Speakers
Description
We present a quantum framework for simulating broad classes of linear PDEs with space-- and time-dependent coefficients, inhomogeneous terms, mixed derivatives, and general boundary data. The method covers Robin boundary conditions, with Neumann, Dirichlet, and periodic cases obtained through the corresponding discretized operators. Starting from finite differences, the framework homogenizes the system, applies Schrödingerisation, and constructs Hamiltonian block-encodings from banded derivative structure and coefficient-function representations. Under efficient input/output assumptions, the evolution-stage cost is polynomial in the one-dimensional grid size $N$ and, in the scenarios detailed in the full version, polynomial in the spatial dimension $d$, giving a polynomial improvement in $N$ and an exponential advantage over the classical $N^d$ scaling for a wide class of PDEs. This complements existing quantum PDE approaches by emphasizing broad coefficient and boundary-condition coverage together with explicit resource accounting. Numerical experiments for a Robin heat equation validate the construction against forward Euler reference solutions. Our approach offers a practical alternative to classical numerical methods for solving PDEs.
| Topic | Quantum algorithms for machine learning applications |
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| Additional Topic | Encoding and processing of data in quantum systems |