Tensor-network approach to quantum optical state evolution beyond the Fock basis

Nikolay Kapridov; Egor Tiunov; Dmitry Chermoshentsev

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arXiv · 2511.15295

Tensor-network approach to quantum optical state evolution beyond the Fock basis

Nikolay Kapridov·Egor Tiunov·Dmitry Chermoshentsev

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Abstract

Understanding the quantum evolution of light in nonlinear media is central to the development of next-generation quantum technologies. Yet, modeling these processes remains computationally demanding, as the required resources grow rapidly with photon number and phase-space resolution. Here, we introduce a tensor-network approach that efficiently captures the dynamics of nonlinear optical systems in a continuous-variable representation. Using the matrix product state (MPS) formalism, both quantum states and operators are encoded in a highly compressed form, enabling direct numerical integration of the Schr\"odinger equation. We demonstrate the method by simulating degenerate spontaneous parametric down-conversion (SPDC) and show that it accurately reproduces established theoretical benchmarks - energy conservation, pump depletion, and quadrature squeezing - even in regimes where conventional Fock-basis simulations become infeasible. For high-intensity pump fields $(\alpha=100)$, the MPS representation achieves compression ratios below $3\times10^{-4}$ while preserving physical fidelity. This framework opens a scalable route to modeling multimode quantum light and nonlinear optical phenomena beyond the reach of traditional methods.

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Nikolay Kapridov, Egor Tiunov, Dmitry Chermoshentsev. 2025-11-19. Tensor-network approach to quantum optical state evolution beyond the Fock basis. https://arxiv.org/abs/2511.15295

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