Adiabatic graph-state quantum computation

Abstract :

Measurement-based quantum computation (MBQC) and holonomic quantum computation (HQC) are two very different computational methods. The computation in MBQC is driven by adaptive measurements executed in a particular order on a large entangled state. In contrast in HQC the system starts in the ground subspace of a Hamiltonian which is slowly changed such that a transformation occurs within the subspace. Following the approach of Bacon and Flammia, we show that any measurement-based quantum computation on a graph state with \emph{gflow} can be converted into an adiabatically driven holonomic computation, which we call \emph{adiabatic graph-state quantum computation} (AGQC). We then investigate how properties of AGQC relate to the properties of MBQC, such as computational depth. We identify a trade-off that can be made between the number of adiabatic steps in AGQC and the norm of H˙ as well as the degree of H, in analogy to the trade-off between the number of measurements and classical post-processing seen in MBQC. Finally the effects of performing AGQC with orderings that differ from standard MBQC are investigated.

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https://hal.telecom-paristech.fr/hal-02287095
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Submitted on : Friday, September 13, 2019 - 4:34:53 PM
Last modification on : Saturday, September 14, 2019 - 1:38:55 AM

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  • HAL Id : hal-02287095, version 1

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Citation

Bobby Antonio, Damian Markham, J. Anders. Adiabatic graph-state quantum computation. New Journal of Physics, 2014, 16 (113070). ⟨hal-02287095⟩

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