Nonlinear-ancilla aided quantum algorithm for nonlinear Schrödinger equations

• URL: http://arxiv.org/abs/2403.10102v1
• Date: Fri, 15 Mar 2024 08:48:29 GMT
• Title: Nonlinear-ancilla aided quantum algorithm for nonlinear Schrödinger equations
• Authors: André Großardt,
• Abstract summary: We show how to use a single ancilla qubit that can evolve nonlinearly to efficiently solve generic nonlinear Schr"odinger equations. We propose a realization of such nonlinear qubits via spin-spin coupling of neutral atom qubits to a Bose-Einstein condensate.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 Schr\"odinger 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.

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