Magic of Random Matrix Product States
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866909204457979904 |
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| author | Chen, Liyuan Garcia, Roy J. Bu, Kaifeng Jaffe, Arthur |
| author_facet | Chen, Liyuan Garcia, Roy J. Bu, Kaifeng Jaffe, Arthur |
| contents | Magic, or nonstabilizerness, characterizes how far away a state is from the stabilizer states, making it an important resource in quantum computing, under the formalism of the Gotteman-Knill theorem. In this paper, we study the magic of the $1$-dimensional Random Matrix Product States (RMPSs) using the $L_{1}$-norm measure. We firstly relate the $L_{1}$-norm to the $L_{4}$-norm. We then employ a unitary $4$-design to map the $L_{4}$-norm to a $24$-component statistical physics model. By evaluating partition functions of the model, we obtain a lower bound on the expectation values of the $L_{1}$-norm. This bound grows exponentially with respect to the qudit number $n$, indicating that the $1$D RMPS is highly magical. Our numerical results confirm that the magic grows exponentially in the qubit case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_10350 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Magic of Random Matrix Product States Chen, Liyuan Garcia, Roy J. Bu, Kaifeng Jaffe, Arthur Quantum Physics Other Condensed Matter High Energy Physics - Theory Magic, or nonstabilizerness, characterizes how far away a state is from the stabilizer states, making it an important resource in quantum computing, under the formalism of the Gotteman-Knill theorem. In this paper, we study the magic of the $1$-dimensional Random Matrix Product States (RMPSs) using the $L_{1}$-norm measure. We firstly relate the $L_{1}$-norm to the $L_{4}$-norm. We then employ a unitary $4$-design to map the $L_{4}$-norm to a $24$-component statistical physics model. By evaluating partition functions of the model, we obtain a lower bound on the expectation values of the $L_{1}$-norm. This bound grows exponentially with respect to the qudit number $n$, indicating that the $1$D RMPS is highly magical. Our numerical results confirm that the magic grows exponentially in the qubit case. |
| title | Magic of Random Matrix Product States |
| topic | Quantum Physics Other Condensed Matter High Energy Physics - Theory |
| url | https://arxiv.org/abs/2211.10350 |