Quantum Theory and Application of Contextual Optimal Transport

arXiv:2402.14991v1 Announce Type: new
Abstract: Optimal Transport (OT) has fueled machine learning (ML) applications across many domains. In cases where paired data measurements ($\mu$, $\nu$) are coupled to a context variable $p_i$ , one may aspire to learn a global transportation map that can be parameterized through a potentially unseen con-text. Existing approaches utilize Neural OT and largely rely on Brenier's theorem. Here, we propose a first-of-its-kind quantum computing formulation for amortized optimization of contextualized transportation plans. We exploit a …

abstract application applications arxiv aspire cases context cs.et cs.lg data domains global learn machine machine learning map math.qa q-bio.qm quant-ph quantum text theory through transport transportation type