Dynamic Phases and Robust Quantum Gates

Yueheng Liu, Xin-Ding Zhang

Nonadiabatic Abelian geometric quantum computation has been extensively studied, due to its fast manipulation and inherent noise resistance. However, to obtain the pure geometric phase, the quantum state is required to evolve along some special paths to eliminate the dynamical phase. This leads to increasing evolution time and weakened gate robustness. The unconventional geometric quantum computation is an effective way to solve the above problems. Here, we propose a general approach to realize the unconventional geometric computation. Then, we discuss the effect of the ratio of geometric phase to dynamic phase on the performance of quantum gates. The results show that the selection of ratio corresponds to different quantum gate robustness. Therefore, we can optimize the ratio to get higher-fidelity quantum gates. At last, we construct the ratio-optimized quantum gates in a superconducting circuit and test its robustness. The fidelities of the T-gate, Hadamard H-gate, and controlled phase gate can be obtained as 99.98%, 99.95%, and 99.85%, respectively. Therefore, our scheme provides a promising way to realize large-scale fault-tolerant quantum computation in superconducting circuits.

Vladimir S. Malinovsky, Patrick Hawkins, Svetlana Malinovskaya

Shi-Liang Zhu, Paolo Zanardi A

The realistic application of geometric quantum computation is crucially dependent on an unproved robustness conjecture, claiming that geometric quantum gates are more resilient against random noise than dynamic gates. We propose a suitable model that allows a direct and fair comparison between geometrical and dynamical operations. In the presence of stochastic control errors we find that the maximum of gate fidelity corresponds to quantum gates with a vanishing dynamical phase. This is a clear evidence for the robustness of nonadiabatic geometric quantum computation. The predictions here presented can be experimentally tested in almost all of the already existing quantum computer candidates.

Stefan Scheel, Jiannis K. Pachos, E. A. Hinds +1 more

Fabio Altomare, Jae Hyung Park, Raymond W. Simmonds +3 more

Razmik G. Unanyan, Michael Fleischhauer

A general scheme for an adiabatic geometric phase gate is proposed which is maximally robust against parameter fluctuations. While in systems with SU(2) symmetry geometric phases are accompanied by dynamical phases and are thus not robust, we show that in the more general case of an $\text{SU}(2)\ensuremath{\bigotimes}\text{SU}(2)$ symmetry it is possible to obtain a nonvanishing geometric phase without dynamical contributions. The scheme is illustrated for a phase gate using two systems with dipole-dipole interactions in external laser fields which form an effective four-level system.