Abstract
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(logN). 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[loglog(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.
Original language | English |
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Article number | 040404 |
Journal | Physical Review Letters |
Volume | 132 |
Issue number | 4 |
ISSN | 0031-9007 |
DOIs | |
Publication status | Published - 2024 |
Bibliographical note
Publisher Copyright:© 2024 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.