Quantum--Fluid Correspondence for Systems of Nonrelativistic Spin-$\frac{1}{2}$ Particles

TL;DR

This paper demonstrates that systems of nonrelativistic spin-1/2 particles can be described as fluid flows, extending quantum hydrodynamics to many-particle systems and suggesting a fluid-based realization of quantum computers.

Contribution

It provides a fluid-mechanical derivation of the Pauli equation and generalizes the quantum-hydrodynamic picture to multiple particles and higher dimensions.

Findings

Charged fluids with spin satisfy the Pauli equation.

Multiple such fluids form an Euler flow in 3n dimensions.

Potential realization of n-qubit quantum computers as fluid systems.

Abstract

We show that a charged fluid endowed with an internal spin degree of freedom naturally satisfies the Pauli equation for a nonrelativistic spin-1/2 particle, and that a collection of n such interacting fluids can be reformulated as an Euler flow in 3n dimensions, thereby providing a natural representation of a system of n Pauli particles. These results provide a fluid-mechanical derivation of the Pauli equation and extend the Madelung, or quantum-hydrodynamic, picture to many-particle quantum systems. In particular, they imply that an n-qubit quantum computer can, at least in principle, be realized as a suitable combination of n fluids, or equivalently as a 3n-dimensional Euler flow.