Robust diabatic grover search by Landau-Zener-Stückelberg oscillations

Yosi Atia; Yonathan Oren; Nadav Katz

doi:10.3390/e21100937

Robust diabatic grover search by Landau-Zener-Stückelberg oscillations

Yosi Atia^*, Yonathan Oren, Nadav Katz

^*Corresponding author for this work

Racah Institute of Physics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Quantum computation by the adiabatic theorem requires a slowly-varying Hamiltonian with respect to the spectral gap. We show that the Landau-Zener-Stückelberg oscillation phenomenon, which naturally occurs in quantum two-level systems under non-adiabatic periodic drive, can be exploited to find the ground state of an N-dimensional Grover Hamiltonian. The total runtime of this method is O(√2ⁿ), which is equal to the computational time of the Grover algorithm in the quantum circuit model. An additional periodic drive can suppress a large subset of Hamiltonian control errors by using coherent destruction of tunneling, thus outperforming previous algorithms.

Original language	American English
Article number	937
Journal	Entropy
Volume	21
Issue number	10
DOIs	https://doi.org/10.3390/e21100937
State	Published - 1 Oct 2019

Bibliographical note

Funding Information:
Funding: Y.A.’s work is supported by ERC grant number 280157, and Simons foundation grant number 385590 & 385586. Y.O.’s work is supported by ERC grant number 280157, and by ISF grant 1721/17. N.K. is supported by the ERC Project No. 335933.

Publisher Copyright:
© 2019 by the authors.

Keywords

Adiabatic quantum computing
Coherent destruction of tunneling
Quantum algorithms
Quantum control
Quantum error correction
Quantum two-level systems

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10.3390/e21100937

Cite this

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title = "Robust diabatic grover search by Landau-Zener-St{\"u}ckelberg oscillations",

abstract = "Quantum computation by the adiabatic theorem requires a slowly-varying Hamiltonian with respect to the spectral gap. We show that the Landau-Zener-St{\"u}ckelberg oscillation phenomenon, which naturally occurs in quantum two-level systems under non-adiabatic periodic drive, can be exploited to find the ground state of an N-dimensional Grover Hamiltonian. The total runtime of this method is O(√2n), which is equal to the computational time of the Grover algorithm in the quantum circuit model. An additional periodic drive can suppress a large subset of Hamiltonian control errors by using coherent destruction of tunneling, thus outperforming previous algorithms.",

keywords = "Adiabatic quantum computing, Coherent destruction of tunneling, Quantum algorithms, Quantum control, Quantum error correction, Quantum two-level systems",

author = "Yosi Atia and Yonathan Oren and Nadav Katz",

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AU - Oren, Yonathan

AU - Katz, Nadav

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N2 - Quantum computation by the adiabatic theorem requires a slowly-varying Hamiltonian with respect to the spectral gap. We show that the Landau-Zener-Stückelberg oscillation phenomenon, which naturally occurs in quantum two-level systems under non-adiabatic periodic drive, can be exploited to find the ground state of an N-dimensional Grover Hamiltonian. The total runtime of this method is O(√2n), which is equal to the computational time of the Grover algorithm in the quantum circuit model. An additional periodic drive can suppress a large subset of Hamiltonian control errors by using coherent destruction of tunneling, thus outperforming previous algorithms.

AB - Quantum computation by the adiabatic theorem requires a slowly-varying Hamiltonian with respect to the spectral gap. We show that the Landau-Zener-Stückelberg oscillation phenomenon, which naturally occurs in quantum two-level systems under non-adiabatic periodic drive, can be exploited to find the ground state of an N-dimensional Grover Hamiltonian. The total runtime of this method is O(√2n), which is equal to the computational time of the Grover algorithm in the quantum circuit model. An additional periodic drive can suppress a large subset of Hamiltonian control errors by using coherent destruction of tunneling, thus outperforming previous algorithms.

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KW - Coherent destruction of tunneling

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KW - Quantum control

KW - Quantum error correction

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Robust diabatic grover search by Landau-Zener-Stückelberg oscillations

Abstract

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Keywords

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