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

TL;DR

This paper introduces a tensor-network method using matrix product states to efficiently simulate the quantum evolution of nonlinear optical systems in continuous-variable representations, surpassing traditional Fock-basis limitations.

Contribution

The authors develop a novel tensor-network approach that enables scalable and accurate simulation of complex quantum optical processes beyond existing computational capabilities.

Findings

Successfully simulates degenerate spontaneous parametric down-conversion

Achieves high compression ratios while maintaining physical accuracy

Reproduces key theoretical benchmarks such as energy conservation and quadrature squeezing

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 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.