Quantum Theory and Application of Contextual Optimal Transport
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arXiv
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| Main Authors: | , , , , , , , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911998682333184 |
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| author | 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 |
| author_facet | 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 |
| contents | Optimal Transport (OT) has fueled machine learning (ML) across many domains. When paired data measurements $(\boldsymbolμ, \boldsymbolν)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14991 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum Theory and Application of Contextual Optimal Transport 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 Machine Learning Emerging Technologies Quantum Algebra Quantitative Methods Quantum Physics Optimal Transport (OT) has fueled machine learning (ML) across many domains. When paired data measurements $(\boldsymbolμ, \boldsymbolν)$ 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. |
| title | Quantum Theory and Application of Contextual Optimal Transport |
| topic | Machine Learning Emerging Technologies Quantum Algebra Quantitative Methods Quantum Physics |
| url | https://arxiv.org/abs/2402.14991 |