A Quantum-Like Tensor State Model for Bivariate Time Seriesin Forestry and Residential Construction

Abstract

Aim: To develop and empirically evaluate a quantum-like tensor state model for bivariate time series, focusing on the joint dynamics of timber harvesting and residential construction across Polish regions.

Methodology: Two related processes were encoded in a four-dimensional complex Hilbert space as a tensor product state whose residual dynamics were governed by a parametrised two-qubit unitary operator acting as a nonlinear second-stage correction to pooled OLS forecasts. The model was estimated on panel data for 16 voivodeships over 2005–2025 and compared with linear, autoregressive, polynomial, and tree-based residual benchmarks using MSE and MAE.

Results: The tensor model substantially reduced global forecast errors for harvesting amplitudes relative to all benchmarks and achieved competitive performance for construction, with statistically significant gains over linear and low-order nonlinear specifications and win rates above 80–90% of regions for harvesting, while its accuracy was broadly comparable to a shallow regression tree for construction.

Implications and recommendations: The findings indicate that quantum-inspired tensor state models can serve as practically useful tools for forecasting and interpreting time-varying cross-sector dependence in regional panels, supporting planning and risk assessment in forestry construction systems. Future research should extend the framework to multisector settings, richer entangling kernels, and partially regionalised operators, and explore applications to other domains with nonlinear, time-varying co-movement.

Originality/value: This study provides one of the first applications of a quantum-like two-qubit tensor state model to classical economic time series, demonstrating that a low-dimensional unitary evolution can yield forecast accuracy at least comparable to strong classical benchmarks while offering a compact, interpretable representation of joint dynamics and entanglement-like interactions between sectors.