Nonlinear-ancilla aided quantum algorithm for nonlinear Schr\"odinger equations

• DOI: 10.48550/arxiv.2403.10102
• Publication Date: 2024-01-01
• Authors: Großardt, André
• Keywords: Quantum Physics; FOS: Physical sciences; Quantum Physics (quant-ph)

We present an algorithm that uses a single ancilla qubit that can evolve nonlinearly, and show how to use it to efficiently solve generic nonlinear Schrödinger equations, including nonlocal Hartree equations and the Navier-Stokes equation for an irrotational, non-viscous flow. We propose a realization of such nonlinear qubits via spin-spin coupling of neutral atom qubits to a Bose-Einstein condensate. The results suggest that the use of nonlinear ancillas can provide substantial speedups compared to exclusively linear qubit devices.