second-order moment observables respectively. Our results establish continuous-variable photonics as a suitable programmable analog platform for large-scale advection equations.

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Mengyu Zhao, Xuezhi Zhu, Nikita Guseynov, Yewei Yuan, Na Wang, Meihong Wang, Yunyun Cao, Shi Jin, Nana Liu, Changde Xie, Kunchi Peng, Xiaolong Su. 2026-05-30. Analog photonic simulator for large-scale transport. https://arxiv.org/abs/2606.00581

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