Adaptive Observation Cost Control for Variational Quantum Eigensolvers

Christopher J. Anders, Kim Andrea Nicoli, Bingting Wu, Naima Elosegui, Samuele Pedrielli, Lena Funcke, Karl Jansen, Stefan Kühn, Shinichi Nakajima
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:1557-1578, 2024.

Abstract

The objective to be minimized in the variational quantum eigensolver (VQE) has a restricted form, which allows a specialized sequential minimal optimization (SMO) that requires only a few observations in each iteration. However, the SMO iteration is still costly due to the observation noise—one observation at a point typically requires averaging over hundreds to thousands of repeated quantum measurement shots for achieving a reasonable noise level. In this paper, we propose an adaptive cost control method, named subspace in confident region (SubsCoRe), for SMO. SubsCoRe uses the Gaussian process (GP) surrogate, and requires it to have low uncertainty over the subspace being updated, so that optimization in each iteration is performed with guaranteed accuracy. Adaptive cost control is performed by setting the required accuracy according to the progress of the optimization, and identifying the minimum number of measurement shots, as well as their distribution, satisfying the SubsCoRe requirement.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-anders24a, title = {Adaptive Observation Cost Control for Variational Quantum Eigensolvers}, author = {Anders, Christopher J. and Nicoli, Kim Andrea and Wu, Bingting and Elosegui, Naima and Pedrielli, Samuele and Funcke, Lena and Jansen, Karl and K\"{u}hn, Stefan and Nakajima, Shinichi}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {1557--1578}, 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/anders24a/anders24a.pdf}, url = {https://proceedings.mlr.press/v235/anders24a.html}, abstract = {The objective to be minimized in the variational quantum eigensolver (VQE) has a restricted form, which allows a specialized sequential minimal optimization (SMO) that requires only a few observations in each iteration. However, the SMO iteration is still costly due to the observation noise—one observation at a point typically requires averaging over hundreds to thousands of repeated quantum measurement shots for achieving a reasonable noise level. In this paper, we propose an adaptive cost control method, named subspace in confident region (SubsCoRe), for SMO. SubsCoRe uses the Gaussian process (GP) surrogate, and requires it to have low uncertainty over the subspace being updated, so that optimization in each iteration is performed with guaranteed accuracy. Adaptive cost control is performed by setting the required accuracy according to the progress of the optimization, and identifying the minimum number of measurement shots, as well as their distribution, satisfying the SubsCoRe requirement.} }
Endnote
%0 Conference Paper %T Adaptive Observation Cost Control for Variational Quantum Eigensolvers %A Christopher J. Anders %A Kim Andrea Nicoli %A Bingting Wu %A Naima Elosegui %A Samuele Pedrielli %A Lena Funcke %A Karl Jansen %A Stefan Kühn %A Shinichi Nakajima %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-anders24a %I PMLR %P 1557--1578 %U https://proceedings.mlr.press/v235/anders24a.html %V 235 %X The objective to be minimized in the variational quantum eigensolver (VQE) has a restricted form, which allows a specialized sequential minimal optimization (SMO) that requires only a few observations in each iteration. However, the SMO iteration is still costly due to the observation noise—one observation at a point typically requires averaging over hundreds to thousands of repeated quantum measurement shots for achieving a reasonable noise level. In this paper, we propose an adaptive cost control method, named subspace in confident region (SubsCoRe), for SMO. SubsCoRe uses the Gaussian process (GP) surrogate, and requires it to have low uncertainty over the subspace being updated, so that optimization in each iteration is performed with guaranteed accuracy. Adaptive cost control is performed by setting the required accuracy according to the progress of the optimization, and identifying the minimum number of measurement shots, as well as their distribution, satisfying the SubsCoRe requirement.
APA
Anders, C.J., Nicoli, K.A., Wu, B., Elosegui, N., Pedrielli, S., Funcke, L., Jansen, K., Kühn, S. & Nakajima, S.. (2024). Adaptive Observation Cost Control for Variational Quantum Eigensolvers. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:1557-1578 Available from https://proceedings.mlr.press/v235/anders24a.html.

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