Sketch Tomography: Hybridizing Classical Shadow and Matrix Product State
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914600980578304 |
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| author | Tang, Xun Chen, Haoxuan Khoo, Yuehaw Ying, Lexing |
| author_facet | Tang, Xun Chen, Haoxuan Khoo, Yuehaw Ying, Lexing |
| contents | We introduce Sketch Tomography, an efficient procedure for quantum state tomography based on the classical shadow protocol used for quantum observable estimations. The procedure applies to the case where the ground truth quantum state is a matrix product state (MPS). The density matrix of the ground truth state admits a tensor train ansatz as a result of the MPS assumption, and we estimate the tensor components of the ansatz through a series of observable estimations, thus outputting an approximation of the density matrix. The procedure is provably convergent with a sample complexity that scales quadratically in the system size. We conduct extensive numerical experiments to show that the procedure outputs an accurate approximation to the quantum state. For observable estimation tasks involving moderately large subsystems, we show that our procedure gives rise to a more accurate estimation than the classical shadow protocol. We also show that sketch tomography is more accurate in observable estimation than quantum states trained from the maximum likelihood estimation formulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03333 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sketch Tomography: Hybridizing Classical Shadow and Matrix Product State Tang, Xun Chen, Haoxuan Khoo, Yuehaw Ying, Lexing Quantum Physics Numerical Analysis Statistics Theory Computational Physics Machine Learning We introduce Sketch Tomography, an efficient procedure for quantum state tomography based on the classical shadow protocol used for quantum observable estimations. The procedure applies to the case where the ground truth quantum state is a matrix product state (MPS). The density matrix of the ground truth state admits a tensor train ansatz as a result of the MPS assumption, and we estimate the tensor components of the ansatz through a series of observable estimations, thus outputting an approximation of the density matrix. The procedure is provably convergent with a sample complexity that scales quadratically in the system size. We conduct extensive numerical experiments to show that the procedure outputs an accurate approximation to the quantum state. For observable estimation tasks involving moderately large subsystems, we show that our procedure gives rise to a more accurate estimation than the classical shadow protocol. We also show that sketch tomography is more accurate in observable estimation than quantum states trained from the maximum likelihood estimation formulation. |
| title | Sketch Tomography: Hybridizing Classical Shadow and Matrix Product State |
| topic | Quantum Physics Numerical Analysis Statistics Theory Computational Physics Machine Learning |
| url | https://arxiv.org/abs/2512.03333 |