Quantum Optimal Control for Pauli Operators Based on Spin-1/2 System

Abstract

Quantum control is an important field for quantum computing and quantum simulation. The key of quantum control is to realize quantum logic operators with high fidelity. In this work, based on spin-1/2 system, the optimal simulation of three Pauli logic operators are 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 fidelity (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 required to optimize Pauli z operator is the most. In addition, the comparison shows that when the fidelity reach 0.9999, the population of the quantum final state can reach the ideal theoretical expectation. Besides, the optimization fidelity of Hadamard gate can also reach 0.9999 based on spin-1/2 system. Finally, the study on the phase evolution of quantum states shows that the phase difference between the initial and final quantum states of optimized Pauli x and Pauli z logic operator are π/2 respectively, and there is no phase difference between the final quantum state and the initial quantum state after the evolution of optimized Pauli y operator.