Preparation of Matrix Product States with Log-Depth Quantum Circuits
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Standard
Preparation of Matrix Product States with Log-Depth Quantum Circuits. / Malz, Daniel; Styliaris, Georgios; Wei, Zhi Yuan; Cirac, J. Ignacio.
I: Physical Review Letters, Bind 132, Nr. 4, 040404, 2024.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
TY - JOUR
T1 - Preparation of Matrix Product States with Log-Depth Quantum Circuits
AU - Malz, Daniel
AU - Styliaris, Georgios
AU - Wei, Zhi Yuan
AU - Cirac, J. Ignacio
N1 - 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.
PY - 2024
Y1 - 2024
N2 - 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.
AB - 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.
U2 - 10.1103/PhysRevLett.132.040404
DO - 10.1103/PhysRevLett.132.040404
M3 - Journal article
C2 - 38335337
AN - SCOPUS:85183628013
VL - 132
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 4
M1 - 040404
ER -
ID: 381724599