Optimal control of quantum mechanical system with weighted energy cost functional

Anatoliy G. Butkovskiy, Yu. I. Samoilenko

B. C. Roy, Pradip Das

In this paper we have synthesized optimal control of multi-level quantum system by representing unitary operator in terms of the projection operators of the Hamiltonian of the system. We have solved the steering problem for multi-level quantum systems minimizing energy cost functional of the control. The optimal control problem of the time evolution of quantum spin of Pauli two-level system subjected to an external field with the minimum energy function is also illustrated and formulated in terms of the quantum spin up and spin down states of the Pauli two-level system.

哲郎 伊丹

Domenico D’Alessandro, M. Dahleh

We study the manipulation of two-level quantum systems. This research is motivated by the design of quantum mechanical logic gates which perform prescribed logic operations on a two-level quantum system, a quantum bit. We consider the problem of driving the evolution operator to a desired state, while minimizing the energy-type cost. Mathematically, this problem translates into an optimal control problem for systems varying on the Lie group of special unitary matrices, with cost that is quadratic in the control. We develop a comprehensive theory of optimal control for two-level quantum systems. In particular, we prove the 'normality' of the given problem and the 'regularity' of the optimal control functions. The impact of the results of the paper on nuclear magnetic resonance experiments and quantum computation is discussed.

Yinghua Ji, Juju Hu

Utilizing the method of optimal control, we investigated the tactics of decoherence suppression in the open quantum circuit system containing superconducting qubits. We first discussed the modeling of the system under the optimal control. Then, we designed a control law by means of optimal control. The simulation results indicate that the flip time of qubits can be effectively manipulated through changing the weight coefficients of the cost function, which provides a new way for manipulating the decoherence.

T. S. Mahesh, Priya Batra, M. Harshanth Ram