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Journal Articles IEEE Transactions on Automatic Control Year : 2021

Feedback exponential stabilization of GHZ states of multi-qubit systems

Abstract

In this paper, we consider stochastic master equations describing the evolution of a multi-qubit system interacting with electromagnetic fields undergoing continuous-time measurements. By considering multiple z-type (Pauli z matrix on different qubits) and x-type (Pauli x matrix on all qubits) measurements and one control Hamiltonian, we provide general conditions on the feedback controller and the control Hamiltonian ensuring almost sure exponential convergence to a predetermined Greenberger-Horne-Zeilinger (GHZ) state, which is assumed to be a common eigenstate of the measurement operators. We provide explicit expressions of feedback controllers satisfying such conditions. We also consider the case of only z-type measurements and multiple control Hamiltonians, and we discuss asymptotic convergence towards a predetermined GHZ state. Finally, we demonstrate the effectiveness of our methodology for a three-qubit system through numerical simulations.

Dates and versions

hal-03015479 , version 1 (19-11-2020)

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Cite

Weichao Liang, Nina Amini, Paolo Mason. Feedback exponential stabilization of GHZ states of multi-qubit systems. IEEE Transactions on Automatic Control, 2021, ⟨10.1109/tac.2021.3095034⟩. ⟨hal-03015479⟩
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