Quantum natural stochastic pairwise coordinate descent
Abstract Variational quantum algorithms, optimized using gradient-based methods, often exhibit sub-optimal convergence performance due to their dependence on Euclidean geometry. Quantum natural gradient descent (QNGD) is a more efficient method that incorporates the geometry of the state space via a...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2025-07-01
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| Series: | npj Quantum Information |
| Online Access: | https://doi.org/10.1038/s41534-025-01047-4 |
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| _version_ | 1849402043632975872 |
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| author | Mohammad Aamir Sohail Mohsen Heidari S. Sandeep Pradhan |
| author_facet | Mohammad Aamir Sohail Mohsen Heidari S. Sandeep Pradhan |
| author_sort | Mohammad Aamir Sohail |
| collection | DOAJ |
| description | Abstract Variational quantum algorithms, optimized using gradient-based methods, often exhibit sub-optimal convergence performance due to their dependence on Euclidean geometry. Quantum natural gradient descent (QNGD) is a more efficient method that incorporates the geometry of the state space via a quantum information metric. However, QNGD is computationally intensive and suffers from high sample complexity. In this work, we formulate a novel quantum information metric and construct an unbiased estimator for this metric using single-shot measurements. We develop a quantum optimization algorithm that leverages the geometry of the state space via this estimator while avoiding full-state tomography, as in conventional techniques. We provide the convergence analysis of the algorithm under mild conditions. Furthermore, we provide experimental results that demonstrate the better sample complexity and faster convergence of our algorithm compared to the state-of-the-art approaches. Our results illustrate the algorithm’s ability to avoid saddle points and local minima. |
| format | Article |
| id | doaj-art-131fc61bafe3457e9de80beac854de86 |
| institution | Kabale University |
| issn | 2056-6387 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | npj Quantum Information |
| spelling | doaj-art-131fc61bafe3457e9de80beac854de862025-08-20T03:37:38ZengNature Portfolionpj Quantum Information2056-63872025-07-0111111210.1038/s41534-025-01047-4Quantum natural stochastic pairwise coordinate descentMohammad Aamir Sohail0Mohsen Heidari1S. Sandeep Pradhan2Department of EECS, University of MichiganDepartment of Computer Science, Indiana UniversityDepartment of EECS, University of MichiganAbstract Variational quantum algorithms, optimized using gradient-based methods, often exhibit sub-optimal convergence performance due to their dependence on Euclidean geometry. Quantum natural gradient descent (QNGD) is a more efficient method that incorporates the geometry of the state space via a quantum information metric. However, QNGD is computationally intensive and suffers from high sample complexity. In this work, we formulate a novel quantum information metric and construct an unbiased estimator for this metric using single-shot measurements. We develop a quantum optimization algorithm that leverages the geometry of the state space via this estimator while avoiding full-state tomography, as in conventional techniques. We provide the convergence analysis of the algorithm under mild conditions. Furthermore, we provide experimental results that demonstrate the better sample complexity and faster convergence of our algorithm compared to the state-of-the-art approaches. Our results illustrate the algorithm’s ability to avoid saddle points and local minima.https://doi.org/10.1038/s41534-025-01047-4 |
| spellingShingle | Mohammad Aamir Sohail Mohsen Heidari S. Sandeep Pradhan Quantum natural stochastic pairwise coordinate descent npj Quantum Information |
| title | Quantum natural stochastic pairwise coordinate descent |
| title_full | Quantum natural stochastic pairwise coordinate descent |
| title_fullStr | Quantum natural stochastic pairwise coordinate descent |
| title_full_unstemmed | Quantum natural stochastic pairwise coordinate descent |
| title_short | Quantum natural stochastic pairwise coordinate descent |
| title_sort | quantum natural stochastic pairwise coordinate descent |
| url | https://doi.org/10.1038/s41534-025-01047-4 |
| work_keys_str_mv | AT mohammadaamirsohail quantumnaturalstochasticpairwisecoordinatedescent AT mohsenheidari quantumnaturalstochasticpairwisecoordinatedescent AT ssandeeppradhan quantumnaturalstochasticpairwisecoordinatedescent |