Quantum optimal control for Pauli operators based on spin-1/2 system

Quantum control is an important basis for quantum computing, quantum com-munication and quantum simulation. The key of quantum control is to realize quantum logicoperators with high fidelity. In this paper, based on spin-1/2 system, the optimal simulationof three Pauli logic operators is carried out by using quantum optimal control theory. Under Pauli z spin-presentation, the results show that under the given quantum initial state, the Pauli operators achieve the expected target quantum state with a high fidelity of 0.9999. When the control pulse is applied on x-axis, the number of iterations required to optimize Pauli x operator to achieve the target state is the least, and the number of iterations requiredto optimize Pauli z operator is the most. In addition, the comparison shows that when thefidelity reach 0.9999, the population of the quantum final state can reach the ideal theoreti-cal expectation. Besides, the optimization fidelity of Hadamard gate can also reaches 0.9999 based on spin-1/2 system. Finally, the study on the phase evolution of quantum states showsthat the phase difference between the initial and final quantum states of optimized Pauli xand Pauli z logic operator is π/2, and there is no phase difference between the final quantumstate and the initial quantum state after the evolution of optimized Pauli y operator.