Many methods solve Poisson equations by using grid techniques which discretize the problem in each dimension. Most of these algorithms are subject to the curse of dimensionality, so that they need exponential runtime.
Researchers at Friedrich-Alexander-Universität Erlangen-Nürenberg, Germany, have proposed a quantum algorithm running in polylog time to produce a quantum state representing the solution of the Poisson equation.
They demonstrated a quantum simulation of an extended circuit design based on this algorithm is made on a classical computer. The purpose is to test an efficient circuit design which can break the curse of dimensionality on a quantum computer.
Due to the exponential rise of the Hilbert space this design is optimized on a small number of qubits.
The team used Microsoft’s Quantum Development Kit and its simulator of an ideal quantum computer to validate the correctness of this algorithm.