Measurement-Based Control for Minimizing Energy Functions in Quantum Systems
arXiv:2304.09023 · doi:10.1016/j.ifacol.2023.10.111
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.
arXiv commentAccepted for IFAC 2023 - 22nd World Congress of the International Federation of Automatic Control
References in corpus (8)
- Variational Quantum Algorithms
- Analysis of Lyapunov Method for Control of Quantum States
- Analysis of Lyapunov Method for Control of Quantum Systems
- From pulses to circuits and back again: A quantum optimal control perspective on variational quantum algorithms
- Feedback stabilization of quantum ensembles: a global convergence analysis on complex flag manifolds
- Quantum feedback by discrete quantum non-demolition measurements: towards on-demand generation of photon-number states
- Efficient optical quantum information processing
- Lyapunov control-inspired strategies for quantum combinatorial optimization