Quantum Walk v1: Theoretical Moisture Dispersion in Soil

By Martin Castellanos Cubides Publications May 12, 2025

As part of my final project for Quantum Simulation Lab, I developed a theoretical model using a modified Continuous Quantum Walk to simulate how moisture disperses in soil. This work focused on designing the framework and equations to represent soil patches as qubits with evolving interactions over time. While this phase established the foundational theory, incorporating real-world data and environmental effects was left for future expansion (covered in Quantum Walk v2: Experimental Form Fitting).

Quantum Walk for Moisture Dispersion in Soil: One and Two Dimensions

Martin Castellanos-Cubides

Abstract

We simulate moisture dispersion in soil using a quantum walk framework, modeling each soil
patch as a lattice site with dynamically updated coupling constants based on local gradients. This
approach captures intuitive diffusion behavior while highlighting the limitations of classical simulation in higher dimensions, motivating future implementation on quantum hardware for real-time
environmental control in enclosed agricultural systems.

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**1D Simulation:** The first proof of concept, we go from high moisture to low moisture and settle at an even equilibrium

**1D Simulation:** A faulty simulation with unphysical wave-like dispersion. Some time after equilibrium a runaway effect causes pileup in the center before redispersing to the equilibrium

**1D Simulation:** A simulation from both ends after correcting for the unphysical pile up of phase transitions from a runaway gradient. We reach equilibrium and stay there.

Back to Portfolio Quantum Walk v2: Experimental Form Fitting