Robustness Of Quantum Computation Of Complex Quantum Dynamics

A quantum computer could perform certain computations much more efficient than its classical counterpart by exploiting the superposition principle and the interferences of quantum mechanics. Although the advances in the field of quantum computation were great in the last two decades, there is no scalable quantum information processors yet come into existence. One of the major reasons of this fact is the noise and imperfections, arising due to the interactions among the qubits or the couplings with the environment, destroy the operationality of quantum computation severely. Thus exploring the robustness features of quantum information processing system in presence of various imperfections will be very helpful to design fault-tolerant quantum information processor.A historical overview of quantum computation and the recent development on the research of its robustness are summarized firstly in this paper. Then the quantum kicked Harper model, which behaves a complex quantum dynamics, as well as its simulation algorithm are presented. Based on the random matrix theory and the Husimi function approach, the statistical properties of the quasi-energy and the eigenstates of the quantum kicked Harper, both in regular and chaotic regime, were studied. After that, the effects of various imperfections on the quantum computation which are indicated by several important physical quantities, such as fidelity, the timescales for reliable quantum computation and dynamical localization length etc., were analyzed using the fidelity perturbation method and the quantum trajectory approach. Once the strength of imperfections above a certain threshold, quantum chaos sets in and leads to unreliable quantum computation. It was demonstrated that the threshold for static imperfections are much smaller than that of the random noise in quantum gate operations. The fidelity drops exponentially in the presence of random noise, while it is Gaussian decrease in the case of static imperfections. Taking the phase damping channel as the dissipative model, it was shown that the dynamical localization for the quantum kicked Harper and the stochastic web in phase space are destroyed by moderate levels of dissipation. And the robustness of the quantum computation under dissipative imperfections is independent of the integrable or chaotic nature of the underlying dynamics. Since the unitary evolution is destroyed by the dissipative imperfections, the quantum computation of the open QKH model is no longer reversible. Furthermore, the random dynamical decoupling methods which are originally proposed to suppress the dissipative imperfections are used to combat the static imperfections in the quantum computation. Applications of the theory of robust quantum computation to the quantum constructive control of quantum two-level systems are described in the end.