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

Racah Institute of Physics

The Hebrew University of Jerusalem

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

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

Keywords

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

All Science Journal Classification (ASJC) codes

Information Systems
Mathematical Physics
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Electrical and Electronic Engineering

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10.3390/e21100937

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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",

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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.

KW - Adiabatic quantum computing

KW - Coherent destruction of tunneling

KW - Quantum algorithms

KW - Quantum control

KW - Quantum error correction

KW - Quantum two-level systems

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VL - 21

JO - Entropy

JF - Entropy

IS - 10

M1 - 937

ER -

Robust diabatic grover search by Landau-Zener-Stückelberg oscillations

Abstract

Keywords

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