Realization of quantum gates by Lyapunov control

Marek Sawerwain, Joanna Wiśniewska

Jie Wen, Shuang Cong, Xu‐Bo Zou

This paper studies the realization of the quantum Hadamard gate of spin with a single electron. First the canonical form of the unitary rotation gate which is feasibly applied in plane control fields is given. Because the Hadamard gate can't be realized directly by applying the plane control fields, so the matrix operator of Hadamard gate is decomposed into two matrices which are feasible in canonical forms. These two canonical matrices correspond to the rotate-operation and reflect-operation of the vector coordinates on the Bloch sphere, respectively. Then the Hadamard gate can be realized in two steps by choosing appropriate control fields, in such a way the realization of Hadamard gate becomes to design external tailored control fields. Finally, the control fields are designed based on Lyapunov method. Numerical simulation experiments and results analysis are given.

Shuai Liu, Du Ran, Zhi‐Cheng Shi +2 more

Abstract A scheme to implement the controlled‐NOT (CNOT) gate for quantum systems is proposed, which is based on Lyapunov control. The scheme does not require precise control of the interaction time since the system is stable when the control fields vanish. In particular, the control fields can be easily obtained by most initial states. As an example, the CNOT gate is realized for two atoms trapped in an optical cavity by exploiting two disturbance cases. Compared to continuous disturbance, the fidelity of the CNOT gate is higher under impulsive disturbance, however, interaction times are much longer. Numerical simulations indicate that the scheme is robust against variations of control parameters and decoherence caused by atomic spontaneous emission and cavity decay. Therefore, the scheme may provide useful applications in quantum computation.

Sen Kuang, Shuang Cong

Shouwei Zhao, Hai Lin, Zhengui Xue

Nourallah Ghaeminezhad, Shuang Cong

The preparation of the maximum entangled states, i.e., the Bell states is studied in this paper. The Cartan decomposition and the Lyapunov control methods are used to design the control laws for some operations in realizing the Hadamard and CNOT gates to prepare the Bell states. The numerical simulation experiments show that for some proper control parameters in the designed control laws, the Hadamard and CNOT gates are realized and the stable Bell states are prepared in a short time.