One-Dimensional Nonlinear Quantum Walks

TL;DR

This paper investigates nonlinear quantum walks on one-dimensional paths and cycles, demonstrating their ability to trap quantum states for potential use in quantum memory and timing applications.

Contribution

It analytically proves that nonlinear quantum walks can be trapped with high fidelity, contrasting with linear walks, and proposes their use in quantum information storage and transfer.

Findings

Nonlinear quantum walks can be trapped with arbitrary fidelity.

Trapping enables potential quantum memory and timing applications.

Contrasts with linear quantum walks that spread quickly.

Abstract

We explore a continuous-time quantum walk starting at a single vertex on the discrete path and cycle with a cubic nonlinearity. Such nonlinearities arise in Bose-Einstein condensates described by the Gross-Pitaevskii equation or by nonlinear optical waveguide arrays. We analytically prove that the nonlinear quantum walk can be trapped to arbitrary fidelity depending on the coefficient of the nonlinear term. This contrasts with linear quantum walks, which are known for spreading quickly in one dimension. We propose that this trapping can be used for timing in quantum state transfer, where a qubit is held at a node until it is ready to be transferred, and it can also be held again at the receiving node. This scheme can also be interpreted as a form of quantum memory, with the trap and transfer corresponding to the storage and release of quantum information.