Preparation of Matrix Product States with Log-Depth Quantum Circuits
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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.
| Originalsprog | Engelsk |
|---|---|
| Artikelnummer | 040404 |
| Tidsskrift | Physical Review Letters |
| Vol/bind | 132 |
| Udgave nummer | 4 |
| ISSN | 0031-9007 |
| DOI | |
| Status | Udgivet - 2024 |
Bibliografisk note
Funding Information:
We thank Yujie Liu, Miguel Frías Pérez, and Rahul Trivedi for insightful discussions. D. M. acknowledges support from the Novo Nordisk Fonden under Grants No. NNF22OC0071934 and No. NNF20OC0059939. G. S. is supported by the Alexander von Humboldt Foundation. The research is part of the Munich Quantum Valley, which is supported by the Bavarian State Government with funds from the Hightech Agenda Bayern Plus. We acknowledge funding from the German Federal Ministry of Education and Research (BMBF) through EQUAHUMO (Grant No. 13N16066) within the funding program quantum technologies—from basic research to market. The numerical calculations were performed using the ITensor Library .
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.
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