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

• URL: http://arxiv.org/abs/2511.15295v2
• Date: Mon, 24 Nov 2025 12:35:07 GMT
• Title: Tensor-network approach to quantum optical state evolution beyond the Fock basis
• Authors: Nikolay Kapridov, Egor Tiunov, Dmitry Chermoshentsev,
• Abstract summary: We introduce a tensor-network approach that efficiently captures the dynamics of nonlinear optical systems.<n>Using the matrix product state (MPS) formalism, both quantum states and operators are encoded in a highly compressed form.<n>This framework opens a scalable route to modeling multimode quantum light and nonlinear optical phenomena.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 above $3\cdot 10^3$ 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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