A geometrical quantum phase effect

Subhashish Banerjee, C. M. Chandrashekar, Arun Kumar Pati

Geometric phase plays an important role in evolution of pure or mixed quantum states. However, when a system undergoes decoherence the development of geometric phase may be inhibited. Here we show that when a quantum system interacts with two competing environments there can be enhancement of geometric phase. This effect is akin to a Parrondo-like effect on the geometric phase which results from quantum frustration of decoherence. Our result suggests that the mechanism of two competing decoherence can be useful in fault-tolerant holonomic quantum computation.

J H Hannay

Da-Wei Luo, J. Q. You, Hai-Qing Lin +2 more

Geometric phases have been shown to be feasible in implementing quantum gates to perform quantum information processing. For all the realistic applications, the environmental influence on the geometric phase and decoherence such as memory effects must be properly considered in order to achieve the required precision in geometric quantum computation. In this paper, we study the geometric phase for a generic open quantum system based on a microscopic model. A remarkable feature of the open system's geometric phase obtained from our theoretical formulation is that the geometric phase can be obtained regardless of the existence of the master equations, while the environmental noise features such as memory effects are fully accounted for. We demonstrate that the geometric phases for a general open quantum system can be fundamentally modified by its non-Markovian environments.

Zhiyuan Chen, Liping Guo, Fengfeng Luo

Geometric phases are investigated for a Josephson qubit interacting with the Markovian and non-Markovian environments at arbitrary temperature according to a kinematic approach. In order to obtain the condition allowing experimental observation of geometric phase, we also estimate the decoherence times. The result shows that the Aharonov-Anandan phase may be different from the Berry phase under the environment perturbations. By comparing with the numerical result of the geometric phase as a function of the initial angle, we find that at low temperature, the effect of Markovian environment is larger than the non-Markovian one on the geometric phase. An approach is proposed to understand the accumulative effects of the geometric phase and its robustness to high-frequency noise, which may be helpful for geometric quantum information processing.

Z.S. Wang, Chunfeng Wu, Xun‐Li Feng +4 more