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

Abstract

Quantum control is an important basis for quantum computing, quantum communication and quantum simulation. The key of quantum control is to realize quantum logic operators with high fidelity. In this paper, based on spin-1/2 system, the optimal simulation of 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 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 reaches 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 is π/2, and there is no phase difference between the final quantum state and the initial quantum state after the evolution of optimized Pauli y operator.

Quantum Gate Generation in Two-Level Open Quantum Systems by Coherent and Incoherent Photons Found with Gradient Search

“…Quantum speed limit for a controlled qubit moving inside a leaky cavity has been studied [41]. Preparation of single qubit and two-qubit gates has been studied, e.g., in [32,[42][43][44][45][46][47][48][49], etc.…”

Quantum Gate Generation in Two-Level Open Quantum Systems by Coherent and Incoherent Photons Found with Gradient Search

“…Quantum speed limit for a controlled qubit moving inside a leaky cavity has been studied [41]. Preparation of single qubit and two-qubit gates has been studied, e.g., in [42,43,44,32,45,46,47,48,49], etc.…”