Preparation of Matrix Product States with Log-Depth Quantum Circuits

Research output: Contribution to journal › Journal article › Research › peer-review

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Preparation of Matrix Product States with Log-Depth Quantum Circuits. / Malz, Daniel; Styliaris, Georgios; Wei, Zhi Yuan; Cirac, J. Ignacio.

In: Physical Review Letters, Vol. 132, No. 4, 040404, 2024.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Malz, D, Styliaris, G, Wei, ZY & Cirac, JI 2024, 'Preparation of Matrix Product States with Log-Depth Quantum Circuits', Physical Review Letters, vol. 132, no. 4, 040404. https://doi.org/10.1103/PhysRevLett.132.040404

APA

Malz, D., Styliaris, G., Wei, Z. Y., & Cirac, J. I. (2024). Preparation of Matrix Product States with Log-Depth Quantum Circuits. Physical Review Letters, 132(4), [040404]. https://doi.org/10.1103/PhysRevLett.132.040404

Vancouver

Malz D, Styliaris G, Wei ZY, Cirac JI. Preparation of Matrix Product States with Log-Depth Quantum Circuits. Physical Review Letters. 2024;132(4). 040404. https://doi.org/10.1103/PhysRevLett.132.040404

Author

Malz, Daniel ; Styliaris, Georgios ; Wei, Zhi Yuan ; Cirac, J. Ignacio. / Preparation of Matrix Product States with Log-Depth Quantum Circuits. In: Physical Review Letters. 2024 ; Vol. 132, No. 4.

Bibtex

@article{dde708fd5a034020ace05fb16bf32a24,
title = "Preparation of Matrix Product States with Log-Depth Quantum Circuits",
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. ",
author = "Daniel Malz and Georgios Styliaris and Wei, {Zhi Yuan} and Cirac, {J. Ignacio}",
note = "Publisher Copyright: {\textcopyright} 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.",
year = "2024",
doi = "10.1103/PhysRevLett.132.040404",
language = "English",
volume = "132",
journal = "Physical Review Letters",
issn = "0031-9007",
publisher = "American Physical Society",
number = "4",

}

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