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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

quant-phphysics.comp-phphysics.opticsSubmitted Nov 19, 2025• Announced Nov 20, 2025• 0 citations• Revised Sep 17, 2026 (v6)
v1 · Nov 19, 2025v2 · Nov 24, 2025v3 · Jun 22, 2026v4 · Jun 23, 2026v5 · Aug 12, 2026v6 · Sep 17, 2026
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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 Schrödinger 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 $(α=100)$, 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.

Comments
13 pages, 5 figures

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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 Schrödinger 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 (α=100)(α=100)(α=100), the MPS representation achieves compression ratios below 3×10−43\times10^{-4}3×10−4 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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