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arXiv:2011.00097 · IEEE Transactions on Automatic Control

Feedback Exponential Stabilization of GHZ States of Multiqubit Systems

Weichao Liang, Nina H. Amini, Paolo Mason

Published Jul 7, 2021• 13 citations
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Abstract

In this article, we consider stochastic master equations describing the evolution of a multiqubit 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. We show that local stability in probability holds true, however due to the absence of random displacements generated by$x$-type measurements, the reachability of a neighborhood of a predetermined GHZ state is not clear. In this case, we provide a heuristic discussion on some conditions which may ensure asymptotic convergence toward the target state. Finally, we demonstrate the effectiveness of our methodology for a three-qubit system through numerical simulations.

DOI
10.1109/tac.2021.3095034

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