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arXiv · 2605.20464

Self-Trapping Bounds for Continuous-Time Nonlinear Quantum Walks on Path and Cycle Graphs

Yujia Shi·Thomas G. Wong
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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. When the nonlinearity is sufficiently strong, the walker remains localized at its initial vertex, a phenomenon known as self-trapping. This contrasts with linear quantum walks, which are known for spreading quickly in one dimension. While self-trapping has been known numerically, we introduce an analytical method that proves self-trapping and yields a quantitative relationship between the nonlinearity coefficient and the trapping probability. 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.

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Yujia Shi, Thomas G. Wong. 2026-05-19. Self-Trapping Bounds for Continuous-Time Nonlinear Quantum Walks on Path and Cycle Graphs. https://doi.org/10.1088/1402-4896%2Faea02d

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