Measurement-Based Control for Minimizing Energy Functions in Quantum Systems

• URL: http://arxiv.org/abs/2304.09023v1
• Date: Tue, 18 Apr 2023 14:36:06 GMT
• Title: Measurement-Based Control for Minimizing Energy Functions in Quantum Systems
• Authors: Henrik Glavind Clausen, Salahuddin Abdul Rahman, \"Ozkan Karabacak, Rafal Wisniewski
• Abstract summary: In variational quantum algorithms (VQAs) the most common objective is to find the minimum energy eigenstate of a given energy Hamiltonian. We consider the general problem of finding a sufficient control Hamiltonian structure that ensures convergence to the minimum energy eigenstate of a given energy function. By including quantum non-demolition (QND) measurements in the loop, convergence to a pure state can be ensured from an arbitrary mixed initial state.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: In variational quantum algorithms (VQAs), the most common objective is to find the minimum energy eigenstate of a given energy Hamiltonian. In this paper, we consider the general problem of finding a sufficient control Hamiltonian structure that, under a given feedback control law, ensures convergence to the minimum energy eigenstate of a given energy function. By including quantum non-demolition (QND) measurements in the loop, convergence to a pure state can be ensured from an arbitrary mixed initial state. Based on existing results on strict control Lyapunov functions, we formulate a semidefinite optimization problem, whose solution defines a non-unique control Hamiltonian, which is sufficient to ensure almost sure convergence to the minimum energy eigenstate under the given feedback law and the action of QND measurements. A numerical example is provided to showcase the proposed methodology.

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