Quantum Theory and Application of Contextual Optimal Transport

Nicola Mariella, Albert Akhriev, Francesco Tacchino, Christa Zoufal, Juan Carlos Gonzalez-Espitia, Benedek Harsanyi, Eugene Koskin, Ivano Tavernelli, Stefan Woerner, Marianna Rapsomaniki, Sergiy Zhuk, Jannis Born
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:34822-34845, 2024.

Abstract

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 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-mariella24a, title = {Quantum Theory and Application of Contextual Optimal Transport}, author = {Mariella, Nicola and Akhriev, Albert and Tacchino, Francesco and Zoufal, Christa and Gonzalez-Espitia, Juan Carlos and Harsanyi, Benedek and Koskin, Eugene and Tavernelli, Ivano and Woerner, Stefan and Rapsomaniki, Marianna and Zhuk, Sergiy and Born, Jannis}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {34822--34845}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/mariella24a/mariella24a.pdf}, url = {https://proceedings.mlr.press/v235/mariella24a.html}, abstract = {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 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.} }
Endnote
%0 Conference Paper %T Quantum Theory and Application of Contextual Optimal Transport %A Nicola Mariella %A Albert Akhriev %A Francesco Tacchino %A Christa Zoufal %A Juan Carlos Gonzalez-Espitia %A Benedek Harsanyi %A Eugene Koskin %A Ivano Tavernelli %A Stefan Woerner %A Marianna Rapsomaniki %A Sergiy Zhuk %A Jannis Born %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-mariella24a %I PMLR %P 34822--34845 %U https://proceedings.mlr.press/v235/mariella24a.html %V 235 %X 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 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.
APA
Mariella, N., Akhriev, A., Tacchino, F., Zoufal, C., Gonzalez-Espitia, J.C., Harsanyi, B., Koskin, E., Tavernelli, I., Woerner, S., Rapsomaniki, M., Zhuk, S. & Born, J.. (2024). Quantum Theory and Application of Contextual Optimal Transport. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:34822-34845 Available from https://proceedings.mlr.press/v235/mariella24a.html.

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