@inproceedings {733,
	title = {Quantum simulation for the 1D heat equation with a central Gaussian barrier potential via Schr{\"o}dingerization},
	booktitle = {Proceedings of the 44th Samahang Pisika ng Pilipinas Physics Conference},
	year = {2026},
	month = {17-20 Jun 2026},
	pages = {SPP-2026-3C-05},
	address = {Los Ba{\~n}os},
	abstract = {We present a quantum simulation of the 1D heat equation with a central Gaussian barrier using the Schr{\"o}dingerization method. The non-unitary nature of the heat equation is subverted through a warped phase transformation. This transforms the heat equation into a unitary operator that can be evolved in a quantum circuit. Quantum simulations were performed using Qiskit with nx = 6 position registers and np = 2, 4, 6 momentum registers. The accuracy of the quantum simulation was evaluated by getting the l{\texttwosuperior} error relative to the classical matrix exponentiation method. Results show that increasing the momentum registers np and reducing the timestep Δt both reduce the simulation error, correctly reproducing the M-shaped solution induced by the Gaussian barrier.},
	url = {https://proceedings.spp-online.org/article/view/SPP-2026-3C-05},
	author = {Red Christian F. Hernandez and Cristine D. Villagonzalo}
}
