تقرير
Quantum Theory and Application of Contextual Optimal Transport
| العنوان: | Quantum Theory and Application of Contextual Optimal Transport |
|---|---|
| المؤلفون: | Mariella, Nicola, Akhriev, Albert, Tacchino, Francesco, Zoufal, Christa, Gonzalez-Espitia, Juan Carlos, Harsanyi, Benedek, Koskin, Eugene, Tavernelli, Ivano, Woerner, Stefan, Rapsomaniki, Marianna, Zhuk, Sergiy, Born, Jannis |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics Quantum Physics Quantitative Biology |
| مصطلحات موضوعية: | Computer Science - Machine Learning, Computer Science - Emerging Technologies, Mathematics - Quantum Algebra, Quantitative Biology - Quantitative Methods, Quantum Physics |
| الوصف: | Optimal Transport (OT) has fueled machine learning (ML) across many domains. When paired data measurements $(\boldsymbol{\mu}, \boldsymbol{\nu})$ are coupled to covariates, a challenging conditional distribution learning setting arises. Existing approaches for learning a $\textit{global}$ transport map parameterized through a potentially unseen context 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 direct link between doubly stochastic matrices and unitary operators thus unravelling a natural connection between OT and quantum computation. We verify our method (QontOT) on synthetic and real data by predicting variations in cell type distributions conditioned on drug dosage. Importantly we conduct a 24-qubit hardware experiment on a task challenging for classical computers and report a performance that cannot be matched with our classical neural OT approach. In sum, this is a first step toward learning to predict contextualized transportation plans through quantum computing. Comment: ICML 2024 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2402.14991 |
| رقم الأكسشن: | edsarx.2402.14991 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |