Selective and efficient quantum state tomography for multi-qubit systems
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910091802836992 |
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| author | Patel, Aniket Gaikwad, Akshay Huang, Tangyou Kockum, Anton Frisk Abad, Tahereh |
| author_facet | Patel, Aniket Gaikwad, Akshay Huang, Tangyou Kockum, Anton Frisk Abad, Tahereh |
| contents | Quantum state tomography (QST) is a crucial tool for characterizing quantum states. However, QST becomes impractical for reconstructing multi-qubit density matrices since data sets and computational costs grow exponentially with qubit number. In this Letter, we introduce selective and efficient QST (SEEQST), an approach for efficiently estimating multiple selected elements of an arbitrary $N$-qubit density matrix. We show that any $N$-qubit density matrix can be partitioned into $2^N$ subsets, each containing $2^N$ elements. With SEEQST, any such subset can be accurately estimated from just two experiments with only single-qubit measurements. The complexity for estimating any subset remains constant regardless of Hilbert-space dimension, so SEEQST can find the full density matrix using $2^{N+1} - 1$ experiments, where standard methods would use $3^N$ experiments. We provide a circuit decomposition for the SEEQST experiments, demonstrating that their maximum circuit depth scales logarithmically with $N$ assuming all-to-all connectivity. The Python code for SEEQST is publicly available at \href{https://github.com/aniket-ae/SEEQST}{github.com/aniket-ae/SEEQST}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20979 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Selective and efficient quantum state tomography for multi-qubit systems Patel, Aniket Gaikwad, Akshay Huang, Tangyou Kockum, Anton Frisk Abad, Tahereh Quantum Physics Quantum state tomography (QST) is a crucial tool for characterizing quantum states. However, QST becomes impractical for reconstructing multi-qubit density matrices since data sets and computational costs grow exponentially with qubit number. In this Letter, we introduce selective and efficient QST (SEEQST), an approach for efficiently estimating multiple selected elements of an arbitrary $N$-qubit density matrix. We show that any $N$-qubit density matrix can be partitioned into $2^N$ subsets, each containing $2^N$ elements. With SEEQST, any such subset can be accurately estimated from just two experiments with only single-qubit measurements. The complexity for estimating any subset remains constant regardless of Hilbert-space dimension, so SEEQST can find the full density matrix using $2^{N+1} - 1$ experiments, where standard methods would use $3^N$ experiments. We provide a circuit decomposition for the SEEQST experiments, demonstrating that their maximum circuit depth scales logarithmically with $N$ assuming all-to-all connectivity. The Python code for SEEQST is publicly available at \href{https://github.com/aniket-ae/SEEQST}{github.com/aniket-ae/SEEQST}. |
| title | Selective and efficient quantum state tomography for multi-qubit systems |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2503.20979 |