Preparation of matrix product states with log-depth quantum circuits
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866929222908379136 |
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| author | Malz, Daniel Styliaris, Georgios Wei, Zhi-Yuan Cirac, J. Ignacio |
| author_facet | Malz, Daniel Styliaris, Georgios Wei, Zhi-Yuan Cirac, J. Ignacio |
| contents | We consider the preparation of matrix product states (MPS) on quantum devices via quantum circuits of local gates. We first prove that faithfully preparing translation-invariant normal MPS of $N$ sites requires a circuit depth $T=Ω(\log N)$. We then introduce an algorithm based on the renormalization-group transformation to prepare normal MPS with an error $ε$ in depth $T=O(\log (N/ε))$, which is optimal. We also show that measurement and feedback leads to an exponential speedup of the algorithm, to $T=O(\log\log (N/ε))$. Measurements also allow one to prepare arbitrary translation-invariant MPS, including long-range non-normal ones, in the same depth. Finally, the algorithm naturally extends to inhomogeneous MPS. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_01696 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Preparation of matrix product states with log-depth quantum circuits Malz, Daniel Styliaris, Georgios Wei, Zhi-Yuan Cirac, J. Ignacio Quantum Physics Statistical Mechanics Strongly Correlated Electrons We consider the preparation of matrix product states (MPS) on quantum devices via quantum circuits of local gates. We first prove that faithfully preparing translation-invariant normal MPS of $N$ sites requires a circuit depth $T=Ω(\log N)$. We then introduce an algorithm based on the renormalization-group transformation to prepare normal MPS with an error $ε$ in depth $T=O(\log (N/ε))$, which is optimal. We also show that measurement and feedback leads to an exponential speedup of the algorithm, to $T=O(\log\log (N/ε))$. Measurements also allow one to prepare arbitrary translation-invariant MPS, including long-range non-normal ones, in the same depth. Finally, the algorithm naturally extends to inhomogeneous MPS. |
| title | Preparation of matrix product states with log-depth quantum circuits |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2307.01696 |