Probabilistic state synthesis based on optimal convex approximation
Abstract When preparing a pure state with a quantum circuit, there is an unavoidable approximation error due to the compilation error in fault-tolerant implementation. A recently proposed approach called probabilistic state synthesis, where the circuit is probabilistically sampled, is able to reduce...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Nature Portfolio
2024-01-01
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| Series: | npj Quantum Information |
| Online Access: | https://doi.org/10.1038/s41534-023-00793-7 |
| _version_ | 1797362994929205248 |
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| author | Seiseki Akibue Go Kato Seiichiro Tani |
| author_facet | Seiseki Akibue Go Kato Seiichiro Tani |
| author_sort | Seiseki Akibue |
| collection | DOAJ |
| description | Abstract When preparing a pure state with a quantum circuit, there is an unavoidable approximation error due to the compilation error in fault-tolerant implementation. A recently proposed approach called probabilistic state synthesis, where the circuit is probabilistically sampled, is able to reduce the approximation error compared to conventional deterministic synthesis. In this paper, we demonstrate that the optimal probabilistic synthesis quadratically reduces the approximation error. Moreover, we show that a deterministic synthesis algorithm can be efficiently converted into a probabilistic one that achieves this quadratic error reduction. We also numerically demonstrate how this conversion reduces the T-count and analytically prove that this conversion halves an information-theoretic lower bound on the circuit size. In order to derive these results, we prove general theorems about the optimal convex approximation of a quantum state. Furthermore, we demonstrate that this theorem can be used to analyze an entanglement measure. |
| first_indexed | 2024-03-08T16:15:14Z |
| format | Article |
| id | doaj.art-617f1e95071a4ddab61f735ed9750f44 |
| institution | Directory Open Access Journal |
| issn | 2056-6387 |
| language | English |
| last_indexed | 2024-03-08T16:15:14Z |
| publishDate | 2024-01-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | npj Quantum Information |
| spelling | doaj.art-617f1e95071a4ddab61f735ed9750f442024-01-07T12:38:14ZengNature Portfolionpj Quantum Information2056-63872024-01-011011910.1038/s41534-023-00793-7Probabilistic state synthesis based on optimal convex approximationSeiseki Akibue0Go Kato1Seiichiro Tani2NTT Communication Science Laboratories, NTT CorporationAdvanced ICT Research Institute, NICTNTT Communication Science Laboratories, NTT CorporationAbstract When preparing a pure state with a quantum circuit, there is an unavoidable approximation error due to the compilation error in fault-tolerant implementation. A recently proposed approach called probabilistic state synthesis, where the circuit is probabilistically sampled, is able to reduce the approximation error compared to conventional deterministic synthesis. In this paper, we demonstrate that the optimal probabilistic synthesis quadratically reduces the approximation error. Moreover, we show that a deterministic synthesis algorithm can be efficiently converted into a probabilistic one that achieves this quadratic error reduction. We also numerically demonstrate how this conversion reduces the T-count and analytically prove that this conversion halves an information-theoretic lower bound on the circuit size. In order to derive these results, we prove general theorems about the optimal convex approximation of a quantum state. Furthermore, we demonstrate that this theorem can be used to analyze an entanglement measure.https://doi.org/10.1038/s41534-023-00793-7 |
| spellingShingle | Seiseki Akibue Go Kato Seiichiro Tani Probabilistic state synthesis based on optimal convex approximation npj Quantum Information |
| title | Probabilistic state synthesis based on optimal convex approximation |
| title_full | Probabilistic state synthesis based on optimal convex approximation |
| title_fullStr | Probabilistic state synthesis based on optimal convex approximation |
| title_full_unstemmed | Probabilistic state synthesis based on optimal convex approximation |
| title_short | Probabilistic state synthesis based on optimal convex approximation |
| title_sort | probabilistic state synthesis based on optimal convex approximation |
| url | https://doi.org/10.1038/s41534-023-00793-7 |
| work_keys_str_mv | AT seisekiakibue probabilisticstatesynthesisbasedonoptimalconvexapproximation AT gokato probabilisticstatesynthesisbasedonoptimalconvexapproximation AT seiichirotani probabilisticstatesynthesisbasedonoptimalconvexapproximation |