Adaptive sampling-based optimization of quantics tensor trains for noisy functions: Applications to quantum simulations
Tensor cross interpolation (TCI) is a powerful technique for learning a tensor train (TT) by adaptively sampling a target tensor based on an interpolation formula. However, when the tensor evaluations contain random noise, optimizing the TT is more advantageous than interpolating the noise. Here, we...
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2025-08-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.19.2.038 |
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| author | Kohtaroh Sakaue, Hiroshi Shinaoka, Rihito Sakurai |
| author_facet | Kohtaroh Sakaue, Hiroshi Shinaoka, Rihito Sakurai |
| author_sort | Kohtaroh Sakaue, Hiroshi Shinaoka, Rihito Sakurai |
| collection | DOAJ |
| description | Tensor cross interpolation (TCI) is a powerful technique for learning a tensor train (TT) by adaptively sampling a target tensor based on an interpolation formula. However, when the tensor evaluations contain random noise, optimizing the TT is more advantageous than interpolating the noise. Here, we propose a new method that starts with an initial guess of TT and optimizes it using non-linear least-squares by fitting it to measured points obtained from TCI. We use quantics TCI (QTCI) in this method and demonstrate its effectiveness on sine and two-time correlation functions, with each evaluated with random noise. The resulting QTT exhibits increased robustness against noise compared to the QTCI method. Furthermore, we employ this optimized QTT of the correlation function in quantum simulation based on pseudo-imaginary-time evolution, resulting in ground-state energy with higher accuracy than the QTCI or Monte Carlo methods. |
| format | Article |
| id | doaj-art-9dda34e7c27a4cd68a34d4fe68cc3be0 |
| institution | Kabale University |
| issn | 2542-4653 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj-art-9dda34e7c27a4cd68a34d4fe68cc3be02025-08-20T04:01:01ZengSciPostSciPost Physics2542-46532025-08-0119203810.21468/SciPostPhys.19.2.038Adaptive sampling-based optimization of quantics tensor trains for noisy functions: Applications to quantum simulationsKohtaroh Sakaue, Hiroshi Shinaoka, Rihito SakuraiTensor cross interpolation (TCI) is a powerful technique for learning a tensor train (TT) by adaptively sampling a target tensor based on an interpolation formula. However, when the tensor evaluations contain random noise, optimizing the TT is more advantageous than interpolating the noise. Here, we propose a new method that starts with an initial guess of TT and optimizes it using non-linear least-squares by fitting it to measured points obtained from TCI. We use quantics TCI (QTCI) in this method and demonstrate its effectiveness on sine and two-time correlation functions, with each evaluated with random noise. The resulting QTT exhibits increased robustness against noise compared to the QTCI method. Furthermore, we employ this optimized QTT of the correlation function in quantum simulation based on pseudo-imaginary-time evolution, resulting in ground-state energy with higher accuracy than the QTCI or Monte Carlo methods.https://scipost.org/SciPostPhys.19.2.038 |
| spellingShingle | Kohtaroh Sakaue, Hiroshi Shinaoka, Rihito Sakurai Adaptive sampling-based optimization of quantics tensor trains for noisy functions: Applications to quantum simulations SciPost Physics |
| title | Adaptive sampling-based optimization of quantics tensor trains for noisy functions: Applications to quantum simulations |
| title_full | Adaptive sampling-based optimization of quantics tensor trains for noisy functions: Applications to quantum simulations |
| title_fullStr | Adaptive sampling-based optimization of quantics tensor trains for noisy functions: Applications to quantum simulations |
| title_full_unstemmed | Adaptive sampling-based optimization of quantics tensor trains for noisy functions: Applications to quantum simulations |
| title_short | Adaptive sampling-based optimization of quantics tensor trains for noisy functions: Applications to quantum simulations |
| title_sort | adaptive sampling based optimization of quantics tensor trains for noisy functions applications to quantum simulations |
| url | https://scipost.org/SciPostPhys.19.2.038 |
| work_keys_str_mv | AT kohtarohsakauehiroshishinaokarihitosakurai adaptivesamplingbasedoptimizationofquanticstensortrainsfornoisyfunctionsapplicationstoquantumsimulations |