Gradient-descent methods for fast quantum state tomography
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| Název: | Gradient-descent methods for fast quantum state tomography |
|---|---|
| Autoři: | Gaikwad, Akshay, 1993, Torres, Manuel Sebastian, Ahmed, Shahnawaz, 1995, Frisk Kockum, Anton, 1987 |
| Zdroj: | Kvantsimulering och kvantkommunikation med stora atomer Open Superconducting Quantum Computers (OpenSuperQPlus) Quantum Science and Technology. 10(4) |
| Témata: | gradient descent optimization, density matrix parameterization, quantum state tomography |
| Popis: | Quantum state tomography (QST) is a widely employed technique for characterizing the state of a quantum system. However, it is plagued by two fundamental challenges: computational and experimental complexity grows exponentially with the number of qubits, rendering experimental implementation and data post-processing arduous even for moderately sized systems. Here, we introduce gradient-descent (GD) algorithms for the post-processing step of QST in discrete- and continuous-variable systems. To ensure physically valid state reconstruction at each iteration step of the algorithm, we use various density-matrix parameterizations: Cholesky decomposition, Stiefel manifold, and projective normalization. These parameterizations have the added benefit of enabling a rank-controlled ansatz, which simplifies reconstruction when there is prior information about the system. We benchmark the performance of our GD-QST techniques against state-of-the-art methods, including constrained convex optimization, conditional generative adversarial networks, and iterative maximum likelihood estimation. Our comparison focuses on time complexity, iteration counts, data requirements, state rank, and robustness against noise. We find that rank-controlled ansatzes in our stochastic mini-batch GD-QST algorithms effectively handle noisy and incomplete data sets, yielding significantly higher reconstruction fidelity than other methods. Simulations achieving full-rank seven-qubit QST in under three minutes on a standard laptop, with 18 GB of RAM and no dedicated GPU, highlight that GD-QST is computationally more efficient and outperforms other techniques in most scenarios, offering a promising avenue for characterizing noisy intermediate-scale quantum devices. Our Python code for GD-QST algorithms is publicly available at github.com/mstorresh/GD-QST. |
| Popis souboru: | electronic |
| Přístupová URL adresa: | https://research.chalmers.se/publication/548723 https://research.chalmers.se/publication/548723/file/548723_Fulltext.pdf |
| Databáze: | SwePub |
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| Items | – Name: Title Label: Title Group: Ti Data: Gradient-descent methods for fast quantum state tomography – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Gaikwad%2C+Akshay%22">Gaikwad, Akshay</searchLink>, 1993<br /><searchLink fieldCode="AR" term="%22Torres%2C+Manuel+Sebastian%22">Torres, Manuel Sebastian</searchLink><br /><searchLink fieldCode="AR" term="%22Ahmed%2C+Shahnawaz%22">Ahmed, Shahnawaz</searchLink>, 1995<br /><searchLink fieldCode="AR" term="%22Frisk+Kockum%2C+Anton%22">Frisk Kockum, Anton</searchLink>, 1987 – Name: TitleSource Label: Source Group: Src Data: <i>Kvantsimulering och kvantkommunikation med stora atomer Open Superconducting Quantum Computers (OpenSuperQPlus) Quantum Science and Technology</i>. 10(4) – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22gradient+descent+optimization%22">gradient descent optimization</searchLink><br /><searchLink fieldCode="DE" term="%22density+matrix+parameterization%22">density matrix parameterization</searchLink><br /><searchLink fieldCode="DE" term="%22quantum+state+tomography%22">quantum state tomography</searchLink> – Name: Abstract Label: Description Group: Ab Data: Quantum state tomography (QST) is a widely employed technique for characterizing the state of a quantum system. However, it is plagued by two fundamental challenges: computational and experimental complexity grows exponentially with the number of qubits, rendering experimental implementation and data post-processing arduous even for moderately sized systems. Here, we introduce gradient-descent (GD) algorithms for the post-processing step of QST in discrete- and continuous-variable systems. To ensure physically valid state reconstruction at each iteration step of the algorithm, we use various density-matrix parameterizations: Cholesky decomposition, Stiefel manifold, and projective normalization. These parameterizations have the added benefit of enabling a rank-controlled ansatz, which simplifies reconstruction when there is prior information about the system. We benchmark the performance of our GD-QST techniques against state-of-the-art methods, including constrained convex optimization, conditional generative adversarial networks, and iterative maximum likelihood estimation. Our comparison focuses on time complexity, iteration counts, data requirements, state rank, and robustness against noise. We find that rank-controlled ansatzes in our stochastic mini-batch GD-QST algorithms effectively handle noisy and incomplete data sets, yielding significantly higher reconstruction fidelity than other methods. Simulations achieving full-rank seven-qubit QST in under three minutes on a standard laptop, with 18 GB of RAM and no dedicated GPU, highlight that GD-QST is computationally more efficient and outperforms other techniques in most scenarios, offering a promising avenue for characterizing noisy intermediate-scale quantum devices. Our Python code for GD-QST algorithms is publicly available at github.com/mstorresh/GD-QST. – Name: Format Label: File Description Group: SrcInfo Data: electronic – Name: URL Label: Access URL Group: URL Data: <link linkTarget="URL" linkTerm="https://research.chalmers.se/publication/548723" linkWindow="_blank">https://research.chalmers.se/publication/548723</link><br /><link linkTarget="URL" linkTerm="https://research.chalmers.se/publication/548723/file/548723_Fulltext.pdf" linkWindow="_blank">https://research.chalmers.se/publication/548723/file/548723_Fulltext.pdf</link> |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1088/2058-9565/ae0baa Languages: – Text: English Subjects: – SubjectFull: gradient descent optimization Type: general – SubjectFull: density matrix parameterization Type: general – SubjectFull: quantum state tomography Type: general Titles: – TitleFull: Gradient-descent methods for fast quantum state tomography Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Gaikwad, Akshay – PersonEntity: Name: NameFull: Torres, Manuel Sebastian – PersonEntity: Name: NameFull: Ahmed, Shahnawaz – PersonEntity: Name: NameFull: Frisk Kockum, Anton IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 20589565 – Type: issn-locals Value: SWEPUB_FREE – Type: issn-locals Value: CTH_SWEPUB Numbering: – Type: volume Value: 10 – Type: issue Value: 4 Titles: – TitleFull: Kvantsimulering och kvantkommunikation med stora atomer Open Superconducting Quantum Computers (OpenSuperQPlus) Quantum Science and Technology Type: main |
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