2025/05/27 by Ellen Devereux, Animesh Datta, Devereux, Ellen +1 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Medicine · #FOS: Physical sciences #MRI in cancer diagnosis #Quantum Physics (quant-ph) #Scientific Computing and Data Management #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2505.21221
openalex publication_date 2025/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We present four quantum algorithms for solving a multidimensional drift-diffusion equation. They rely on a quantum linear system solver, a quantum Hamiltonian simulation, a quantum random walk, and the quantum Fourier transform. We compare the complexities of these methods to their classical counterparts, finding that diagonalization via the quantum Fourier transform offers a quantum computational advantage for solving linear partial differential equations at a fixed final time. We employ a multidimensional amplitude estimation process to extract the full probability distribution from the quantum computer.